diff --git a/Project.toml b/Project.toml
index 1694b99..9ca7500 100644
--- a/Project.toml
+++ b/Project.toml
@@ -20,7 +20,7 @@ AbstractPermutations = "0.3"
 Cyclotomics = "0.3"
 GroupsCore = "0.5"
 DynamicPolynomials = "0.6"
-PermutationGroups = "0.6.2"
+PermutationGroups = "0.6.3"
 PrecompileTools = "1"
 PrettyTables = "2"
 Primes = "0.4, 0.5"
diff --git a/examples/action_polynomials.jl b/examples/action_polynomials.jl
index 1ec8f01..9a4cbad 100644
--- a/examples/action_polynomials.jl
+++ b/examples/action_polynomials.jl
@@ -1,8 +1,5 @@
 using DynamicPolynomials
-const DP = DynamicPolynomials
-using GroupsCore
-
-const SW = SymbolicWedderburn
+import DynamicPolynomials as DP
 
 # Defining action on polynomials by acting on terms and monomials:
 function SW.action(a::SW.Action, el::GroupElement, poly::DP.AbstractPolynomial)
diff --git a/examples/dihedral.jl b/examples/dihedral.jl
index 07edae9..9f7f4d8 100644
--- a/examples/dihedral.jl
+++ b/examples/dihedral.jl
@@ -88,3 +88,6 @@ function GroupsCore.order(T::Type, el::DihedralElement)
     iszero(el.id) && return T(1)
     return T(div(el.n, gcd(el.n, el.id)))
 end
+
+# this is needed for using them in StarAlgebra:
+SA.comparable(::Type{DihedralElement}) = (a, b) -> hash(a) < hash(b)
diff --git a/examples/ex_C2_linear.jl b/examples/ex_C2_linear.jl
index 8f41874..cd9bace 100644
--- a/examples/ex_C2_linear.jl
+++ b/examples/ex_C2_linear.jl
@@ -40,10 +40,7 @@ using Test
 @testset "Decompose in basis" begin
     g = gens(G, 1)
 
-    basis = StarAlgebras.FixedBasis(
-        monomials([x, y], 0:4),
-        StarAlgebras.DiracMStructure(*),
-    )
+    basis = SA.FixedBasis(monomials([x, y], 0:4), SA.DiracMStructure(*))
     k = SymbolicWedderburn.action(By90Rotation(), g, basis[2])
     ehom = SymbolicWedderburn.ExtensionHomomorphism(By90Rotation(), basis)
     idcs, vals = SymbolicWedderburn.decompose(k, ehom)
@@ -60,10 +57,8 @@ end
 
 @testset "induced Matrix Representation" begin
     g = gens(G, 1)
-    monomial_basis = StarAlgebras.FixedBasis(
-        monomials([x, y], 0:4),
-        StarAlgebras.DiracMStructure(*),
-    )
+    monomial_basis =
+        SA.FixedBasis(monomials([x, y], 0:4), SA.DiracMStructure(*))
     ehom =
         SymbolicWedderburn.ExtensionHomomorphism(By90Rotation(), monomial_basis)
     m = droptol!(SymbolicWedderburn.induce(By90Rotation(), ehom, g), 1e-15)
diff --git a/examples/ex_S4.jl b/examples/ex_S4.jl
index 82b2898..4b72676 100644
--- a/examples/ex_S4.jl
+++ b/examples/ex_S4.jl
@@ -1,12 +1,3 @@
-using SymbolicWedderburn
-using PermutationGroups
-
-using DynamicPolynomials
-
-include(joinpath(@__DIR__, "action_polynomials.jl"))
-include(joinpath(@__DIR__, "sos_problem.jl"))
-include(joinpath(@__DIR__, "solver.jl"))
-
 const N = 4
 @polyvar x[1:N]
 
diff --git a/examples/ex_robinson_form.jl b/examples/ex_robinson_form.jl
index 9b709ed..a63ecb7 100644
--- a/examples/ex_robinson_form.jl
+++ b/examples/ex_robinson_form.jl
@@ -11,7 +11,7 @@ using LinearAlgebra
 using SparseArrays
 
 using SymbolicWedderburn
-using SymbolicWedderburn.StarAlgebras
+import SymbolicWedderburn.SA as SA
 using DynamicPolynomials
 
 # definitions of general actions on polynomials:
diff --git a/examples/run_examples.jl b/examples/run_examples.jl
index c3765e0..00d7cff 100644
--- a/examples/run_examples.jl
+++ b/examples/run_examples.jl
@@ -1,7 +1,24 @@
 using Pkg
 Pkg.activate(@__DIR__)
 Pkg.instantiate()
+
+module Examples
+using LinearAlgebra
+using SparseArrays
+
+using GroupsCore
+import SymbolicWedderburn as SW
+import SymbolicWedderburn.StarAlgebras as SA
+using PermutationGroups
+import PermutationGroups.AP as AP
+
+include(joinpath(@__DIR__, "action_polynomials.jl"))
+include(joinpath(@__DIR__, "sos_problem.jl"))
+include(joinpath(@__DIR__, "solver.jl"))
+
 include(joinpath(@__DIR__, "ex_C2_linear.jl"))
 include(joinpath(@__DIR__, "ex_S4.jl"))
 include(joinpath(@__DIR__, "ex_motzkin.jl"))
 include(joinpath(@__DIR__, "ex_robinson_form.jl"))
+
+end
diff --git a/examples/solver.jl b/examples/solver.jl
index dfb279a..fd10ffa 100644
--- a/examples/solver.jl
+++ b/examples/solver.jl
@@ -1,4 +1,3 @@
-using JuMP
 import SCS
 
 function scs_optimizer(;
diff --git a/examples/sos_problem.jl b/examples/sos_problem.jl
index 049c3d6..9c7cd24 100644
--- a/examples/sos_problem.jl
+++ b/examples/sos_problem.jl
@@ -1,16 +1,7 @@
-using LinearAlgebra
-using SparseArrays
-
-using GroupsCore
-
-using DynamicPolynomials
-using SymbolicWedderburn
-import SymbolicWedderburn.StarAlgebras
-
 using JuMP
 
-function DynamicPolynomials.coefficients(p, b::StarAlgebras.FixedBasis)
-    return DynamicPolynomials.coefficients(p, b.elts)
+function DP.coefficients(p, b::SA.FixedBasis)
+    return DP.coefficients(p, b.elts)
 end
 
 function invariant_constraint!(
@@ -28,19 +19,13 @@ function invariant_constraint!(
 end
 
 function sos_problem(poly::AbstractPolynomial)
-    vars = DynamicPolynomials.variables(poly)
+    vars = DP.variables(poly)
 
-    basis_psd = DynamicPolynomials.monomials(
-        vars,
-        0:DynamicPolynomials.maxdegree(poly)÷2,
-    )
+    basis_psd = DP.monomials(vars, 0:DP.maxdegree(poly)÷2)
 
-    basis_constraints = StarAlgebras.FixedBasis(
-        DynamicPolynomials.monomials(
-            vars,
-            0:DynamicPolynomials.maxdegree(poly),
-        ),
-        StarAlgebras.DiracMStructure(*),
+    basis_constraints = SA.FixedBasis(
+        DP.monomials(vars, 0:DP.maxdegree(poly)),
+        SA.DiracMStructure(*),
     )
 
     M = [basis_constraints[x*y] for x in basis_psd, y in basis_psd]
@@ -54,7 +39,7 @@ function sos_problem(poly::AbstractPolynomial)
 
     objective = poly - t
     for (idx, b) in enumerate(basis_constraints)
-        c = DynamicPolynomials.coefficient(objective, b)
+        c = DP.coefficient(objective, b)
         JuMP.@constraint sos_model LinearAlgebra.dot(P, M .== idx) == c
     end
 
@@ -64,7 +49,7 @@ end
 function sos_problem(
     poly::AbstractPolynomial,
     invariant_vs::AbstractVector,
-    basis_constraints::StarAlgebras.AbstractBasis,
+    basis_constraints::SA.AbstractBasis,
     basis_psd,
     T=Float64,
 )
@@ -80,7 +65,7 @@ function sos_problem(
     # preallocating
     M_orb = similar(M, T)
 
-    C = DynamicPolynomials.coefficients(poly - t, basis_constraints)
+    C = DP.coefficients(poly - t, basis_constraints)
 
     for iv in invariant_vs
         c = dot(C, iv)
@@ -94,18 +79,18 @@ end
 
 function sos_problem(
     poly::AbstractPolynomial,
-    wedderburn::SymbolicWedderburn.WedderburnDecomposition,
+    wedderburn::SW.WedderburnDecomposition,
     basis_psd;
 )
     m = JuMP.Model()
 
-    M = let basis_constraints = SymbolicWedderburn.basis(wedderburn)
+    M = let basis_constraints = SA.basis(wedderburn)
         [basis_constraints[x*y] for x in basis_psd, y in basis_psd]
     end
 
     JuMP.@variable m t
     JuMP.@objective m Max t
-    psds = map(SymbolicWedderburn.direct_summands(wedderburn)) do ds
+    psds = map(SW.direct_summands(wedderburn)) do ds
         dim = size(ds, 1)
         P = JuMP.@variable m [1:dim, 1:dim] Symmetric
         JuMP.@constraint m P in PSDCone()
@@ -116,15 +101,13 @@ function sos_problem(
     # Mπs = zeros.(eltype(wedderburn), size.(psds))
     M_orb = similar(M, eltype(wedderburn))
 
-    C = DynamicPolynomials.coefficients(
-        poly - t,
-        SymbolicWedderburn.basis(wedderburn),
-    )
+    C = DP.coefficients(poly - t, SW.basis(wedderburn))
+
     for iv in invariant_vectors(wedderburn)
         c = dot(C, iv)
         M_orb = invariant_constraint!(M_orb, M, iv)
-        # Mπs = SymbolicWedderburn.diagonalize!(Mπs, M_orb, wedderburn)
-        Mπs = SymbolicWedderburn.diagonalize(M_orb, wedderburn)
+        # Mπs = SW.diagonalize!(Mπs, M_orb, wedderburn)
+        Mπs = SW.diagonalize(M_orb, wedderburn)
 
         JuMP.@constraint m sum(
             dot(Mπ, Pπ) for (Mπ, Pπ) in zip(Mπs, psds) if !iszero(Mπ)
@@ -136,18 +119,19 @@ end
 function sos_problem(
     poly::AbstractPolynomial,
     G::Group,
-    action::SymbolicWedderburn.Action,
+    action::SW.Action,
     T=Float64;
     decompose_psd=true,
     semisimple=false
 )
-    max_deg = DynamicPolynomials.maxdegree(poly)
-    vars = DynamicPolynomials.variables(poly)
-    basis_psd = DynamicPolynomials.monomials(vars, 0:max_deg÷2)
-    basis_constraints = DynamicPolynomials.monomials(vars, 0:max_deg)
+    max_deg = DP.maxdegree(poly)
+    vars = DP.variables(poly)
+    basis_psd = DP.monomials(vars, 0:max_deg÷2)
+    basis_constraints = DP.monomials(vars, 0:max_deg)
 
     if decompose_psd == true
-        wedderburn, symmetry_adaptation_time = @timed WedderburnDecomposition(
+        wedderburn, symmetry_adaptation_time =
+            @timed SW.WedderburnDecomposition(
             T,
             G,
             action,
@@ -160,15 +144,9 @@ function sos_problem(
             @timed sos_problem(poly, wedderburn, basis_psd)
     else
         (invariant_vs, basis_cnstr), symmetry_adaptation_time = @timed let G = G
-            basis = StarAlgebras.FixedBasis(
-                basis_constraints,
-                StarAlgebras.DiracMStructure(*),
-            )
-
-            tblG = SymbolicWedderburn.Characters.CharacterTable(
-                Rational{Int},
-                G,
-            )
+            basis = SA.FixedBasis(basis_constraints, SA.DiracMStructure(*))
+
+            tblG = SW.Characters.CharacterTable(Rational{Int}, G)
             iv = invariant_vectors(tblG, action, basis)
             iv, basis
         end
diff --git a/src/SymbolicWedderburn.jl b/src/SymbolicWedderburn.jl
index 2bf05c2..38e2bfc 100644
--- a/src/SymbolicWedderburn.jl
+++ b/src/SymbolicWedderburn.jl
@@ -10,6 +10,7 @@ import AbstractPermutations as AP
 import AbstractPermutations: degree
 import PermutationGroups as PG
 using StarAlgebras
+import StarAlgebras as SA
 
 export symmetry_adapted_basis, WedderburnDecomposition
 export basis,
@@ -25,6 +26,7 @@ import .Characters: row_echelon_form!
 import .Characters.FiniteFields
 
 include("ext_homomorphisms.jl")
+include("ext_hom_schreier.jl")
 include("actions.jl")
 include("group_action_error.jl")
 include("action_characters.jl")
diff --git a/src/actions.jl b/src/actions.jl
index 95b7bad..e89db90 100644
--- a/src/actions.jl
+++ b/src/actions.jl
@@ -13,38 +13,6 @@ of elements in `S` one can then represent `g` as a permutation of degree `|S|`.
 """
 abstract type ByPermutations <: Action end
 
-function action(
-    ::ByPermutations,
-    g::AP.AbstractPermutation,
-    v::AbstractVector,
-)
-    return [v[i^g] for i in eachindex(v)]
-end
-
-"""
-    action(hom::InducedActionHomomorphism, g::GroupElement, x)
-Return the result of `g` acting on `x` through action homomorphism `hom`.
-
-This can be understood as first evaluating the homomorphism: `h = hom(g)` and
-then computing `x^h`, the action of the result on `x`.
-"""
-function action(
-    hom::InducedActionHomomorphism{<:ByPermutations},
-    g::GroupElement,
-    v::AbstractVector,
-)
-    return action(action(hom), induce(hom, g), v)
-end
-
-coeff_type(::ByPermutations) = Int
-
-function induce(::ByPermutations, hom::ExtensionHomomorphism, g::GroupElement)
-    I = _int_type(hom)
-    return PG.Perm{I}(
-        vec(I[hom[action(action(hom), g, f)] for f in basis(hom)]),
-    )
-end
-
 """
     ByLinearTransformation <: Action
 A type of action where a group acts through linear transformations on an
@@ -59,48 +27,6 @@ implemented to return a (possibly sparse) decomposition of `v` in `B`.
 """
 abstract type ByLinearTransformation <: Action end
 
-function action(
-    hom::InducedActionHomomorphism{<:ByLinearTransformation},
-    g::GroupElement,
-    v::AbstractVector,
-)
-    return induce(hom, g) * v
-end
-
-function coeff_type(ac::ByLinearTransformation)
-    throw("No fallback is provided for $(typeof(ac)). You need to implement
-          `coeff_type(::$(typeof(ac)))`.")
-end
-
-function induce(
-    ac::ByLinearTransformation,
-    hom::InducedActionHomomorphism,
-    g::GroupElement,
-)
-    I = Int[]
-    J = Int[]
-    V = coeff_type(ac)[]
-
-    for (i, f) in enumerate(basis(hom))
-        k = action(action(hom), g, f)
-        idcs, vals = decompose(k, hom)
-        append!(I, fill(i, length(idcs)))
-        append!(J, idcs)
-        append!(V, vals)
-    end
-    n = length(basis(hom))
-    return sparse(I, J, V, n, n)
-end
-
-# disabmiguation:
-function induce(
-    ac::ByLinearTransformation,
-    hom::CachedExtensionHomomorphism,
-    g::GroupElement,
-)
-    return _induce(ac, hom, g)
-end
-
 """
     decompose(v, hom::InducedActionHomomorphism)
 Decompose element `v` in basis `basis(hom)` provided by `hom`.
@@ -144,13 +70,93 @@ action(act::BySignedPermutations, g, eₖ) == (eₗ, u)
 """
 abstract type BySignedPermutations <: ByLinearTransformation end
 
+## coeff_types
+coeff_type(::ByPermutations) = Int
+function coeff_type(ac::ByLinearTransformation)
+    throw("No fallback is provided for $(typeof(ac)). You need to implement
+          `coeff_type(::$(typeof(ac)))`.")
+end
 coeff_type(::BySignedPermutations) = Int # lets not worry about roots of unity
 
+## actions on AbstractVectors
+
+function action(::ByPermutations, g::AP.AbstractPermutation, v::AbstractVector)
+    # permuting coordinates
+    return [v[i^g] for i in eachindex(v)]
+end
+
+"""
+    action(hom::InducedActionHomomorphism, g::GroupElement, x)
+Return the result of `g` acting on `x` through action homomorphism `hom`.
+
+This can be understood as first evaluating the homomorphism: `h = hom(g)` and
+then computing `x^h`, the action of the result on `x`.
+"""
+function action(
+    hom::InducedActionHomomorphism{<:ByPermutations},
+    g::GroupElement,
+    v::AbstractVector,
+)
+    return action(action(hom), induce(hom, g), v)
+end
+
+function action(
+    hom::InducedActionHomomorphism{<:ByLinearTransformation},
+    g::GroupElement,
+    v::AbstractVector,
+)
+    return induce(hom, g) * v
+end
+
+# Inducing action via action homomorphism
+
+function induce(hom::InducedActionHomomorphism, g::GroupElement)
+    return induce(action(hom), hom, g)
+end
+
+function induce(ac::Action, hom::InducedActionHomomorphism, g::GroupElement)
+    return throw(
+        """No fallback is provided for $(typeof(ac)).
+        You need to implement
+        `induce(::$(typeof(ac)), ::$(typeof(hom)), ::$(typeof(g)))`.""",
+    )
+end
+
+function induce(
+    ::ByPermutations,
+    hom::H,
+    g::GroupElement,
+) where {H<:InducedActionHomomorphism}
+    I = _int_type(hom)
+    v = vec(I[hom[action(action(hom), g, f)] for f in basis(hom)])
+    return PG.Perm{I}(v; check = false)
+end
+
+function induce(
+    ac::ByLinearTransformation,
+    hom::H,
+    g::GroupElement,
+) where {H<:InducedActionHomomorphism}
+    I = Int[]
+    J = Int[]
+    V = coeff_type(ac)[]
+
+    for (i, f) in enumerate(basis(hom))
+        k = action(action(hom), g, f)
+        idcs, vals = decompose(k, hom)
+        append!(I, fill(i, length(idcs)))
+        append!(J, idcs)
+        append!(V, vals)
+    end
+    n = length(basis(hom))
+    return sparse(I, J, V, n, n)
+end
+
 function induce(
     ac::BySignedPermutations,
-    hom::InducedActionHomomorphism,
+    hom::H,
     g::GroupElement,
-)
+) where {H<:InducedActionHomomorphism}
     I = Int[]
     J = Int[]
     V = coeff_type(ac)[]
@@ -165,6 +171,23 @@ function induce(
     return sparse(I, J, V, n, n)
 end
 
+# disabmiguation methods for custom implementations of InducedActionHomomorphism
+function induce(
+    ac::ByPermutations,
+    hom::CachedExtensionHomomorphism,
+    g::GroupElement,
+)
+    return _induce(ac, hom, g)
+end
+
+function induce(
+    ac::ByLinearTransformation,
+    hom::CachedExtensionHomomorphism,
+    g::GroupElement,
+)
+    return _induce(ac, hom, g)
+end
+
 # disabmiguation
 function induce(
     ac::BySignedPermutations,
@@ -173,3 +196,27 @@ function induce(
 )
     return _induce(ac, hom, g)
 end
+
+function induce(
+    ac::ByPermutations,
+    shom::SchreierExtensionHomomorphism,
+    g::GroupElement,
+)
+    return _induce(ac, shom, g)
+end
+
+function induce(
+    ac::ByLinearTransformation,
+    shom::SchreierExtensionHomomorphism,
+    g::GroupElement,
+)
+    return _induce(ac, shom, g)
+end
+
+function induce(
+    ac::BySignedPermutations,
+    shom::SchreierExtensionHomomorphism,
+    g::GroupElement,
+)
+    return _induce(ac, shom, g)
+end
diff --git a/src/ext_hom_schreier.jl b/src/ext_hom_schreier.jl
new file mode 100644
index 0000000..74c3c3d
--- /dev/null
+++ b/src/ext_hom_schreier.jl
@@ -0,0 +1,68 @@
+struct SchreierExtensionHomomorphism{
+    A,
+    T,
+    E<:InducedActionHomomorphism{A,T},
+    Ch,
+    St,
+} <: InducedActionHomomorphism{A,T}
+    ehom::E
+    cache::Ch
+    schreier_tree::St
+    memoize::Bool
+    lock::Base.Threads.SpinLock
+end
+
+SA.basis(h::SchreierExtensionHomomorphism) = basis(h.ehom)
+action(h::SchreierExtensionHomomorphism) = action(h.ehom)
+
+function SchreierExtensionHomomorphism(
+    G::Group,
+    action::Action,
+    basis;
+    memoize = false,
+)
+    hom = ExtensionHomomorphism(action, basis)
+    cache = Dict(s => induce(hom, s) for s in gens(G))
+    cache[one(G)] = induce(hom, one(G))
+    sehom = SchreierExtensionHomomorphism(
+        hom,
+        cache,
+        PG.SchreierTransversal(one(G), gens(G), *),
+        memoize,
+        Threads.SpinLock(),
+    )
+
+    return sehom
+end
+
+function memoize!(sehom::SchreierExtensionHomomorphism, val, g, lck = true)
+    if lck
+        lock(sehom.lock) do
+            return sehom.cache[g] = val
+        end
+    else
+        sehom.cache[g] = val
+    end
+    return sehom
+end
+
+function _induce(
+    ac::Action,
+    sehom::SchreierExtensionHomomorphism,
+    g::GroupElement,
+)
+    if g in keys(sehom.cache)
+        return sehom.cache[g]
+    else
+        s = sehom.schreier_tree.representatives[g]
+        sI = induce(ac, sehom, s)
+        hI = induce(ac, sehom, g * inv(s))
+        gI = hI * sI
+
+        if sehom.memoize
+            memoize!(sehom, gI, g)
+        end
+
+        return gI
+    end
+end
diff --git a/src/ext_homomorphisms.jl b/src/ext_homomorphisms.jl
index 490b368..99f93f4 100644
--- a/src/ext_homomorphisms.jl
+++ b/src/ext_homomorphisms.jl
@@ -16,7 +16,7 @@ end
 AP.degree(hom::InducedActionHomomorphism) = length(basis(hom))
 
 coeff_type(hom::InducedActionHomomorphism) = coeff_type(action(hom))
-_int_type(basis::StarAlgebras.AbstractBasis) = StarAlgebras.key_type(basis)
+_int_type(basis::SA.AbstractBasis) = SA.key_type(basis)
 _int_type(hom::InducedActionHomomorphism) = _int_type(basis(hom))
 
 # Exceeding typemax(UInt32) here would mean e.g. that you're trying to block-diagonalize
@@ -24,26 +24,14 @@ _int_type(hom::InducedActionHomomorphism) = _int_type(basis(hom))
 _int_type(::Type{<:Action}) = UInt32
 _int_type(ac::Action) = _int_type(typeof(ac))
 
-function induce(hom::InducedActionHomomorphism, g::GroupElement)
-    return induce(action(hom), hom, g)
-end
-
-function induce(ac::Action, hom::InducedActionHomomorphism, g::GroupElement)
-    return throw(
-        """No fallback is provided for $(typeof(ac)).
-        You need to implement
-        `induce(::$(typeof(ac)), ::$(typeof(hom)), ::$(typeof(g)))`.""",
-    )
-end
-
-struct ExtensionHomomorphism{A<:Action,T,B<:StarAlgebras.ExplicitBasis{T}} <:
+struct ExtensionHomomorphism{A<:Action,T,B<:SA.ExplicitBasis{T}} <:
        InducedActionHomomorphism{A,T}
     action::A
     basis::B
 end
 
 # interface:
-StarAlgebras.basis(hom::ExtensionHomomorphism) = hom.basis
+SA.basis(hom::ExtensionHomomorphism) = hom.basis
 action(hom::ExtensionHomomorphism) = hom.action
 
 struct CachedExtensionHomomorphism{A,T,G,H,E<:InducedActionHomomorphism{A,T}} <:
@@ -59,7 +47,7 @@ function CachedExtensionHomomorphism{G,H}(
     return CachedExtensionHomomorphism(hom, Dict{G,H}(), Threads.SpinLock())
 end
 
-StarAlgebras.basis(h::CachedExtensionHomomorphism) = basis(h.ehom)
+SA.basis(h::CachedExtensionHomomorphism) = basis(h.ehom)
 action(h::CachedExtensionHomomorphism) = action(h.ehom)
 
 function CachedExtensionHomomorphism(
diff --git a/src/group_action_error.jl b/src/group_action_error.jl
index f9bc5db..4022754 100644
--- a/src/group_action_error.jl
+++ b/src/group_action_error.jl
@@ -174,9 +174,9 @@ end
 function check_group_action(
     G::Group,
     act::Action,
-    basis::StarAlgebras.ExplicitBasis;
+    basis::SA.ExplicitBasis;
     full_check = false,
 )
-    ehom = CachedExtensionHomomorphism(G, act, basis; precompute = false)
+    ehom = SchreierExtensionHomomorphism(G, act, basis; memoize = false)
     return check_group_action(G, ehom; full_check = full_check)
 end
diff --git a/src/matrix_projections.jl b/src/matrix_projections.jl
index 8d34846..cce8480 100644
--- a/src/matrix_projections.jl
+++ b/src/matrix_projections.jl
@@ -10,7 +10,7 @@ function _preallocate(::Type{T}, sizes::Tuple, sizehint) where {T}
 end
 
 __hint(χ::Character) = length(conjugacy_classes(χ))
-__hint(α::AlgebraElement) = count(!iszero, StarAlgebras.coeffs(α))
+__hint(α::AlgebraElement) = count(!iszero, SA.coeffs(α))
 
 _projection_size(m::AbstractMatrix) = size(m)
 _projection_size(::Nothing, χ::Character) = (d = degree(parent(χ)); (d, d))
@@ -299,7 +299,7 @@ function matrix_representation_acc!(
     I = UInt32[]
     J = UInt32[]
     V = eltype(result)[]
-    for (idx, val) in StarAlgebras.nonzero_pairs(StarAlgebras.coeffs(α))
+    for (idx, val) in SA.nonzero_pairs(SA.coeffs(α))
         g = b[idx]
         iszero(val) && continue
         for i in 1:size(result, 1)
@@ -321,7 +321,7 @@ function matrix_representation_acc!(
     I = UInt32[]
     J = UInt32[]
     V = eltype(result)[]
-    for (idx, val) in StarAlgebras.nonzero_pairs(StarAlgebras.coeffs(α))
+    for (idx, val) in SA.nonzero_pairs(SA.coeffs(α))
         iszero(val) && continue
         g = induce(hom, b[idx])
         @assert g isa PG.Perm
@@ -341,7 +341,7 @@ function matrix_representation_acc!(
     α::AlgebraElement,
 )
     b = basis(parent(α))
-    for (idx, val) in StarAlgebras.nonzero_pairs(StarAlgebras.coeffs(α))
+    for (idx, val) in SA.nonzero_pairs(SA.coeffs(α))
         iszero(val) && continue
         result .+= val .* induce(hom, inv(b[idx]))
     end
diff --git a/src/minimal_projections.jl b/src/minimal_projections.jl
index f06c8a1..50f6874 100644
--- a/src/minimal_projections.jl
+++ b/src/minimal_projections.jl
@@ -6,18 +6,15 @@ function _group_algebra(G::Group)
         convert(UInt16, min(order(Int, G), typemax(UInt16) >> 2))
     end
 
-    fb = StarAlgebras.FixedBasis(
-        vec(collect(G)),
-        StarAlgebras.DiracMStructure(*),
-        (l, l),
-    )
+    fb = SA.FixedBasis(vec(collect(G)), SA.DiracMStructure(*), (l, l))
+    SA.complete!(fb.table)
     return StarAlgebra(G, fb)
 end
 
 Base.parent(A::StarAlgebra{<:Group}) = A.object
-StarAlgebras.star(g::GroupElement) = inv(g)
+SA.star(g::GroupElement) = inv(g)
 
-function StarAlgebras.AlgebraElement(
+function SA.AlgebraElement(
     χ::AbstractClassFunction,
     RG::StarAlgebra{<:Group},
 )
@@ -116,7 +113,7 @@ end
 
 function (χ::AbstractClassFunction)(α::AlgebraElement{<:StarAlgebra{<:Group}})
     @assert parent(χ) === parent(parent(α))
-    return sum(α(g) * χ(g) for g in StarAlgebras.supp(α))
+    return sum(α(g) * χ(g) for g in SA.supp(α))
 end
 
 function minimal_rank_projection(
diff --git a/src/sa_basis.jl b/src/sa_basis.jl
index e14792a..0403425 100644
--- a/src/sa_basis.jl
+++ b/src/sa_basis.jl
@@ -137,11 +137,11 @@ function symmetry_adapted_basis(
     semisimple = false,
 )
     tbl = CharacterTable(S, G)
-    ehom = CachedExtensionHomomorphism(
+    ehom = SchreierExtensionHomomorphism(
         parent(tbl),
         action,
         basis;
-        precompute = true,
+        memoize = true,
     )
     check_group_action(G, ehom; full_check = false)
     return symmetry_adapted_basis(
@@ -161,11 +161,11 @@ function symmetry_adapted_basis(
     semisimple = false,
 )
     tbl = CharacterTable(S, G)
-    ehom = CachedExtensionHomomorphism(
+    ehom = SchreierExtensionHomomorphism(
         parent(tbl),
         action,
         basis;
-        precompute = true,
+        memoize = true,
     )
     check_group_action(G, ehom; full_check = false)
     return symmetry_adapted_basis(T, tbl, ehom; semisimple = semisimple)
diff --git a/src/wedderburn_decomposition.jl b/src/wedderburn_decomposition.jl
index fc2c055..7413592 100644
--- a/src/wedderburn_decomposition.jl
+++ b/src/wedderburn_decomposition.jl
@@ -43,8 +43,8 @@ function WedderburnDecomposition(
         T,
         G,
         action,
-        StarAlgebras.FixedBasis(basis_full, StarAlgebras.DiracMStructure(*)),
-        StarAlgebras.FixedBasis(basis_half, StarAlgebras.DiracMStructure(*)),
+        SA.FixedBasis(basis_full, SA.DiracMStructure(*)),
+        SA.FixedBasis(basis_half, SA.DiracMStructure(*)),
         S;
         semisimple = semisimple,
     )
@@ -54,15 +54,15 @@ function WedderburnDecomposition(
     T::Type,
     G::Group,
     action::Action,
-    basis_full::StarAlgebras.ExplicitBasis,
-    basis_half::StarAlgebras.ExplicitBasis,
+    basis_full::SA.ExplicitBasis,
+    basis_half::SA.ExplicitBasis,
     S = Rational{Int};
     semisimple = false,
 )
     tbl = CharacterTable(S, G)
     invariants = Threads.@spawn invariant_vectors(tbl, action, basis_full)
 
-    ehom = CachedExtensionHomomorphism(G, action, basis_half; precompute = true)
+    ehom = SchreierExtensionHomomorphism(G, action, basis_half; memoize = true)
     check_group_action(G, ehom; full_check = false)
 
     Uπs = Threads.@spawn symmetry_adapted_basis(
@@ -93,7 +93,7 @@ function Base.show(io::IO, wbdec::SymbolicWedderburn.WedderburnDecomposition)
 end
 
 invariant_vectors(wbdec::WedderburnDecomposition) = wbdec.invariants
-StarAlgebras.basis(wbdec::WedderburnDecomposition) = wbdec.basis
+SA.basis(wbdec::WedderburnDecomposition) = wbdec.basis
 direct_summands(wbdec::WedderburnDecomposition) = wbdec.Uπs
 function Base.eltype(wbdec::WedderburnDecomposition)
     return eltype(eltype(direct_summands(wbdec)))
@@ -155,7 +155,7 @@ end
 function invariant_vectors(
     tbl::Characters.CharacterTable,
     act::Action,
-    basis::StarAlgebras.ExplicitBasis,
+    basis::SA.ExplicitBasis,
 )
     triv_χ =
         Characters.Character{Rational{Int}}(Characters.trivial_character(tbl))
@@ -173,7 +173,7 @@ end
 function invariant_vectors(
     tbl::Characters.CharacterTable,
     act::Union{<:ByPermutations,<:BySignedPermutations},
-    basis::StarAlgebras.ExplicitBasis,
+    basis::SA.ExplicitBasis,
 )
     return invariant_vectors(parent(tbl), act, basis)
 end
@@ -181,7 +181,7 @@ end
 function invariant_vectors(
     G::Group,
     act::ByPermutations,
-    basis::StarAlgebras.ExplicitBasis{T,I},
+    basis::SA.ExplicitBasis{T,I},
 ) where {T,I}
     tovisit = trues(length(basis))
     invariant_vs = Vector{SparseVector{Rational{Int},I}}()
@@ -224,7 +224,7 @@ end
 function invariant_vectors(
     G::Group,
     act::BySignedPermutations,
-    basis::StarAlgebras.ExplicitBasis{T,I},
+    basis::SA.ExplicitBasis{T,I},
 ) where {T,I}
     ordG = order(Int, G)
     elts = collect(G)
diff --git a/test/action_dihedral.jl b/test/action_dihedral.jl
index 0fd3755..03e9e36 100644
--- a/test/action_dihedral.jl
+++ b/test/action_dihedral.jl
@@ -1,37 +1,3 @@
-using LinearAlgebra
-using SparseArrays
-
-using SymbolicWedderburn
-using DynamicPolynomials
-
-include(joinpath(dirname(@__DIR__), "examples", "action_polynomials.jl"))
-include(joinpath(dirname(@__DIR__), "examples", "dihedral.jl"))
-include(joinpath(dirname(@__DIR__), "examples", "sos_problem.jl"))
-
-using JuMP
-import SCS
-
-function scs_optimizer(;
-    accel = 0,
-    alpha = 1.5,
-    eps = 1e-6,
-    max_iters = 10_000,
-    verbose = true,
-)
-    return JuMP.optimizer_with_attributes(
-        SCS.Optimizer,
-        "acceleration_lookback" => accel,
-        "acceleration_interval" => 10,
-        "alpha" => alpha,
-        "eps_abs" => eps,
-        "eps_rel" => eps,
-        "linear_solver" => SCS.DirectSolver,
-        "max_iters" => max_iters,
-        "warm_start" => true,
-        "verbose" => verbose,
-    )
-end
-
 @polyvar x y
 const robinson_form =
     x^6 + y^6 - x^4 * y^2 - y^4 * x^2 - x^4 - y^4 - x^2 - y^2 + 3x^2 * y^2 + 1
@@ -54,10 +20,6 @@ function SymbolicWedderburn.action(
     return mono([x, y] => [sign_x * var_x, sign_y * var_y])
 end
 
-function StarAlgebras.comparable(::Type{DihedralElement})
-    return (a, b) -> hash(a) < hash(b)
-end
-
 @testset "Dihedral Action" begin
     G = DihedralGroup(4)
     @test all(
diff --git a/test/action_invalid.jl b/test/action_invalid.jl
index 7f4db27..2a5ba50 100644
--- a/test/action_invalid.jl
+++ b/test/action_invalid.jl
@@ -1,8 +1,3 @@
-using SymbolicWedderburn
-using DynamicPolynomials
-
-include(joinpath(dirname(@__DIR__), "examples", "action_polynomials.jl"))
-
 @testset "Catching invalid actions" begin
     include(joinpath(dirname(pathof(GroupsCore)), "..", "test", "cyclic.jl"))
     struct CyclicAction <: OnMonomials end
@@ -22,10 +17,7 @@ include(joinpath(dirname(@__DIR__), "examples", "action_polynomials.jl"))
     G = CyclicGroup(4)
     act = CyclicAction()
     @polyvar a[1:2]
-    basis = StarAlgebras.FixedBasis(
-        monomials(a, 0:2),
-        StarAlgebras.DiracMStructure(*),
-    )
+    basis = SA.FixedBasis(monomials(a, 0:2), SA.DiracMStructure(*))
 
     @test_throws SymbolicWedderburn.GroupActionError SymbolicWedderburn.check_group_action(
         G,
diff --git a/test/action_linear.jl b/test/action_linear.jl
index 81cda43..0ad4e50 100644
--- a/test/action_linear.jl
+++ b/test/action_linear.jl
@@ -1,5 +1,3 @@
-using DynamicPolynomials
-
 using GroupsCore
 include(joinpath(dirname(pathof(GroupsCore)), "..", "test", "cyclic.jl"))
 
@@ -20,13 +18,13 @@ function SymbolicWedderburn.action(
 end
 
 function SymbolicWedderburn.decompose(
-    k::DynamicPolynomials.AbstractPolynomialLike,
+    k::DP.AbstractPolynomialLike,
     hom::SymbolicWedderburn.InducedActionHomomorphism,
 )
     # correct only if basis(hom) == monomials
     I = SymbolicWedderburn._int_type(hom)
-    indcs = I[hom[mono] for mono in DynamicPolynomials.monomials(k)]
-    coeffs = DynamicPolynomials.coefficients(k)
+    indcs = I[hom[mono] for mono in DP.monomials(k)]
+    coeffs = DP.coefficients(k)
 
     return indcs, coeffs
 end
@@ -34,7 +32,7 @@ end
 @testset "Linear Actions" begin
     G = CyclicGroup(2)
     monomial_basis = let monoms = monomials([x, y], 0:4)
-        StarAlgebras.FixedBasis(monoms, StarAlgebras.DiracMStructure(*))
+        SA.FixedBasis(monoms, SA.DiracMStructure(*))
     end
     ehom =
         SymbolicWedderburn.ExtensionHomomorphism(By90Rotation(), monomial_basis)
diff --git a/test/action_permutation.jl b/test/action_permutation.jl
index 18e28ef..08e1bf1 100644
--- a/test/action_permutation.jl
+++ b/test/action_permutation.jl
@@ -1,5 +1,3 @@
-include("free_words.jl")
-
 struct OnLetters <: SymbolicWedderburn.ByPermutations end
 function SymbolicWedderburn.action(
     ::OnLetters,
@@ -26,10 +24,7 @@ end
         @test SymbolicWedderburn.action(OnLetters(), PG.perm"(2,3)", w) ==
               Word(A, [1, 3, 2, 3, 1])
 
-        StarAlgebras.FixedBasis(
-            allwords(FreeWords(A), radius),
-            StarAlgebras.DiracMStructure(*),
-        )
+        SA.FixedBasis(allwords(FreeWords(A), radius), SA.DiracMStructure(*))
     end
 
     G = PG.PermGroup(PG.perm"(1,2,3)", PG.perm"(1,2)") # G acts on words permuting letters
@@ -38,23 +33,13 @@ end
     @test SymbolicWedderburn.check_group_action(G, OnLettersSigned(), fb_words)
 
     action = OnLetters()
-    tbl = SymbolicWedderburn.CharacterTable(Rational{Int}, G)
-    ehom = SymbolicWedderburn.CachedExtensionHomomorphism(
-        G,
-        action,
-        fb_words;
-        precompute = true,
-    )
-    @test all(g ∈ keys(ehom.cache) for g in G) # we actually cached
+    ehom = SymbolicWedderburn.ExtensionHomomorphism(action, fb_words)
     @test typeof(SymbolicWedderburn.induce(ehom, one(G))) == PG.Perm{UInt32}
 
-    let T = UInt16
+    let T = UInt16, fb_words = fb_words
         l = length(fb_words)
-        fb_words = StarAlgebras.FixedBasis(
-            collect(fb_words),
-            StarAlgebras.DiracMStructure(*),
-            T.((l, l)),
-        )
+        fb_words =
+            SA.FixedBasis(collect(fb_words), SA.DiracMStructure(*), T.((l, l)))
         @test SymbolicWedderburn.check_group_action(G, OnLetters(), fb_words)
         @test SymbolicWedderburn.check_group_action(
             G,
@@ -63,19 +48,42 @@ end
         )
 
         action = OnLetters()
-        tbl = SymbolicWedderburn.CharacterTable(Rational{Int}, G)
-        ehom = SymbolicWedderburn.CachedExtensionHomomorphism(
-            G,
-            action,
-            fb_words;
-            precompute = true,
-        )
-        @test all(g ∈ keys(ehom.cache) for g in G) # we actually cached
+        ehom = SymbolicWedderburn.ExtensionHomomorphism(action, fb_words)
         @test typeof(SymbolicWedderburn.induce(ehom, one(G))) == PG.Perm{T}
     end
 
+    schrhom = SymbolicWedderburn.SchreierExtensionHomomorphism(
+        G,
+        action,
+        fb_words;
+        memoize = false,
+    )
+
+    @test all(
+        SymbolicWedderburn.induce(ehom, g) ==
+        SymbolicWedderburn.induce(schrhom, g) for g in G
+    )
+    @test length(schrhom.cache) == ngens(G) + 1
+
+    schrhom = SymbolicWedderburn.SchreierExtensionHomomorphism(
+        G,
+        action,
+        fb_words;
+        memoize = true,
+    )
+
+    @test all(
+        SymbolicWedderburn.induce(ehom, g) ==
+        SymbolicWedderburn.induce(schrhom, g) for g in G
+    )
+    @test length(schrhom.cache) == order(Int, G)
+
+    tbl = SymbolicWedderburn.CharacterTable(Rational{Int}, G)
     ψ = SymbolicWedderburn.action_character(ehom, tbl)
     @test SymbolicWedderburn.multiplicities(ψ) == [23, 18, 40]
+    ψ = SymbolicWedderburn.action_character(schrhom, tbl)
+    @test SymbolicWedderburn.multiplicities(ψ) == [23, 18, 40]
+
     irr = SymbolicWedderburn.irreducible_characters(tbl)
     multips = SymbolicWedderburn.multiplicities(ψ)
     @test dot(SymbolicWedderburn.degree.(irr), multips) == length(basis(ehom))
@@ -93,19 +101,19 @@ end
     @testset "semisimple decomposition" begin
         let i = 1
             χ, m, s = irr[i], multips[i], simple[i]
-            b = SymbolicWedderburn.image_basis(ehom, χ)
+            b = SymbolicWedderburn.image_basis(schrhom, χ)
             @test size(b, 1) == SymbolicWedderburn.degree(χ) * m == 23
         end
 
         let i = 2
             χ, m, s = irr[i], multips[i], simple[i]
-            b = SymbolicWedderburn.image_basis(ehom, χ)
+            b = SymbolicWedderburn.image_basis(schrhom, χ)
             @test size(b, 1) == SymbolicWedderburn.degree(χ) * m == 18
         end
 
         let i = 3
             χ, m, s = irr[i], multips[i], simple[i]
-            b = SymbolicWedderburn.image_basis(ehom, χ)
+            b = SymbolicWedderburn.image_basis(schrhom, χ)
             @test size(b, 1) == SymbolicWedderburn.degree(χ) * m == 80
         end
 
@@ -147,11 +155,7 @@ end
         RG = let G = G
             v = collect(G)
             l = convert(UInt16, length(v))
-            b = StarAlgebras.FixedBasis(
-                v,
-                StarAlgebras.DiracMStructure(*),
-                (l, l),
-            )
+            b = SA.FixedBasis(v, SA.DiracMStructure(*), (l, l))
             StarAlgebra(G, b)
         end
 
diff --git a/test/dixon.jl b/test/dixon.jl
index 90e5cdf..b36211e 100644
--- a/test/dixon.jl
+++ b/test/dixon.jl
@@ -226,7 +226,8 @@ end
     end
 
     @time @testset "SmallPermGroups" begin
-        for (ord, groups) in SmallPermGroups
+        for ord in 2:30
+            groups = SmallPermGroups[ord]
             @testset "SmallGroup($ord, $n)" for (n, G) in enumerate(groups)
                 @test Characters.irreducible_characters(G) isa
                       Vector{<:Characters.Character}
diff --git a/test/free_words.jl b/test/free_words.jl
index 069d7be..4d5da79 100644
--- a/test/free_words.jl
+++ b/test/free_words.jl
@@ -30,7 +30,7 @@ function Base.:*(w::Word, z::Word)
     return Word(w.alphabet, [w.letters; z.letters])
 end
 
-function StarAlgebras.star(w::Word)
+function SA.star(w::Word)
     # star(:a) = :b
     # star(:b) = :a
     # star(:c) = :c
diff --git a/test/runtests.jl b/test/runtests.jl
index 6c16ad8..9f5c67e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -9,20 +9,25 @@ import PermutationGroups as PG
 using Cyclotomics
 
 using SymbolicWedderburn
+import SymbolicWedderburn as SW
 using SymbolicWedderburn.FiniteFields
+import SymbolicWedderburn.SA as SA
 using SymbolicWedderburn.StarAlgebras
 
+# action on free words
+include("free_words.jl")
 include("action_permutation.jl")
+
+# actions on polynomials
+include(joinpath(dirname(@__DIR__), "examples", "action_polynomials.jl"))
+include(joinpath(dirname(@__DIR__), "examples", "dihedral.jl"))
+include(joinpath(dirname(@__DIR__), "examples", "sos_problem.jl"))
+include(joinpath(dirname(@__DIR__), "examples", "solver.jl"))
+
 include("action_linear.jl")
 include("action_dihedral.jl")
 include("action_invalid.jl")
 
-if VERSION >= v"1.7.0" && !haskey(ENV, "CI")
-    @testset "Examples" begin
-        include("../examples/run_examples.jl")
-    end
-end
-
 include("smallgroups.jl")
 @testset "Characters" begin
     import SymbolicWedderburn.Characters
@@ -35,3 +40,37 @@ end
 
 include("projections.jl")
 include("sa_basis.jl")
+
+if VERSION >= v"1.7.0" && !haskey(ENV, "CI")
+    @testset "Examples" begin
+        include("../examples/run_examples.jl")
+    end
+end
+
+# Small groups generation:
+#= GAP code:
+H := [];
+for i in [1..63] do
+    Add(H, List(AllSmallGroups(i), G->Image(IsomorphismPermGroup(G))));
+od;
+PrintTo("/tmp/groups.gap", H);
+=#
+
+#=julia code
+GAPgroups_str = join(readlines("/tmp/groups.gap"), "");
+GAPgroups_str = replace(GAPgroups_str, "Group"=>"\nPermGroup");
+GAPgroups_str = replace(GAPgroups_str, r" *"=>"");
+perm_regex = r"((\(\d+(,\d+)*\)?)+)";
+let fn = joinpath(@__DIR__, "smallgroups.jl")
+    open(fn, "w") do file
+
+        print(file, """
+        import PermutationGroups: PermGroup, @perm_str
+
+        const SmallPermGroups = """)
+        println(file, replace(GAPgroups_str, perm_regex=> s"perm\"\1\""))
+    end
+    read(fn, String)
+end
+=#
+
diff --git a/test/sa_basis.jl b/test/sa_basis.jl
index fcd9e91..dd43ee1 100644
--- a/test/sa_basis.jl
+++ b/test/sa_basis.jl
@@ -1,5 +1,3 @@
-using SymbolicWedderburn.StarAlgebras
-
 @testset "affordable real degrees/dot" begin
     G = SmallPermGroups[10][2] # C₂⊕C₅
     tbl = SymbolicWedderburn.CharacterTable(Rational{Int}, G)
@@ -33,11 +31,7 @@ end
 
         RG = let G = G
             l = order(UInt16, G)
-            b = StarAlgebras.FixedBasis(
-                collect(G),
-                StarAlgebras.DiracMStructure(*),
-                (l, l),
-            )
+            b = SA.FixedBasis(collect(G), SA.DiracMStructure(*), (l, l))
             StarAlgebra(G, b)
         end
 
diff --git a/test/smallgroups.jl b/test/smallgroups.jl
index c7165fe..ace6d1c 100644
--- a/test/smallgroups.jl
+++ b/test/smallgroups.jl
@@ -1,350 +1,1600 @@
-#= GAP code:
-H := [];
-for i in [2..30] do
-    Add(H, List(AllSmallGroups(i), G->Image(IsomorphismPermGroup(G))));
-od;
-PrintTo("/tmp/groups.gap", H);
-=#
-
-#=julia code
-GAPgroups_str = join(readlines("/tmp/group.gap"), "");
-GAPgroups_str = replace(GAPgroups_str, "Group"=>"\nPermGroup");
-GAPgroups_str = replace(GAPgroups_str, r" *"=>"");
-perm_regex = r"((\(\d+(,\d+)*\)?)+)";
-print(Meta.parse(replace(GAPgroups_str, perm_regex=> s"perm\"\1\"")))
-=#
-
 import PermutationGroups: PermGroup, @perm_str
 
-const SmallPermGroups = Dict(
-    i + 1 => x for (i, x) in enumerate([
-        [PermGroup([perm"(1,2)"])],
-        [PermGroup([perm"(1,2,3)"])],
-        [PermGroup([perm"(1,2,3,4)"]), PermGroup([perm"(1,2)", perm"(3,4)"])],
-        [PermGroup([perm"(1,2,3,4,5)"])],
-        [
-            PermGroup([perm"(1,2)(3,6)(4,5)", perm"(1,3,5)(2,4,6)"]),
-            PermGroup([perm"(1,2)", perm"(3,4,5)"]),
-        ],
-        [PermGroup([perm"(1,2,3,4,5,6,7)"])],
-        [
-            PermGroup([perm"(1,2,3,4,5,6,7,8)"]),
-            PermGroup([perm"(1,2)", perm"(3,4,5,6)"]),
-            PermGroup([
-                perm"(1,2)(3,8)(4,6)(5,7)",
-                perm"(1,3)(2,5)(4,7)(6,8)",
-                perm"(1,4)(2,6)(3,7)(5,8)",
-            ]),
-            PermGroup([
-                perm"(1,2,4,6)(3,8,7,5)",
-                perm"(1,3,4,7)(2,5,6,8)",
-                perm"(1,4)(2,6)(3,7)(5,8)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)"]),
-        ],
-        [
-            PermGroup([perm"(1,2,3,4,5,6,7,8,9)"]),
-            PermGroup([perm"(1,2,3)", perm"(4,5,6)"]),
-        ],
-        [
-            PermGroup([
-                perm"(1,2)(3,10)(4,9)(5,8)(6,7)",
-                perm"(1,3,5,7,9)(2,4,6,8,10)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4,5,6,7)"]),
-        ],
-        [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11)"])],
-        [
-            PermGroup([
-                perm"(1,2,3,5)(4,10,7,12)(6,11,9,8)",
-                perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,12)",
-                perm"(1,4,8)(2,6,10)(3,7,11)(5,9,12)",
-            ]),
-            PermGroup([perm"(1,2,3)", perm"(4,5,6,7)"]),
-            PermGroup([
-                perm"(1,2,5)(3,7,12)(4,11,9)(6,10,8)",
-                perm"(1,3)(2,6)(4,8)(5,9)(7,11)(10,12)",
-                perm"(1,4)(2,7)(3,8)(5,10)(6,11)(9,12)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,5)(4,10)(6,8)(7,12)(9,11)",
-                perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,12)",
-                perm"(1,4,8)(2,6,10)(3,7,11)(5,9,12)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7)"]),
-        ],
-        [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13)"])],
-        [
-            PermGroup([
-                perm"(1,2)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)",
-                perm"(1,3,5,7,9,11,13)(2,4,6,8,10,12,14)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9)"]),
-        ],
-        [PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8)"])],
-        [
-            PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)"]),
-            PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8)"]),
-            PermGroup([
-                perm"(1,2,5,8)(3,12,10,16)(4,7,11,14)(6,15,13,9)",
-                perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)",
-                perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)",
-                perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
-            ]),
-            PermGroup([
-                perm"(1,2,5,8)(3,12,10,16)(4,7,11,14)(6,15,13,9)",
-                perm"(1,3,4,9)(2,6,7,12)(5,10,11,15)(8,13,14,16)",
-                perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)",
-                perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10)"]),
-            PermGroup([
-                perm"(1,2,4,7,5,8,11,14)(3,13,9,16,10,6,15,12)",
-                perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)",
-                perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)",
-                perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,12)(4,14)(5,8)(6,9)(7,11)(10,16)(13,15)",
-                perm"(1,3)(2,6)(4,15)(5,10)(7,16)(8,13)(9,11)(12,14)",
-                perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)",
-                perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
-            ]),
-            PermGroup([
-                perm"(1,2,5,8)(3,12,10,16)(4,14,11,7)(6,15,13,9)",
-                perm"(1,3)(2,6)(4,15)(5,10)(7,16)(8,13)(9,11)(12,14)",
-                perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)",
-                perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
-            ]),
-            PermGroup([
-                perm"(1,2,5,8)(3,12,10,16)(4,14,11,7)(6,15,13,9)",
-                perm"(1,3,5,10)(2,6,8,13)(4,15,11,9)(7,16,14,12)",
-                perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)",
-                perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8)"]),
-            PermGroup([
-                perm"(1,2)(3,13)(4,7)(5,8)(6,10)(9,16)(11,14)(12,15)",
-                perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)",
-                perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)",
-                perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
-            ]),
-            PermGroup([
-                perm"(1,2,5,8)(3,13,10,6)(4,7,11,14)(9,16,15,12)",
-                perm"(1,3,5,10)(2,6,8,13)(4,9,11,15)(7,12,14,16)",
-                perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)",
-                perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,13)(4,7)(5,8)(6,10)(9,16)(11,14)(12,15)",
-                perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)",
-                perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)",
-                perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8)"]),
-        ],
-        [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)"])],
-        [
-            PermGroup([
-                perm"(1,2)(3,18)(4,12)(5,17)(6,9)(7,16)(8,15)(10,14)(11,13)",
-                perm"(1,3,7,4,8,13,9,14,17)(2,5,10,6,11,15,12,16,18)",
-                perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11)"]),
-            PermGroup([
-                perm"(1,2)(3,5)(4,12)(6,9)(7,10)(8,16)(11,14)(13,18)(15,17)",
-                perm"(1,3,7)(2,5,10)(4,8,13)(6,11,15)(9,14,17)(12,16,18)",
-                perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,10)(4,12)(5,7)(6,9)(8,18)(11,17)(13,16)(14,15)",
-                perm"(1,3,7)(2,5,10)(4,8,13)(6,11,15)(9,14,17)(12,16,18)",
-                perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8)"]),
-        ],
-        [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)"])],
-        [
-            PermGroup([
-                perm"(1,2,3,5)(4,18,7,20)(6,19,9,16)(8,14,11,17)(10,15,13,12)",
-                perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,20)",
-                perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)",
-            ]),
-            PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9)"]),
-            PermGroup([
-                perm"(1,2,3,5)(4,10,19,17)(6,11,20,12)(7,13,16,14)(8,18,15,9)",
-                perm"(1,3)(2,5)(4,19)(6,20)(7,16)(8,15)(9,18)(10,17)(11,12)(13,14)",
-                perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,5)(4,18)(6,16)(7,20)(8,14)(9,19)(10,12)(11,17)(13,15)",
-                perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,20)",
-                perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9)"]),
-        ],
-        [
-            PermGroup([
-                perm"(1,2,4)(3,8,16)(5,10,12)(6,14,7)(9,20,19)(11,21,15)(13,18,17)",
-                perm"(1,3,6,9,12,15,18)(2,5,8,11,14,17,20)(4,7,10,13,16,19,21)",
-            ]),
-            PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10)"]),
-        ],
-        [
-            PermGroup([
-                perm"(1,2)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)",
-                perm"(1,3,5,7,9,11,13,15,17,19,21)(2,4,6,8,10,12,14,16,18,20,22)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11,12,13)"]),
-        ],
-        [
-            PermGroup([
-                perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)",
-            ]),
-        ],
-        [
-            PermGroup([
-                perm"(1,2,3,6,4,7,9,13)(5,16,10,21,11,22,17,24)(8,18,14,19,15,23,20,12)",
-                perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)",
-                perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
-                perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
-            ]),
-            PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11)"]),
-            PermGroup([
-                perm"(1,2,6)(3,8,20)(4,16,13)(5,9,15)(7,14,10)(11,18,24)(12,23,21)(17,22,19)",
-                perm"(1,3,5,11)(2,7,9,17)(4,19,12,10)(6,13,15,21)(8,23,18,16)(14,24,22,20)",
-                perm"(1,4,5,12)(2,8,9,18)(3,10,11,19)(6,14,15,22)(7,16,17,23)(13,20,21,24)",
-                perm"(1,5)(2,9)(3,11)(4,12)(6,15)(7,17)(8,18)(10,19)(13,21)(14,22)(16,23)(20,24)",
-            ]),
-            PermGroup([
-                perm"(1,2,4,7)(3,13,9,6)(5,16,11,22)(8,19,15,12)(10,24,17,21)(14,18,20,23)",
-                perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)",
-                perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
-                perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,6)(4,7)(5,16)(8,12)(9,13)(10,21)(11,22)(14,18)(15,19)(17,24)(20,23)",
-                perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)",
-                perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
-                perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,13)(4,7)(5,16)(6,9)(8,12)(10,24)(11,22)(14,23)(15,19)(17,21)(18,20)",
-                perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)",
-                perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
-                perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
-            ]),
-            PermGroup([
-                perm"(1,2,4,7)(3,6,9,13)(5,16,11,22)(8,19,15,12)(10,21,17,24)(14,23,20,18)",
-                perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)",
-                perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
-                perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,13)(4,7)(5,16)(6,9)(8,12)(10,24)(11,22)(14,23)(15,19)(17,21)(18,20)",
-                perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)",
-                perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
-                perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9)"]),
-            PermGroup([
-                perm"(1,2)(3,14)(4,7)(5,8)(6,10)(9,21)(11,15)(12,16)(13,18)(17,24)(19,22)(20,23)",
-                perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)",
-                perm"(1,4,11)(2,7,15)(3,9,17)(5,12,19)(6,13,20)(8,16,22)(10,18,23)(14,21,24)",
-                perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,19)(13,21)(15,22)(17,23)(20,24)",
-            ]),
-            PermGroup([
-                perm"(1,2,5,8)(3,14,10,6)(4,7,12,16)(9,21,18,13)(11,15,19,22)(17,24,23,20)",
-                perm"(1,3,5,10)(2,6,8,14)(4,9,12,18)(7,13,16,21)(11,17,19,23)(15,20,22,24)",
-                perm"(1,4,11)(2,7,15)(3,9,17)(5,12,19)(6,13,20)(8,16,22)(10,18,23)(14,21,24)",
-                perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,19)(13,21)(15,22)(17,23)(20,24)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,13)(4,8)(5,7)(6,9)(10,21)(11,20)(12,16)(14,18)(15,17)(19,24)(22,23)",
-                perm"(1,3,9)(2,6,13)(4,11,23)(5,19,17)(7,15,24)(8,22,20)(10,18,12)(14,21,16)",
-                perm"(1,4)(2,7)(3,10)(5,12)(6,14)(8,16)(9,17)(11,19)(13,20)(15,22)(18,23)(21,24)",
-                perm"(1,5)(2,8)(3,11)(4,12)(6,15)(7,16)(9,18)(10,19)(13,21)(14,22)(17,23)(20,24)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,6)(4,7)(5,8)(9,13)(10,14)(11,15)(12,16)(17,20)(18,21)(19,22)(23,24)",
-                perm"(1,3,9)(2,6,13)(4,11,23)(5,19,17)(7,15,24)(8,22,20)(10,18,12)(14,21,16)",
-                perm"(1,4)(2,7)(3,10)(5,12)(6,14)(8,16)(9,17)(11,19)(13,20)(15,22)(18,23)(21,24)",
-                perm"(1,5)(2,8)(3,11)(4,12)(6,15)(7,16)(9,18)(10,19)(13,21)(14,22)(17,23)(20,24)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,6)(4,7)(5,16)(8,12)(9,13)(10,21)(11,22)(14,18)(15,19)(17,24)(20,23)",
-                perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)",
-                perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
-                perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8,9)"]),
-        ],
-        [
-            PermGroup([
-                perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)",
-            ]),
-            PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10)"]),
-        ],
-        [
-            PermGroup([
-                perm"(1,2)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)",
-                perm"(1,3,5,7,9,11,13,15,17,19,21,23,25)(2,4,6,8,10,12,14,16,18,20,22,24,26)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11,12,13,14,15)"]),
-        ],
-        [
-            PermGroup([
-                perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)",
-            ]),
-            PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11,12)"]),
-            PermGroup([
-                perm"(1,2,5)(3,14,25)(4,7,12)(6,19,17)(8,26,24)(9,22,11)(10,15,20)(13,27,16)(18,23,21)",
-                perm"(1,3,8)(2,6,13)(4,9,16)(5,11,18)(7,14,21)(10,17,23)(12,19,24)(15,22,26)(20,25,27)",
-                perm"(1,4,10)(2,7,15)(3,9,17)(5,12,20)(6,14,22)(8,16,23)(11,19,25)(13,21,26)(18,24,27)",
-            ]),
-            PermGroup([
-                perm"(1,2,5,4,7,12,10,15,20)(3,14,25,9,22,11,17,6,19)(8,26,24,16,13,27,23,21,18)",
-                perm"(1,3,8)(2,6,13)(4,9,16)(5,11,18)(7,14,21)(10,17,23)(12,19,24)(15,22,26)(20,25,27)",
-                perm"(1,4,10)(2,7,15)(3,9,17)(5,12,20)(6,14,22)(8,16,23)(11,19,25)(13,21,26)(18,24,27)",
-            ]),
-            PermGroup([perm"(1,2,3)", perm"(4,5,6)", perm"(7,8,9)"]),
-        ],
-        [
-            PermGroup([
-                perm"(1,2,3,5)(4,26,7,28)(6,27,9,24)(8,22,11,25)(10,23,13,20)(12,18,15,21)(14,19,17,16)",
-                perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,28)",
-                perm"(1,4,8,12,16,20,24)(2,6,10,14,18,22,26)(3,7,11,15,19,23,27)(5,9,13,17,21,25,28)",
-            ]),
-            PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11)"]),
-            PermGroup([
-                perm"(1,2)(3,5)(4,26)(6,24)(7,28)(8,22)(9,27)(10,20)(11,25)(12,18)(13,23)(14,16)(15,21)(17,19)",
-                perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,28)",
-                perm"(1,4,8,12,16,20,24)(2,6,10,14,18,22,26)(3,7,11,15,19,23,27)(5,9,13,17,21,25,28)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9,10,11)"]),
-        ],
-        [
-            PermGroup([
-                perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)",
-            ]),
-        ],
-        [
-            PermGroup([
-                perm"(1,2)(3,5)(4,12)(6,9)(7,10)(8,18)(11,15)(13,16)(14,24)(17,21)(19,22)(20,28)(23,26)(25,30)(27,29)",
-                perm"(1,3,7,13,19)(2,5,10,16,22)(4,8,14,20,25)(6,11,17,23,27)(9,15,21,26,29)(12,18,24,28,30)",
-                perm"(1,4,9)(2,6,12)(3,8,15)(5,11,18)(7,14,21)(10,17,24)(13,20,26)(16,23,28)(19,25,29)(22,27,30)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,5)(4,24)(6,21)(7,10)(8,28)(9,18)(11,26)(12,15)(13,30)(14,23)(16,29)(17,20)(19,27)(22,25)",
-                perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,27)(21,26,29)(24,28,30)",
-                perm"(1,4,9,15,21)(2,6,12,18,24)(3,8,14,20,26)(5,11,17,23,28)(7,13,19,25,29)(10,16,22,27,30)",
-            ]),
-            PermGroup([
-                perm"(1,2)(3,10)(4,24)(5,7)(6,21)(8,30)(9,18)(11,29)(12,15)(13,28)(14,27)(16,26)(17,25)(19,23)(20,22)",
-                perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,27)(21,26,29)(24,28,30)",
-                perm"(1,4,9,15,21)(2,6,12,18,24)(3,8,14,20,26)(5,11,17,23,28)(7,13,19,25,29)(10,16,22,27,30)",
-            ]),
-            PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9,10)"]),
-        ],
-    ])
-)
+const SmallPermGroups = [
+    [PermGroup(perm"()")],
+    [PermGroup([perm"(1,2)"])],
+    [PermGroup([perm"(1,2,3)"])],
+    [PermGroup([perm"(1,2,3,4)"]), PermGroup([perm"(1,2)", perm"(3,4)"])],
+    [PermGroup([perm"(1,2,3,4,5)"])],
+    [
+        PermGroup([perm"(1,2)(3,6)(4,5)", perm"(1,3,5)(2,4,6)"]),
+        PermGroup([perm"(1,2)", perm"(3,4,5)"]),
+    ],
+    [PermGroup([perm"(1,2,3,4,5,6,7)"])],
+    [
+        PermGroup([perm"(1,2,3,4,5,6,7,8)"]),
+        PermGroup([perm"(1,2)", perm"(3,4,5,6)"]),
+        PermGroup([
+            perm"(1,2)(3,8)(4,6)(5,7)",
+            perm"(1,3)(2,5)(4,7)(6,8)",
+            perm"(1,4)(2,6)(3,7)(5,8)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,6)(3,8,7,5)",
+            perm"(1,3,4,7)(2,5,6,8)",
+            perm"(1,4)(2,6)(3,7)(5,8)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)"]),
+    ],
+    [
+        PermGroup([perm"(1,2,3,4,5,6,7,8,9)"]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2)(3,10)(4,9)(5,8)(6,7)",
+            perm"(1,3,5,7,9)(2,4,6,8,10)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5,6,7)"]),
+    ],
+    [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11)"])],
+    [
+        PermGroup([
+            perm"(1,2,3,5)(4,10,7,12)(6,11,9,8)",
+            perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,12)",
+            perm"(1,4,8)(2,6,10)(3,7,11)(5,9,12)",
+        ]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6,7)"]),
+        PermGroup([
+            perm"(1,2,5)(3,7,12)(4,11,9)(6,10,8)",
+            perm"(1,3)(2,6)(4,8)(5,9)(7,11)(10,12)",
+            perm"(1,4)(2,7)(3,8)(5,10)(6,11)(9,12)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,5)(4,10)(6,8)(7,12)(9,11)",
+            perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,12)",
+            perm"(1,4,8)(2,6,10)(3,7,11)(5,9,12)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7)"]),
+    ],
+    [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13)"])],
+    [
+        PermGroup([
+            perm"(1,2)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)",
+            perm"(1,3,5,7,9,11,13)(2,4,6,8,10,12,14)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9)"]),
+    ],
+    [PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8)"])],
+    [
+        PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)"]),
+        PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8)"]),
+        PermGroup([
+            perm"(1,2,5,8)(3,12,10,16)(4,7,11,14)(6,15,13,9)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)",
+            perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,8)(3,12,10,16)(4,7,11,14)(6,15,13,9)",
+            perm"(1,3,4,9)(2,6,7,12)(5,10,11,15)(8,13,14,16)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)",
+            perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10)"]),
+        PermGroup([
+            perm"(1,2,4,7,5,8,11,14)(3,13,9,16,10,6,15,12)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)",
+            perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)",
+            perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,12)(4,14)(5,8)(6,9)(7,11)(10,16)(13,15)",
+            perm"(1,3)(2,6)(4,15)(5,10)(7,16)(8,13)(9,11)(12,14)",
+            perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)",
+            perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,8)(3,12,10,16)(4,14,11,7)(6,15,13,9)",
+            perm"(1,3)(2,6)(4,15)(5,10)(7,16)(8,13)(9,11)(12,14)",
+            perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)",
+            perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,8)(3,12,10,16)(4,14,11,7)(6,15,13,9)",
+            perm"(1,3,5,10)(2,6,8,13)(4,15,11,9)(7,16,14,12)",
+            perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)",
+            perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8)"]),
+        PermGroup([
+            perm"(1,2)(3,13)(4,7)(5,8)(6,10)(9,16)(11,14)(12,15)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)",
+            perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,8)(3,13,10,6)(4,7,11,14)(9,16,15,12)",
+            perm"(1,3,5,10)(2,6,8,13)(4,9,11,15)(7,12,14,16)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,15)(13,16)",
+            perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,13)(4,7)(5,8)(6,10)(9,16)(11,14)(12,15)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,15)(14,16)",
+            perm"(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,12,13,16)",
+            perm"(1,5)(2,8)(3,10)(4,11)(6,13)(7,14)(9,15)(12,16)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8)"]),
+    ],
+    [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)"])],
+    [
+        PermGroup([
+            perm"(1,2)(3,18)(4,12)(5,17)(6,9)(7,16)(8,15)(10,14)(11,13)",
+            perm"(1,3,7,4,8,13,9,14,17)(2,5,10,6,11,15,12,16,18)",
+            perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11)"]),
+        PermGroup([
+            perm"(1,2)(3,5)(4,12)(6,9)(7,10)(8,16)(11,14)(13,18)(15,17)",
+            perm"(1,3,7)(2,5,10)(4,8,13)(6,11,15)(9,14,17)(12,16,18)",
+            perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,10)(4,12)(5,7)(6,9)(8,18)(11,17)(13,16)(14,15)",
+            perm"(1,3,7)(2,5,10)(4,8,13)(6,11,15)(9,14,17)(12,16,18)",
+            perm"(1,4,9)(2,6,12)(3,8,14)(5,11,16)(7,13,17)(10,15,18)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8)"]),
+    ],
+    [PermGroup([perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)"])],
+    [
+        PermGroup([
+            perm"(1,2,3,5)(4,18,7,20)(6,19,9,16)(8,14,11,17)(10,15,13,12)",
+            perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,20)",
+            perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)",
+        ]),
+        PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9)"]),
+        PermGroup([
+            perm"(1,2,3,5)(4,10,19,17)(6,11,20,12)(7,13,16,14)(8,18,15,9)",
+            perm"(1,3)(2,5)(4,19)(6,20)(7,16)(8,15)(9,18)(10,17)(11,12)(13,14)",
+            perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,5)(4,18)(6,16)(7,20)(8,14)(9,19)(10,12)(11,17)(13,15)",
+            perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,20)",
+            perm"(1,4,8,12,16)(2,6,10,14,18)(3,7,11,15,19)(5,9,13,17,20)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,4)(3,8,16)(5,10,12)(6,14,7)(9,20,19)(11,21,15)(13,18,17)",
+            perm"(1,3,6,9,12,15,18)(2,5,8,11,14,17,20)(4,7,10,13,16,19,21)",
+        ]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)",
+            perm"(1,3,5,7,9,11,13,15,17,19,21)(2,4,6,8,10,12,14,16,18,20,22)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11,12,13)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,6,4,7,9,13)(5,16,10,21,11,22,17,24)(8,18,14,19,15,23,20,12)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
+            perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
+        ]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11)"]),
+        PermGroup([
+            perm"(1,2,6)(3,8,20)(4,16,13)(5,9,15)(7,14,10)(11,18,24)(12,23,21)(17,22,19)",
+            perm"(1,3,5,11)(2,7,9,17)(4,19,12,10)(6,13,15,21)(8,23,18,16)(14,24,22,20)",
+            perm"(1,4,5,12)(2,8,9,18)(3,10,11,19)(6,14,15,22)(7,16,17,23)(13,20,21,24)",
+            perm"(1,5)(2,9)(3,11)(4,12)(6,15)(7,17)(8,18)(10,19)(13,21)(14,22)(16,23)(20,24)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,7)(3,13,9,6)(5,16,11,22)(8,19,15,12)(10,24,17,21)(14,18,20,23)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
+            perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,16)(8,12)(9,13)(10,21)(11,22)(14,18)(15,19)(17,24)(20,23)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
+            perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,13)(4,7)(5,16)(6,9)(8,12)(10,24)(11,22)(14,23)(15,19)(17,21)(18,20)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,20)(12,18,19,23)(16,21,22,24)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
+            perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,7)(3,6,9,13)(5,16,11,22)(8,19,15,12)(10,21,17,24)(14,23,20,18)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
+            perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,13)(4,7)(5,16)(6,9)(8,12)(10,24)(11,22)(14,23)(15,19)(17,21)(18,20)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
+            perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9)"]),
+        PermGroup([
+            perm"(1,2)(3,14)(4,7)(5,8)(6,10)(9,21)(11,15)(12,16)(13,18)(17,24)(19,22)(20,23)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)",
+            perm"(1,4,11)(2,7,15)(3,9,17)(5,12,19)(6,13,20)(8,16,22)(10,18,23)(14,21,24)",
+            perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,19)(13,21)(15,22)(17,23)(20,24)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,8)(3,14,10,6)(4,7,12,16)(9,21,18,13)(11,15,19,22)(17,24,23,20)",
+            perm"(1,3,5,10)(2,6,8,14)(4,9,12,18)(7,13,16,21)(11,17,19,23)(15,20,22,24)",
+            perm"(1,4,11)(2,7,15)(3,9,17)(5,12,19)(6,13,20)(8,16,22)(10,18,23)(14,21,24)",
+            perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,19)(13,21)(15,22)(17,23)(20,24)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,13)(4,8)(5,7)(6,9)(10,21)(11,20)(12,16)(14,18)(15,17)(19,24)(22,23)",
+            perm"(1,3,9)(2,6,13)(4,11,23)(5,19,17)(7,15,24)(8,22,20)(10,18,12)(14,21,16)",
+            perm"(1,4)(2,7)(3,10)(5,12)(6,14)(8,16)(9,17)(11,19)(13,20)(15,22)(18,23)(21,24)",
+            perm"(1,5)(2,8)(3,11)(4,12)(6,15)(7,16)(9,18)(10,19)(13,21)(14,22)(17,23)(20,24)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,8)(9,13)(10,14)(11,15)(12,16)(17,20)(18,21)(19,22)(23,24)",
+            perm"(1,3,9)(2,6,13)(4,11,23)(5,19,17)(7,15,24)(8,22,20)(10,18,12)(14,21,16)",
+            perm"(1,4)(2,7)(3,10)(5,12)(6,14)(8,16)(9,17)(11,19)(13,20)(15,22)(18,23)(21,24)",
+            perm"(1,5)(2,8)(3,11)(4,12)(6,15)(7,16)(9,18)(10,19)(13,21)(14,22)(17,23)(20,24)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,16)(8,12)(9,13)(10,21)(11,22)(14,18)(15,19)(17,24)(20,23)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,20)(16,21)(19,23)(22,24)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,20)(16,22)(18,23)(21,24)",
+            perm"(1,5,12)(2,8,16)(3,10,18)(4,11,19)(6,14,21)(7,15,22)(9,17,23)(13,20,24)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8,9)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)",
+        ]),
+        PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)",
+            perm"(1,3,5,7,9,11,13,15,17,19,21,23,25)(2,4,6,8,10,12,14,16,18,20,22,24,26)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5,6,7,8,9,10,11,12,13,14,15)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)",
+        ]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11,12)"]),
+        PermGroup([
+            perm"(1,2,5)(3,14,25)(4,7,12)(6,19,17)(8,26,24)(9,22,11)(10,15,20)(13,27,16)(18,23,21)",
+            perm"(1,3,8)(2,6,13)(4,9,16)(5,11,18)(7,14,21)(10,17,23)(12,19,24)(15,22,26)(20,25,27)",
+            perm"(1,4,10)(2,7,15)(3,9,17)(5,12,20)(6,14,22)(8,16,23)(11,19,25)(13,21,26)(18,24,27)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,4,7,12,10,15,20)(3,14,25,9,22,11,17,6,19)(8,26,24,16,13,27,23,21,18)",
+            perm"(1,3,8)(2,6,13)(4,9,16)(5,11,18)(7,14,21)(10,17,23)(12,19,24)(15,22,26)(20,25,27)",
+            perm"(1,4,10)(2,7,15)(3,9,17)(5,12,20)(6,14,22)(8,16,23)(11,19,25)(13,21,26)(18,24,27)",
+        ]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6)", perm"(7,8,9)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,5)(4,26,7,28)(6,27,9,24)(8,22,11,25)(10,23,13,20)(12,18,15,21)(14,19,17,16)",
+            perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,28)",
+            perm"(1,4,8,12,16,20,24)(2,6,10,14,18,22,26)(3,7,11,15,19,23,27)(5,9,13,17,21,25,28)",
+        ]),
+        PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11)"]),
+        PermGroup([
+            perm"(1,2)(3,5)(4,26)(6,24)(7,28)(8,22)(9,27)(10,20)(11,25)(12,18)(13,23)(14,16)(15,21)(17,19)",
+            perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,28)",
+            perm"(1,4,8,12,16,20,24)(2,6,10,14,18,22,26)(3,7,11,15,19,23,27)(5,9,13,17,21,25,28)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9,10,11)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2)(3,5)(4,12)(6,9)(7,10)(8,18)(11,15)(13,16)(14,24)(17,21)(19,22)(20,28)(23,26)(25,30)(27,29)",
+            perm"(1,3,7,13,19)(2,5,10,16,22)(4,8,14,20,25)(6,11,17,23,27)(9,15,21,26,29)(12,18,24,28,30)",
+            perm"(1,4,9)(2,6,12)(3,8,15)(5,11,18)(7,14,21)(10,17,24)(13,20,26)(16,23,28)(19,25,29)(22,27,30)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,5)(4,24)(6,21)(7,10)(8,28)(9,18)(11,26)(12,15)(13,30)(14,23)(16,29)(17,20)(19,27)(22,25)",
+            perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,27)(21,26,29)(24,28,30)",
+            perm"(1,4,9,15,21)(2,6,12,18,24)(3,8,14,20,26)(5,11,17,23,28)(7,13,19,25,29)(10,16,22,27,30)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,10)(4,24)(5,7)(6,21)(8,30)(9,18)(11,29)(12,15)(13,28)(14,27)(16,26)(17,25)(19,23)(20,22)",
+            perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,27)(21,26,29)(24,28,30)",
+            perm"(1,4,9,15,21)(2,6,12,18,24)(3,8,14,20,26)(5,11,17,23,28)(7,13,19,25,29)(10,16,22,27,30)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9,10)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,17,12,27)(4,8,14,20)(6,10,16,22)(7,23,18,11)(13,28,25,32)(15,21,26,30)(19,31,29,24)",
+            perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,12,16,25)(8,17,21,28)(9,18,22,29)(14,23,26,31)(20,27,30,32)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11,12)"]),
+        PermGroup([
+            perm"(1,2,4,8,6,10,15,21)(3,19,11,28,13,7,24,17)(5,9,14,20,16,22,26,30)(12,29,23,32,25,18,31,27)",
+            perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,8,14,20,15,21,26,30)(7,23,18,24,19,31,29,11)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,17,12,27)(4,21,14,30)(6,10,16,22)(7,31,18,24)(8,26,20,15)(11,19,23,29)(13,28,25,32)",
+            perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,21,14,30,15,8,26,20)(7,31,18,11,19,23,29,24)",
+            perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,21,14,30,15,8,26,20)(7,31,18,11,19,23,29,24)",
+            perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,25,16,12)(8,17,21,28)(9,29,22,18)(14,31,26,23)(20,32,30,27)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,17,12,27)(4,21,14,30)(6,10,16,22)(7,23,18,11)(8,26,20,15)(13,28,25,32)(19,31,29,24)",
+            perm"(1,3)(2,7)(4,24)(5,12)(6,13)(8,28)(9,18)(10,19)(11,15)(14,31)(16,25)(17,21)(20,32)(22,29)(23,26)(27,30)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,17,12,27)(4,21,14,30)(6,10,16,22)(7,23,18,11)(8,26,20,15)(13,28,25,32)(19,31,29,24)",
+            perm"(1,3,6,13)(2,7,10,19)(4,24,15,11)(5,12,16,25)(8,28,21,17)(9,18,22,29)(14,31,26,23)(20,32,30,27)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,21,14,30,15,8,26,20)(7,23,18,24,19,31,29,11)",
+            perm"(1,3)(2,7)(4,24)(5,12)(6,13)(8,28)(9,18)(10,19)(11,15)(14,31)(16,25)(17,21)(20,32)(22,29)(23,26)(27,30)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,8,14,20,15,21,26,30)(7,23,18,24,19,31,29,11)",
+            perm"(1,3,4,11)(2,7,8,17)(5,12,14,23)(6,13,15,24)(9,18,20,27)(10,19,21,28)(16,25,26,31)(22,29,30,32)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,17,12,27)(4,21,14,30)(6,10,16,22)(7,23,18,11)(8,26,20,15)(13,28,25,32)(19,31,29,24)",
+            perm"(1,3,4,11,6,13,15,24)(2,7,8,17,10,19,21,28)(5,12,14,23,16,25,26,31)(9,18,20,27,22,29,30,32)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,17,12,27)(4,21,14,30)(6,10,16,22)(7,23,18,11)(8,26,20,15)(13,28,25,32)(19,31,29,24)",
+            perm"(1,3,15,24,6,13,4,11)(2,7,21,28,10,19,8,17)(5,12,26,31,16,25,14,23)(9,18,30,32,22,29,20,27)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9,6,10,16,22)(3,17,12,27,13,28,25,32)(4,21,14,30,15,8,26,20)(7,23,18,24,19,31,29,11)",
+            perm"(1,3,4,11,6,13,15,24)(2,7,8,17,10,19,21,28)(5,12,14,23,16,25,26,31)(9,18,20,27,22,29,30,32)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,8,5,9,14,20,6,10,15,21,16,22,26,30)(3,19,11,28,12,29,23,32,13,7,24,17,25,18,31,27)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)",
+            perm"(1,4,5,14,6,15,16,26)(2,8,9,20,10,21,22,30)(3,11,12,23,13,24,25,31)(7,17,18,27,19,28,29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,17)(4,20)(5,22)(6,10)(7,11)(8,14)(9,16)(12,32)(13,28)(15,30)(18,31)(19,24)(21,26)(23,29)(25,27)",
+            perm"(1,3)(2,7)(4,23)(5,25)(6,13)(8,27)(9,29)(10,19)(11,14)(12,16)(15,31)(17,20)(18,22)(21,32)(24,26)(28,30)",
+            perm"(1,4,16,26,6,15,5,14)(2,8,22,30,10,21,9,20)(3,11,25,31,13,24,12,23)(7,17,29,32,19,28,18,27)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,17,13,28)(4,20,15,30)(5,22,16,9)(7,24,19,11)(8,26,21,14)(12,32,25,27)(18,23,29,31)",
+            perm"(1,3)(2,7)(4,23)(5,25)(6,13)(8,27)(9,29)(10,19)(11,14)(12,16)(15,31)(17,20)(18,22)(21,32)(24,26)(28,30)",
+            perm"(1,4,16,26,6,15,5,14)(2,8,22,30,10,21,9,20)(3,11,25,31,13,24,12,23)(7,17,29,32,19,28,18,27)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,17,13,28)(4,20,15,30)(5,22,16,9)(7,24,19,11)(8,26,21,14)(12,32,25,27)(18,23,29,31)",
+            perm"(1,3,6,13)(2,7,10,19)(4,23,15,31)(5,25,16,12)(8,27,21,32)(9,29,22,18)(11,26,24,14)(17,30,28,20)",
+            perm"(1,4,16,26,6,15,5,14)(2,8,22,30,10,21,9,20)(3,11,25,31,13,24,12,23)(7,17,29,32,19,28,18,27)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5,6)", perm"(7,8,9,10)"]),
+        PermGroup([
+            perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,9,16,22)(7,25,19,12)(11,27,24,32)(14,20,26,30)(17,31,28,23)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,9,16,22)(7,25,19,12)(11,27,24,32)(14,20,26,30)(17,31,28,23)",
+            perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,9,16,22)(7,25,19,12)(11,27,24,32)(14,20,26,30)(17,31,28,23)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)",
+            perm"(1,4,5,14)(2,8,9,20)(3,11,12,23)(6,15,16,26)(7,17,18,27)(10,21,22,30)(13,24,25,31)(19,28,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,9,16,22)(7,25,19,12)(11,27,24,32)(14,20,26,30)(17,31,28,23)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,9,16,22)(7,25,19,12)(11,27,24,32)(14,20,26,30)(17,31,28,23)",
+            perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)",
+            perm"(1,4,16,26)(2,8,22,30)(3,11,25,31)(5,14,6,15)(7,17,29,32)(9,20,10,21)(12,23,13,24)(18,27,19,28)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)",
+            perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,18,12,7)(4,21,14,30)(6,10,16,22)(8,26,20,15)(11,32,23,28)(13,29,25,19)(17,24,27,31)",
+            perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)",
+            perm"(1,4,5,14)(2,8,9,20)(3,11,12,23)(6,15,16,26)(7,17,18,27)(10,21,22,30)(13,24,25,31)(19,28,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)",
+            perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,12,16,25)(8,17,21,28)(9,18,22,29)(14,23,26,31)(20,27,30,32)",
+            perm"(1,4,5,14)(2,8,9,20)(3,11,12,23)(6,15,16,26)(7,17,18,27)(10,21,22,30)(13,24,25,31)(19,28,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,18,12,7)(4,21,14,30)(6,10,16,22)(8,26,20,15)(11,32,23,28)(13,29,25,19)(17,24,27,31)",
+            perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,12,16,25)(8,17,21,28)(9,18,22,29)(14,23,26,31)(20,27,30,32)",
+            perm"(1,4,5,14)(2,8,9,20)(3,11,12,23)(6,15,16,26)(7,17,18,27)(10,21,22,30)(13,24,25,31)(19,28,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)",
+            perm"(1,3,16,25)(2,7,22,29)(4,11,26,31)(5,12,6,13)(8,17,30,32)(9,18,10,19)(14,23,15,24)(20,27,21,28)",
+            perm"(1,4,5,14)(2,8,9,20)(3,11,12,23)(6,15,16,26)(7,17,18,27)(10,21,22,30)(13,24,25,31)(19,28,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,9)(6,10)(7,12)(8,15)(11,32)(13,29)(14,30)(16,22)(17,31)(19,25)(20,26)(23,28)(24,27)",
+            perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,18,12,7)(4,21,14,30)(6,10,16,22)(8,26,20,15)(11,32,23,28)(13,29,25,19)(17,24,27,31)",
+            perm"(1,3,5,12)(2,7,9,18)(4,11,14,23)(6,13,16,25)(8,17,20,27)(10,19,22,29)(15,24,26,31)(21,28,30,32)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9,10,11,12)"]),
+        PermGroup([
+            perm"(1,2,5,9,6,10,16,22)(3,19,12,29,13,7,25,18)(4,8,14,20,15,21,26,30)(11,28,23,32,24,17,31,27)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9,6,10,16,22)(3,7,12,18,13,19,25,29)(4,8,14,20,15,21,26,30)(11,17,23,27,24,28,31,32)",
+            perm"(1,3)(2,7)(4,24)(5,12)(6,13)(8,28)(9,18)(10,19)(11,15)(14,31)(16,25)(17,21)(20,32)(22,29)(23,26)(27,30)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,8)(5,22)(6,10)(7,12)(9,16)(11,27)(13,29)(14,30)(15,21)(17,23)(19,25)(20,26)(24,32)(28,31)",
+            perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,22,16,9)(7,25,19,12)(11,27,24,32)(14,30,26,20)(17,31,28,23)",
+            perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,18,13,29)(4,8,15,21)(5,22,16,9)(7,25,19,12)(11,27,24,32)(14,30,26,20)(17,31,28,23)",
+            perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,25,16,12)(8,17,21,28)(9,29,22,18)(14,31,26,23)(20,32,30,27)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,8)(5,22)(6,10)(7,12)(9,16)(11,27)(13,29)(14,30)(15,21)(17,23)(19,25)(20,26)(24,32)(28,31)",
+            perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,22)(6,10)(7,12)(8,15)(9,16)(11,32)(13,29)(14,20)(17,31)(19,25)(23,28)(24,27)(26,30)",
+            perm"(1,3)(2,7)(4,11)(5,25)(6,13)(8,17)(9,29)(10,19)(12,16)(14,31)(15,24)(18,22)(20,32)(21,28)(23,26)(27,30)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,22)(6,10)(7,12)(8,15)(9,16)(11,32)(13,29)(14,20)(17,31)(19,25)(23,28)(24,27)(26,30)",
+            perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,25,16,12)(8,17,21,28)(9,29,22,18)(14,31,26,23)(20,32,30,27)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5,6,16)(2,9,10,22)(3,12,13,25)(4,14,15,26)(7,18,19,29)(8,20,21,30)(11,23,24,31)(17,27,28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8,9,10)"]),
+        PermGroup([
+            perm"(1,2)(3,19)(4,8)(5,9)(6,10)(7,13)(11,28)(12,29)(14,20)(15,21)(16,22)(17,24)(18,25)(23,32)(26,30)(27,31)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,19,13,7)(4,8,15,21)(5,9,16,22)(11,28,24,17)(12,29,25,18)(14,20,26,30)(23,32,31,27)",
+            perm"(1,3,6,13)(2,7,10,19)(4,11,15,24)(5,12,16,25)(8,17,21,28)(9,18,22,29)(14,23,26,31)(20,27,30,32)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,19)(4,8)(5,9)(6,10)(7,13)(11,28)(12,29)(14,20)(15,21)(16,22)(17,24)(18,25)(23,32)(26,30)(27,31)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,17)(9,18)(10,19)(14,23)(15,24)(16,25)(20,27)(21,28)(22,29)(26,31)(30,32)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,19)(4,8)(5,22)(6,10)(7,13)(9,16)(11,28)(12,18)(14,30)(15,21)(17,24)(20,26)(23,27)(25,29)(31,32)",
+            perm"(1,3)(2,7)(4,24)(5,12)(6,13)(8,28)(9,18)(10,19)(11,15)(14,31)(16,25)(17,21)(20,32)(22,29)(23,26)(27,30)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,20)(10,21)(12,23)(13,24)(16,26)(18,27)(19,28)(22,30)(25,31)(29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,19)(4,8)(5,22)(6,10)(7,13)(9,16)(11,28)(12,18)(14,30)(15,21)(17,24)(20,26)(23,27)(25,29)(31,32)",
+            perm"(1,3,6,13)(2,7,10,19)(4,24,15,11)(5,12,16,25)(8,28,21,17)(9,18,22,29)(14,31,26,23)(20,32,30,27)",
+            perm"(1,4,6,15)(2,8,10,21)(3,11,13,24)(5,14,16,26)(7,17,19,28)(9,20,22,30)(12,23,25,31)(18,27,29,32)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,20)(10,22)(11,23)(13,25)(15,26)(17,27)(19,29)(21,30)(24,31)(28,32)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,16)(7,19)(8,21)(9,22)(11,24)(12,25)(14,26)(17,28)(18,29)(20,30)(23,31)(27,32)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4)",
+            perm"(5,6)",
+            perm"(7,8)",
+            perm"(9,10)",
+        ]),
+    ],
+    [PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11,12,13,14)"])],
+    [
+        PermGroup([
+            perm"(1,2)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)",
+            perm"(1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33)(2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)",
+        ]),
+    ],
+    [PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10,11,12)"])],
+    [
+        PermGroup([
+            perm"(1,2,3,6)(4,27,9,32)(5,18,10,26)(7,29,14,22)(8,21,15,13)(11,17,19,25)(12,16,20,24)(23,34,30,36)(28,35,33,31)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,24)(17,25)(18,26)(22,29)(23,30)(27,32)(28,33)(31,35)(34,36)",
+            perm"(1,4,11,13,23,31,5,12,22)(2,7,16,18,28,34,8,17,27)(3,9,19,21,30,35,10,20,29)(6,14,24,26,33,36,15,25,32)",
+            perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)",
+        ]),
+        PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11,12,13)"]),
+        PermGroup([
+            perm"(1,2,6,3,7,14,10,17,24)(4,9,27,11,19,34,21,29,36)(5,20,15,12,30,25,22,35,32)(8,16,23,18,26,31,28,33,13)",
+            perm"(1,3,10)(2,7,17)(4,11,21)(5,12,22)(6,14,24)(8,18,28)(9,19,29)(13,23,31)(15,25,32)(16,26,33)(20,30,35)(27,34,36)",
+            perm"(1,4)(2,8)(3,11)(5,13)(6,15)(7,18)(9,20)(10,21)(12,23)(14,25)(16,27)(17,28)(19,30)(22,31)(24,32)(26,34)(29,35)(33,36)",
+            perm"(1,5)(2,9)(3,12)(4,13)(6,16)(7,19)(8,20)(10,22)(11,23)(14,26)(15,27)(17,29)(18,30)(21,31)(24,33)(25,34)(28,35)(32,36)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,27)(5,18)(7,22)(8,13)(9,32)(10,26)(11,17)(12,16)(14,29)(15,21)(19,25)(20,24)(23,34)(28,31)(30,36)(33,35)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,24)(17,25)(18,26)(22,29)(23,30)(27,32)(28,33)(31,35)(34,36)",
+            perm"(1,4,11,13,23,31,5,12,22)(2,7,16,18,28,34,8,17,27)(3,9,19,21,30,35,10,20,29)(6,14,24,26,33,36,15,25,32)",
+            perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7,8,9,10,11,12,13)"]),
+        PermGroup([
+            perm"(1,2,4,7)(3,6,10,15)(5,18,12,28)(8,23,17,13)(9,14,19,24)(11,27,21,34)(16,31,26,22)(20,33,29,36)(25,35,32,30)",
+            perm"(1,3,9)(2,6,14)(4,10,19)(5,11,20)(7,15,24)(8,16,25)(12,21,29)(13,22,30)(17,26,32)(18,27,33)(23,31,35)(28,34,36)",
+            perm"(1,4)(2,7)(3,10)(5,12)(6,15)(8,17)(9,19)(11,21)(13,23)(14,24)(16,26)(18,28)(20,29)(22,31)(25,32)(27,34)(30,35)(33,36)",
+            perm"(1,5,13)(2,8,18)(3,11,22)(4,12,23)(6,16,27)(7,17,28)(9,20,30)(10,21,31)(14,25,33)(15,26,34)(19,29,35)(24,32,36)",
+        ]),
+        PermGroup([
+            perm"(1,2,3,6)(4,16,9,24)(5,18,10,26)(7,19,14,11)(8,21,15,13)(12,34,20,36)(17,35,25,31)(22,28,29,33)(23,27,30,32)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,24)(17,25)(18,26)(22,29)(23,30)(27,32)(28,33)(31,35)(34,36)",
+            perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,24)(8,17,27)(10,20,29)(13,23,31)(15,25,32)(18,28,34)(21,30,35)(26,33,36)",
+            perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)",
+        ]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6)", perm"(7,8,9,10)"]),
+        PermGroup([
+            perm"(1,2,3,6)(4,28,19,32)(5,34,21,25)(7,30,24,22)(8,35,26,12)(9,33,11,27)(10,36,13,17)(14,23,16,29)(15,31,18,20)",
+            perm"(1,3)(2,6)(4,19)(5,21)(7,24)(8,26)(9,11)(10,13)(12,35)(14,16)(15,18)(17,36)(20,31)(22,30)(23,29)(25,34)(27,33)(28,32)",
+            perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,24)(8,17,27)(10,20,29)(13,23,31)(15,25,32)(18,28,34)(21,30,35)(26,33,36)",
+            perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,18)(8,13)(9,14)(10,26)(11,16)(12,28)(15,21)(17,23)(19,24)(20,33)(22,34)(25,30)(27,31)(29,36)(32,35)",
+            perm"(1,3)(2,6)(4,19)(5,10)(7,24)(8,15)(9,11)(12,29)(13,21)(14,16)(17,32)(18,26)(20,22)(23,35)(25,27)(28,36)(30,31)(33,34)",
+            perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,24)(8,17,27)(10,20,29)(13,23,31)(15,25,32)(18,28,34)(21,30,35)(26,33,36)",
+            perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)",
+        ]),
+        PermGroup([
+            perm"(1,2,6)(3,7,14)(4,9,27)(5,20,15)(8,16,13)(10,17,24)(11,19,34)(12,30,25)(18,26,23)(21,29,36)(22,35,32)(28,33,31)",
+            perm"(1,3,10)(2,7,17)(4,11,21)(5,12,22)(6,14,24)(8,18,28)(9,19,29)(13,23,31)(15,25,32)(16,26,33)(20,30,35)(27,34,36)",
+            perm"(1,4)(2,8)(3,11)(5,13)(6,15)(7,18)(9,20)(10,21)(12,23)(14,25)(16,27)(17,28)(19,30)(22,31)(24,32)(26,34)(29,35)(33,36)",
+            perm"(1,5)(2,9)(3,12)(4,13)(6,16)(7,19)(8,20)(10,22)(11,23)(14,26)(15,27)(17,29)(18,30)(21,31)(24,33)(25,34)(28,35)(32,36)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,18)(8,13)(9,14)(10,26)(11,16)(12,28)(15,21)(17,23)(19,24)(20,33)(22,34)(25,30)(27,31)(29,36)(32,35)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,24)(17,25)(18,26)(22,29)(23,30)(27,32)(28,33)(31,35)(34,36)",
+            perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,24)(8,17,27)(10,20,29)(13,23,31)(15,25,32)(18,28,34)(21,30,35)(26,33,36)",
+            perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,16)(5,18)(7,11)(8,13)(9,24)(10,26)(12,34)(14,19)(15,21)(17,31)(20,36)(22,28)(23,27)(25,35)(29,33)(30,32)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,24)(17,25)(18,26)(22,29)(23,30)(27,32)(28,33)(31,35)(34,36)",
+            perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,24)(8,17,27)(10,20,29)(13,23,31)(15,25,32)(18,28,34)(21,30,35)(26,33,36)",
+            perm"(1,5,13)(2,8,18)(3,10,21)(4,12,23)(6,15,26)(7,17,28)(9,20,30)(11,22,31)(14,25,33)(16,27,34)(19,29,35)(24,32,36)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7)", perm"(8,9,10)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)",
+            perm"(1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37)(2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,4)(3,11,31)(5,13,27)(6,20,19)(7,9,29)(8,22,15)(10,18,17)(12,38,34)(14,39,30)(16,36,32)(21,26,37)(23,28,33)(24,35,25)",
+            perm"(1,3,6,9,12,15,18,21,24,27,30,33,36)(2,5,8,11,14,17,20,23,26,29,32,35,38)(4,7,10,13,16,19,22,25,28,31,34,37,39)",
+        ]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6,7,8,9,10,11,12,13,14,15,16)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,6,4,7,9,13)(5,32,10,37,11,38,17,40)(8,34,14,35,15,39,21,28)(12,24,18,30,19,31,25,36)(16,26,22,27,23,33,29,20)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,36)(28,34,35,39)(32,37,38,40)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)",
+            perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)",
+        ]),
+        PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10,11,12,13)"]),
+        PermGroup([
+            perm"(1,2,3,6,4,7,9,13)(5,16,34,30,11,23,39,36)(8,18,37,27,15,25,40,20)(10,22,35,31,17,29,28,24)(12,32,26,14,19,38,33,21)",
+            perm"(1,3,4,9)(2,6,7,13)(5,34,11,39)(8,37,15,40)(10,35,17,28)(12,26,19,33)(14,38,21,32)(16,30,23,36)(18,27,25,20)(22,31,29,24)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)",
+            perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,7)(3,13,9,6)(5,32,11,38)(8,35,15,28)(10,40,17,37)(12,24,19,31)(14,34,21,39)(16,27,23,20)(18,36,25,30)(22,26,29,33)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,36)(28,34,35,39)(32,37,38,40)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)",
+            perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,32)(8,28)(9,13)(10,37)(11,38)(12,24)(14,34)(15,35)(16,20)(17,40)(18,30)(19,31)(21,39)(22,26)(23,27)(25,36)(29,33)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,36)(28,34,35,39)(32,37,38,40)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)",
+            perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,13)(4,7)(5,32)(6,9)(8,28)(10,40)(11,38)(12,24)(14,39)(15,35)(16,20)(17,37)(18,36)(19,31)(21,34)(22,33)(23,27)(25,30)(26,29)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,36)(28,34,35,39)(32,37,38,40)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)",
+            perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,7)(3,6,9,13)(5,32,11,38)(8,35,15,28)(10,37,17,40)(12,24,19,31)(14,39,21,34)(16,27,23,20)(18,30,25,36)(22,33,29,26)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,36)(32,37)(35,39)(38,40)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)",
+            perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,13)(4,7)(5,32)(6,9)(8,28)(10,40)(11,38)(12,24)(14,39)(15,35)(16,20)(17,37)(18,36)(19,31)(21,34)(22,33)(23,27)(25,30)(26,29)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,36)(32,37)(35,39)(38,40)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)",
+            perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5,6)", perm"(7,8,9,10,11)"]),
+        PermGroup([
+            perm"(1,2)(3,14)(4,7)(5,8)(6,10)(9,22)(11,15)(12,16)(13,18)(17,30)(19,23)(20,24)(21,26)(25,37)(27,31)(28,32)(29,34)(33,40)(35,38)(36,39)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,36)(32,37)(35,39)(38,40)",
+            perm"(1,4,11,19,27)(2,7,15,23,31)(3,9,17,25,33)(5,12,20,28,35)(6,13,21,29,36)(8,16,24,32,38)(10,18,26,34,39)(14,22,30,37,40)",
+            perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,20)(13,22)(15,24)(17,26)(19,28)(21,30)(23,32)(25,34)(27,35)(29,37)(31,38)(33,39)(36,40)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,8)(3,14,10,6)(4,7,12,16)(9,22,18,13)(11,15,20,24)(17,30,26,21)(19,23,28,32)(25,37,34,29)(27,31,35,38)(33,40,39,36)",
+            perm"(1,3,5,10)(2,6,8,14)(4,9,12,18)(7,13,16,22)(11,17,20,26)(15,21,24,30)(19,25,28,34)(23,29,32,37)(27,33,35,39)(31,36,38,40)",
+            perm"(1,4,11,19,27)(2,7,15,23,31)(3,9,17,25,33)(5,12,20,28,35)(6,13,21,29,36)(8,16,24,32,38)(10,18,26,34,39)(14,22,30,37,40)",
+            perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,20)(13,22)(15,24)(17,26)(19,28)(21,30)(23,32)(25,34)(27,35)(29,37)(31,38)(33,39)(36,40)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,7)(3,6,9,13)(5,16,35,31)(8,19,38,20)(10,22,39,36)(11,23,28,24)(12,32,27,15)(14,25,40,26)(17,29,34,30)(18,37,33,21)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,36)(32,37)(35,39)(38,40)",
+            perm"(1,4)(2,7)(3,9)(5,35)(6,13)(8,38)(10,39)(11,28)(12,27)(14,40)(15,32)(16,31)(17,34)(18,33)(19,20)(21,37)(22,36)(23,24)(25,26)(29,30)",
+            perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,32)(8,28)(9,13)(10,37)(11,38)(12,24)(14,34)(15,35)(16,20)(17,40)(18,30)(19,31)(21,39)(22,26)(23,27)(25,36)(29,33)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,36)(32,37)(35,39)(38,40)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,36)(32,38)(34,39)(37,40)",
+            perm"(1,5,12,20,28)(2,8,16,24,32)(3,10,18,26,34)(4,11,19,27,35)(6,14,22,30,37)(7,15,23,31,38)(9,17,25,33,39)(13,21,29,36,40)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6)", perm"(7,8,9,10,11)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2)(3,5)(4,36)(6,33)(7,10)(8,40)(9,30)(11,38)(12,27)(13,42)(14,35)(15,24)(16,41)(17,32)(18,21)(19,39)(20,29)(22,37)(23,26)(25,34)(28,31)",
+            perm"(1,3,7)(2,5,10)(4,14,31)(6,17,34)(8,19,21)(9,26,13)(11,22,24)(12,29,16)(15,38,37)(18,40,39)(20,41,27)(23,42,30)(25,33,32)(28,36,35)",
+            perm"(1,4,9,15,21,27,33)(2,6,12,18,24,30,36)(3,8,14,20,26,32,38)(5,11,17,23,29,35,40)(7,13,19,25,31,37,41)(10,16,22,28,34,39,42)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,5)(4,6)(7,10)(8,11)(9,12)(13,16)(14,17)(15,18)(19,22)(20,23)(21,24)(25,28)(26,29)(27,30)(31,34)(32,35)(33,36)(37,39)(38,40)(41,42)",
+            perm"(1,3,7)(2,5,10)(4,14,31)(6,17,34)(8,19,21)(9,26,13)(11,22,24)(12,29,16)(15,38,37)(18,40,39)(20,41,27)(23,42,30)(25,33,32)(28,36,35)",
+            perm"(1,4,9,15,21,27,33)(2,6,12,18,24,30,36)(3,8,14,20,26,32,38)(5,11,17,23,29,35,40)(7,13,19,25,31,37,41)(10,16,22,28,34,39,42)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,5)(4,12)(6,9)(7,10)(8,18)(11,15)(13,16)(14,24)(17,21)(19,22)(20,30)(23,27)(25,28)(26,36)(29,33)(31,34)(32,40)(35,38)(37,42)(39,41)",
+            perm"(1,3,7,13,19,25,31)(2,5,10,16,22,28,34)(4,8,14,20,26,32,37)(6,11,17,23,29,35,39)(9,15,21,27,33,38,41)(12,18,24,30,36,40,42)",
+            perm"(1,4,9)(2,6,12)(3,8,15)(5,11,18)(7,14,21)(10,17,24)(13,20,27)(16,23,30)(19,26,33)(22,29,36)(25,32,38)(28,35,40)(31,37,41)(34,39,42)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,5)(4,36)(6,33)(7,10)(8,40)(9,30)(11,38)(12,27)(13,42)(14,35)(15,24)(16,41)(17,32)(18,21)(19,39)(20,29)(22,37)(23,26)(25,34)(28,31)",
+            perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,28)(21,26,31)(24,29,34)(27,32,37)(30,35,39)(33,38,41)(36,40,42)",
+            perm"(1,4,9,15,21,27,33)(2,6,12,18,24,30,36)(3,8,14,20,26,32,38)(5,11,17,23,29,35,40)(7,13,19,25,31,37,41)(10,16,22,28,34,39,42)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,10)(4,36)(5,7)(6,33)(8,42)(9,30)(11,41)(12,27)(13,40)(14,39)(15,24)(16,38)(17,37)(18,21)(19,35)(20,34)(22,32)(23,31)(25,29)(26,28)",
+            perm"(1,3,7)(2,5,10)(4,8,13)(6,11,16)(9,14,19)(12,17,22)(15,20,25)(18,23,28)(21,26,31)(24,29,34)(27,32,37)(30,35,39)(33,38,41)(36,40,42)",
+            perm"(1,4,9,15,21,27,33)(2,6,12,18,24,30,36)(3,8,14,20,26,32,38)(5,11,17,23,29,35,40)(7,13,19,25,31,37,41)(10,16,22,28,34,39,42)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9,10,11,12)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,5)(4,42,7,44)(6,43,9,40)(8,38,11,41)(10,39,13,36)(12,34,15,37)(14,35,17,32)(16,30,19,33)(18,31,21,28)(20,26,23,29)(22,27,25,24)",
+            perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,37)(36,39)(38,41)(40,43)(42,44)",
+            perm"(1,4,8,12,16,20,24,28,32,36,40)(2,6,10,14,18,22,26,30,34,38,42)(3,7,11,15,19,23,27,31,35,39,43)(5,9,13,17,21,25,29,33,37,41,44)",
+        ]),
+        PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11,12,13,14,15)"]),
+        PermGroup([
+            perm"(1,2)(3,5)(4,42)(6,40)(7,44)(8,38)(9,43)(10,36)(11,41)(12,34)(13,39)(14,32)(15,37)(16,30)(17,35)(18,28)(19,33)(20,26)(21,31)(22,24)(23,29)(25,27)",
+            perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,37)(36,39)(38,41)(40,43)(42,44)",
+            perm"(1,4,8,12,16,20,24,28,32,36,40)(2,6,10,14,18,22,26,30,34,38,42)(3,7,11,15,19,23,27,31,35,39,43)(5,9,13,17,21,25,29,33,37,41,44)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4)",
+            perm"(5,6,7,8,9,10,11,12,13,14,15)",
+        ]),
+    ],
+    [
+        PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10,11,12,13,14)"]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6)", perm"(7,8,9,10,11)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2)(3,46)(4,45)(5,44)(6,43)(7,42)(8,41)(9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)",
+            perm"(1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45)(2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,7,4,8,11,18,5,9,12,19,14,21,25,32)(6,24,13,35,15,37,26,44,16,38,27,45,29,46,39,48)(10,28,20,30,22,40,33,31,23,41,34,42,36,47,43,17)",
+            perm"(1,3,4,11,5,12,14,25)(2,7,8,18,9,19,21,32)(6,13,15,26,16,27,29,39)(10,20,22,33,23,34,36,43)(17,28,30,40,31,41,42,47)(24,35,37,44,38,45,46,48)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,3)",
+            perm"(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)",
+        ]),
+        PermGroup([
+            perm"(1,2,7)(3,9,44)(4,39,18)(5,11,37)(6,27,20)(8,19,29)(10,21,17)(12,40,35)(13,26,43)(14,41,48)(15,22,45)(16,38,33)(23,36,28)(24,46,42)(25,32,30)(31,47,34)",
+            perm"(1,3,17,30)(2,8,27,40)(4,12,31,42)(5,13,6,14)(7,18,37,45)(9,22,41,47)(10,23,11,24)(15,28,16,29)(19,32,46,48)(20,33,21,34)(25,38,26,39)(35,43,36,44)",
+            perm"(1,4,5,15)(2,9,10,25)(3,12,13,28)(6,16,17,31)(7,19,20,35)(8,22,23,38)(11,26,27,41)(14,29,30,42)(18,32,33,43)(21,36,37,46)(24,39,40,47)(34,44,45,48)",
+            perm"(1,5)(2,10)(3,13)(4,15)(6,17)(7,20)(8,23)(9,25)(11,27)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(22,38)(24,40)(26,41)(29,42)(32,43)(34,45)(36,46)(39,47)(44,48)",
+            perm"(1,6)(2,11)(3,14)(4,16)(5,17)(7,21)(8,24)(9,26)(10,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,39)(23,40)(25,41)(28,42)(32,44)(33,45)(35,46)(38,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,8)(5,9)(6,24)(10,17)(11,18)(12,19)(13,35)(14,21)(15,37)(16,38)(20,28)(22,30)(23,31)(25,32)(26,44)(27,45)(29,46)(33,40)(34,41)(36,42)(39,48)(43,47)",
+            perm"(1,3,4,11,5,12,14,25)(2,7,8,18,9,19,21,32)(6,13,15,26,16,27,29,39)(10,20,22,33,23,34,36,43)(17,28,30,40,31,41,42,47)(24,35,37,44,38,45,46,48)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,19)(4,8)(5,9)(6,24)(7,12)(10,17)(11,32)(13,45)(14,21)(15,37)(16,38)(18,25)(20,41)(22,30)(23,31)(26,48)(27,35)(28,34)(29,46)(33,47)(36,42)(39,44)(40,43)",
+            perm"(1,3,4,11,5,12,14,25)(2,7,8,18,9,19,21,32)(6,13,15,26,16,27,29,39)(10,20,22,33,23,34,36,43)(17,28,30,40,31,41,42,47)(24,35,37,44,38,45,46,48)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,9)(6,24)(7,11)(8,14)(10,17)(12,32)(13,44)(15,46)(16,38)(19,25)(20,40)(22,42)(23,31)(26,35)(27,48)(28,33)(29,37)(30,36)(34,47)(39,45)(41,43)",
+            perm"(1,3,4,11,5,12,14,25)(2,7,8,18,9,19,21,32)(6,13,15,26,16,27,29,39)(10,20,22,33,23,34,36,43)(17,28,30,40,31,41,42,47)(24,35,37,44,38,45,46,48)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,9)(6,24)(7,11)(8,14)(10,17)(12,32)(13,44)(15,46)(16,38)(19,25)(20,40)(22,42)(23,31)(26,35)(27,48)(28,33)(29,37)(30,36)(34,47)(39,45)(41,43)",
+            perm"(1,3,14,25,5,12,4,11)(2,7,21,32,9,19,8,18)(6,13,29,39,16,27,15,26)(10,20,36,43,23,34,22,33)(17,28,42,47,31,41,30,40)(24,35,46,48,38,45,37,44)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,18,12,32)(4,21,14,8)(6,24,16,38)(7,25,19,11)(10,31,23,17)(13,44,27,48)(15,46,29,37)(20,47,34,40)(22,30,36,42)(26,35,39,45)(28,33,41,43)",
+            perm"(1,3,14,25,5,12,4,11)(2,7,21,32,9,19,8,18)(6,13,29,39,16,27,15,26)(10,20,36,43,23,34,22,33)(17,28,42,47,31,41,30,40)(24,35,46,48,38,45,37,44)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,8,5,9,14,21)(3,7,11,18,12,19,25,32)(6,24,15,37,16,38,29,46)(10,30,22,31,23,42,36,17)(13,35,26,44,27,45,39,48)(20,40,33,41,34,47,43,28)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,8,5,9,14,21)(3,19,11,32,12,7,25,18)(6,24,15,37,16,38,29,46)(10,30,22,31,23,42,36,17)(13,45,26,48,27,35,39,44)(20,47,33,28,34,40,43,41)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,8)(3,7,11,18)(5,9,14,21)(6,24,15,37)(10,30,22,17)(12,19,25,32)(13,35,26,44)(16,38,29,46)(20,40,33,28)(23,42,36,31)(27,45,39,48)(34,47,43,41)",
+            perm"(1,3,5,12)(2,7,9,19)(4,11,14,25)(6,13,16,27)(8,18,21,32)(10,20,23,34)(15,26,29,39)(17,28,31,41)(22,33,36,43)(24,35,38,45)(30,40,42,47)(37,44,46,48)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,19,12,7)(4,8,14,21)(6,24,16,38)(10,31,23,17)(11,32,25,18)(13,45,27,35)(15,37,29,46)(20,28,34,41)(22,42,36,30)(26,48,39,44)(33,40,43,47)",
+            perm"(1,3,4,11)(2,7,8,18)(5,12,14,25)(6,13,15,26)(9,19,21,32)(10,20,22,33)(16,27,29,39)(17,28,30,40)(23,34,36,43)(24,35,37,44)(31,41,42,47)(38,45,46,48)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,8)(3,19,11,32)(5,9,14,21)(6,24,15,37)(7,25,18,12)(10,30,22,17)(13,45,26,48)(16,38,29,46)(20,47,33,41)(23,42,36,31)(27,35,39,44)(28,34,40,43)",
+            perm"(1,3,5,12)(2,7,9,19)(4,11,14,25)(6,13,16,27)(8,18,21,32)(10,20,23,34)(15,26,29,39)(17,28,31,41)(22,33,36,43)(24,35,38,45)(30,40,42,47)(37,44,46,48)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,19)(4,8)(5,9)(6,24)(7,12)(10,17)(11,32)(13,45)(14,21)(15,37)(16,38)(18,25)(20,41)(22,30)(23,31)(26,48)(27,35)(28,34)(29,46)(33,47)(36,42)(39,44)(40,43)",
+            perm"(1,3,4,11)(2,7,8,18)(5,12,14,25)(6,13,15,26)(9,19,21,32)(10,20,22,33)(16,27,29,39)(17,28,30,40)(23,34,36,43)(24,35,37,44)(31,41,42,47)(38,45,46,48)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,9)(6,24)(7,11)(8,14)(10,17)(12,32)(13,44)(15,46)(16,38)(19,25)(20,40)(22,42)(23,31)(26,35)(27,48)(28,33)(29,37)(30,36)(34,47)(39,45)(41,43)",
+            perm"(1,3)(2,7)(4,25)(5,12)(6,13)(8,32)(9,19)(10,20)(11,14)(15,39)(16,27)(17,28)(18,21)(22,43)(23,34)(24,35)(26,29)(30,47)(31,41)(33,36)(37,48)(38,45)(40,42)(44,46)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,18,12,32)(4,21,14,8)(6,24,16,38)(7,25,19,11)(10,31,23,17)(13,44,27,48)(15,46,29,37)(20,47,34,40)(22,30,36,42)(26,35,39,45)(28,33,41,43)",
+            perm"(1,3)(2,7)(4,25)(5,12)(6,13)(8,32)(9,19)(10,20)(11,14)(15,39)(16,27)(17,28)(18,21)(22,43)(23,34)(24,35)(26,29)(30,47)(31,41)(33,36)(37,48)(38,45)(40,42)(44,46)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,21)(5,9)(6,24)(7,11)(8,14)(10,17)(12,32)(13,44)(15,46)(16,38)(19,25)(20,40)(22,42)(23,31)(26,35)(27,48)(28,33)(29,37)(30,36)(34,47)(39,45)(41,43)",
+            perm"(1,3,5,12)(2,7,9,19)(4,25,14,11)(6,13,16,27)(8,32,21,18)(10,20,23,34)(15,39,29,26)(17,28,31,41)(22,43,36,33)(24,35,38,45)(30,47,42,40)(37,48,46,44)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,18,12,32)(4,21,14,8)(6,24,16,38)(7,25,19,11)(10,31,23,17)(13,44,27,48)(15,46,29,37)(20,47,34,40)(22,30,36,42)(26,35,39,45)(28,33,41,43)",
+            perm"(1,3,5,12)(2,7,9,19)(4,25,14,11)(6,13,16,27)(8,32,21,18)(10,20,23,34)(15,39,29,26)(17,28,31,41)(22,43,36,33)(24,35,38,45)(30,47,42,40)(37,48,46,44)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,8)(3,19,11,32)(5,9,14,21)(6,24,15,37)(7,25,18,12)(10,30,22,17)(13,45,26,48)(16,38,29,46)(20,47,33,41)(23,42,36,31)(27,35,39,44)(28,34,40,43)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6,7)", perm"(8,9,10,11)"]),
+        PermGroup([
+            perm"(1,2,6,10)(3,19,13,35)(4,8,16,23)(5,9,17,24)(7,28,20,12)(11,33,27,45)(14,21,30,37)(15,22,31,38)(18,41,34,26)(25,43,40,48)(29,36,42,46)(32,47,44,39)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,15)(6,17)(7,19)(8,22)(10,24)(11,26)(13,28)(14,29)(16,31)(18,33)(20,35)(21,36)(23,38)(25,39)(27,41)(30,42)(32,43)(34,45)(37,46)(40,47)(44,48)",
+            perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,19,13,35)(4,8,16,23)(5,9,17,24)(7,28,20,12)(11,33,27,45)(14,21,30,37)(15,22,31,38)(18,41,34,26)(25,43,40,48)(29,36,42,46)(32,47,44,39)",
+            perm"(1,3,5,12)(2,7,9,19)(4,11,15,26)(6,13,17,28)(8,18,22,33)(10,20,24,35)(14,25,29,39)(16,27,31,41)(21,32,36,43)(23,34,38,45)(30,40,42,47)(37,44,46,48)",
+            perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,15)(6,17)(7,19)(8,22)(10,24)(11,26)(13,28)(14,29)(16,31)(18,33)(20,35)(21,36)(23,38)(25,39)(27,41)(30,42)(32,43)(34,45)(37,46)(40,47)(44,48)",
+            perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9,10,11,12,13)"]),
+        PermGroup([
+            perm"(1,2,5,9,6,10,17,24)(3,20,12,35,13,7,28,19)(4,8,15,22,16,23,31,38)(11,34,26,45,27,18,41,33)(14,21,29,36,30,37,42,46)(25,44,39,48,40,32,47,43)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)",
+            perm"(1,5,6,17)(2,9,10,24)(3,12,13,28)(4,15,16,31)(7,19,20,35)(8,22,23,38)(11,26,27,41)(14,29,30,42)(18,33,34,45)(21,36,37,46)(25,39,40,47)(32,43,44,48)",
+            perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,19)(4,8)(5,24)(6,10)(7,12)(9,17)(11,33)(13,35)(14,21)(15,38)(16,23)(18,26)(20,28)(22,31)(25,43)(27,45)(29,46)(30,37)(32,39)(34,41)(36,42)(40,48)(44,47)",
+            perm"(1,3)(2,7)(4,11)(5,28)(6,13)(8,18)(9,35)(10,20)(12,17)(14,25)(15,41)(16,27)(19,24)(21,32)(22,45)(23,34)(26,31)(29,47)(30,40)(33,38)(36,48)(37,44)(39,42)(43,46)",
+            perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)",
+            perm"(1,5,6,17)(2,9,10,24)(3,12,13,28)(4,15,16,31)(7,19,20,35)(8,22,23,38)(11,26,27,41)(14,29,30,42)(18,33,34,45)(21,36,37,46)(25,39,40,47)(32,43,44,48)",
+            perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,19,13,35)(4,8,16,23)(5,24,17,9)(7,28,20,12)(11,33,27,45)(14,21,30,37)(15,38,31,22)(18,41,34,26)(25,43,40,48)(29,46,42,36)(32,47,44,39)",
+            perm"(1,3)(2,7)(4,11)(5,28)(6,13)(8,18)(9,35)(10,20)(12,17)(14,25)(15,41)(16,27)(19,24)(21,32)(22,45)(23,34)(26,31)(29,47)(30,40)(33,38)(36,48)(37,44)(39,42)(43,46)",
+            perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)",
+            perm"(1,5,6,17)(2,9,10,24)(3,12,13,28)(4,15,16,31)(7,19,20,35)(8,22,23,38)(11,26,27,41)(14,29,30,42)(18,33,34,45)(21,36,37,46)(25,39,40,47)(32,43,44,48)",
+            perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,19,13,35)(4,8,16,23)(5,24,17,9)(7,28,20,12)(11,33,27,45)(14,21,30,37)(15,38,31,22)(18,41,34,26)(25,43,40,48)(29,46,42,36)(32,47,44,39)",
+            perm"(1,3,6,13)(2,7,10,20)(4,11,16,27)(5,28,17,12)(8,18,23,34)(9,35,24,19)(14,25,30,40)(15,41,31,26)(21,32,37,44)(22,45,38,33)(29,47,42,39)(36,48,46,43)",
+            perm"(1,4,14)(2,8,21)(3,11,25)(5,15,29)(6,16,30)(7,18,32)(9,22,36)(10,23,37)(12,26,39)(13,27,40)(17,31,42)(19,33,43)(20,34,44)(24,38,46)(28,41,47)(35,45,48)",
+            perm"(1,5,6,17)(2,9,10,24)(3,12,13,28)(4,15,16,31)(7,19,20,35)(8,22,23,38)(11,26,27,41)(14,29,30,42)(18,33,34,45)(21,36,37,46)(25,39,40,47)(32,43,44,48)",
+            perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,18,14,34)(4,9,16,24)(5,8,17,23)(7,27,21,11)(12,33,29,45)(13,32,30,44)(15,38,31,22)(19,41,36,26)(20,40,37,25)(28,48,42,43)(35,39,46,47)",
+            perm"(1,3,11)(2,7,18)(4,30,47)(5,28,40)(6,14,27)(8,37,48)(9,35,44)(10,21,34)(12,41,31)(13,39,16)(15,29,26)(17,42,25)(19,45,38)(20,43,23)(22,36,33)(24,46,32)",
+            perm"(1,4,6,16)(2,8,10,23)(3,12,14,29)(5,31,17,15)(7,19,21,36)(9,38,24,22)(11,25,27,40)(13,42,30,28)(18,32,34,44)(20,46,37,35)(26,47,41,39)(33,48,45,43)",
+            perm"(1,5,6,17)(2,9,10,24)(3,13,14,30)(4,15,16,31)(7,20,21,37)(8,22,23,38)(11,26,27,41)(12,28,29,42)(18,33,34,45)(19,35,36,46)(25,39,40,47)(32,43,44,48)",
+            perm"(1,6)(2,10)(3,14)(4,16)(5,17)(7,21)(8,23)(9,24)(11,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,38)(25,40)(26,41)(28,42)(32,44)(33,45)(35,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,18)(4,9)(5,8)(6,10)(7,11)(12,33)(13,32)(14,34)(15,38)(16,24)(17,23)(19,26)(20,25)(21,27)(22,31)(28,48)(29,45)(30,44)(35,47)(36,41)(37,40)(39,46)(42,43)",
+            perm"(1,3,11)(2,7,18)(4,30,47)(5,28,40)(6,14,27)(8,37,48)(9,35,44)(10,21,34)(12,41,31)(13,39,16)(15,29,26)(17,42,25)(19,45,38)(20,43,23)(22,36,33)(24,46,32)",
+            perm"(1,4,6,16)(2,8,10,23)(3,12,14,29)(5,31,17,15)(7,19,21,36)(9,38,24,22)(11,25,27,40)(13,42,30,28)(18,32,34,44)(20,46,37,35)(26,47,41,39)(33,48,45,43)",
+            perm"(1,5,6,17)(2,9,10,24)(3,13,14,30)(4,15,16,31)(7,20,21,37)(8,22,23,38)(11,26,27,41)(12,28,29,42)(18,33,34,45)(19,35,36,46)(25,39,40,47)(32,43,44,48)",
+            perm"(1,6)(2,10)(3,14)(4,16)(5,17)(7,21)(8,23)(9,24)(11,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,38)(25,40)(26,41)(28,42)(32,44)(33,45)(35,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,3,7)(4,21,11,32)(5,10,12,20)(6,9,13,19)(8,25,18,14)(15,37,26,44)(16,36,27,43)(17,24,28,35)(22,40,33,30)(23,39,34,29)(31,46,41,48)(38,47,45,42)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4,14)(2,8,21)(3,11,25)(5,16,42)(6,31,29)(7,18,32)(9,23,46)(10,38,36)(12,27,47)(13,41,39)(15,30,17)(19,34,48)(20,45,43)(22,37,24)(26,40,28)(33,44,35)",
+            perm"(1,5)(2,9)(3,12)(4,15)(6,17)(7,19)(8,22)(10,24)(11,26)(13,28)(14,29)(16,31)(18,33)(20,35)(21,36)(23,38)(25,39)(27,41)(30,42)(32,43)(34,45)(37,46)(40,47)(44,48)",
+            perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,8)(3,7,12,19)(5,9,15,22)(6,10,16,23)(11,18,25,32)(13,20,28,35)(14,21,29,36)(17,24,31,38)(26,33,39,43)(27,34,40,44)(30,37,42,46)(41,45,47,48)",
+            perm"(1,3,11)(2,7,18)(4,12,25)(5,14,41)(6,30,26)(8,19,32)(9,21,45)(10,37,33)(13,27,17)(15,29,47)(16,42,39)(20,34,24)(22,36,48)(23,46,43)(28,40,31)(35,44,38)",
+            perm"(1,4)(2,8)(3,12)(5,15)(6,16)(7,19)(9,22)(10,23)(11,25)(13,28)(14,29)(17,31)(18,32)(20,35)(21,36)(24,38)(26,39)(27,40)(30,42)(33,43)(34,44)(37,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,13)(4,15)(6,17)(7,20)(8,22)(10,24)(11,26)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(23,38)(25,39)(27,41)(29,42)(32,43)(34,45)(36,46)(40,47)(44,48)",
+            perm"(1,6)(2,10)(3,14)(4,16)(5,17)(7,21)(8,23)(9,24)(11,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,38)(25,40)(26,41)(28,42)(32,44)(33,45)(35,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,8)(5,9)(6,10)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(17,24)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38)(39,43)(40,44)(41,45)(42,46)(47,48)",
+            perm"(1,3,11)(2,7,18)(4,13,39)(5,28,25)(6,14,27)(8,20,43)(9,35,32)(10,21,34)(12,26,15)(16,30,47)(17,42,40)(19,33,22)(23,37,48)(24,46,44)(29,41,31)(36,45,38)",
+            perm"(1,4,6,16)(2,8,10,23)(3,12,14,29)(5,31,17,15)(7,19,21,36)(9,38,24,22)(11,25,27,40)(13,42,30,28)(18,32,34,44)(20,46,37,35)(26,47,41,39)(33,48,45,43)",
+            perm"(1,5,6,17)(2,9,10,24)(3,13,14,30)(4,15,16,31)(7,20,21,37)(8,22,23,38)(11,26,27,41)(12,28,29,42)(18,33,34,45)(19,35,36,46)(25,39,40,47)(32,43,44,48)",
+            perm"(1,6)(2,10)(3,14)(4,16)(5,17)(7,21)(8,23)(9,24)(11,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,38)(25,40)(26,41)(28,42)(32,44)(33,45)(35,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,7,14,21)(4,8,16,23)(5,9,17,24)(11,18,27,34)(12,19,29,36)(13,20,30,37)(15,22,31,38)(25,32,40,44)(26,33,41,45)(28,35,42,46)(39,43,47,48)",
+            perm"(1,3,11)(2,7,18)(4,13,39)(5,28,25)(6,14,27)(8,20,43)(9,35,32)(10,21,34)(12,26,15)(16,30,47)(17,42,40)(19,33,22)(23,37,48)(24,46,44)(29,41,31)(36,45,38)",
+            perm"(1,4,6,16)(2,8,10,23)(3,12,14,29)(5,31,17,15)(7,19,21,36)(9,38,24,22)(11,25,27,40)(13,42,30,28)(18,32,34,44)(20,46,37,35)(26,47,41,39)(33,48,45,43)",
+            perm"(1,5,6,17)(2,9,10,24)(3,13,14,30)(4,15,16,31)(7,20,21,37)(8,22,23,38)(11,26,27,41)(12,28,29,42)(18,33,34,45)(19,35,36,46)(25,39,40,47)(32,43,44,48)",
+            perm"(1,6)(2,10)(3,14)(4,16)(5,17)(7,21)(8,23)(9,24)(11,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,38)(25,40)(26,41)(28,42)(32,44)(33,45)(35,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,7,12,19)(4,21,14,8)(6,24,16,38)(10,31,23,17)(11,32,25,18)(13,35,27,45)(15,46,29,37)(20,41,34,28)(22,30,36,42)(26,48,39,44)(33,40,43,47)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,8)(5,9)(6,24)(10,17)(11,18)(12,19)(13,35)(14,21)(15,37)(16,38)(20,28)(22,30)(23,31)(25,32)(26,44)(27,45)(29,46)(33,40)(34,41)(36,42)(39,48)(43,47)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,21)(5,9)(6,24)(8,14)(10,17)(11,32)(12,19)(13,35)(15,46)(16,38)(18,25)(20,28)(22,42)(23,31)(26,48)(27,45)(29,37)(30,36)(33,47)(34,41)(39,44)(40,43)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,21)(5,9)(6,24)(8,14)(10,17)(11,32)(12,19)(13,35)(15,46)(16,38)(18,25)(20,28)(22,42)(23,31)(26,48)(27,45)(29,37)(30,36)(33,47)(34,41)(39,44)(40,43)",
+            perm"(1,3,5,12)(2,7,9,19)(4,11,14,25)(6,13,16,27)(8,18,21,32)(10,20,23,34)(15,26,29,39)(17,28,31,41)(22,33,36,43)(24,35,38,45)(30,40,42,47)(37,44,46,48)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,8)(5,9)(6,24)(10,17)(11,18)(12,19)(13,35)(14,21)(15,37)(16,38)(20,28)(22,30)(23,31)(25,32)(26,44)(27,45)(29,46)(33,40)(34,41)(36,42)(39,48)(43,47)",
+            perm"(1,3)(2,7)(4,25)(5,12)(6,13)(8,32)(9,19)(10,20)(11,14)(15,39)(16,27)(17,28)(18,21)(22,43)(23,34)(24,35)(26,29)(30,47)(31,41)(33,36)(37,48)(38,45)(40,42)(44,46)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,21)(5,9)(6,24)(8,14)(10,17)(11,32)(12,19)(13,35)(15,46)(16,38)(18,25)(20,28)(22,42)(23,31)(26,48)(27,45)(29,37)(30,36)(33,47)(34,41)(39,44)(40,43)",
+            perm"(1,3,5,12)(2,7,9,19)(4,25,14,11)(6,13,16,27)(8,32,21,18)(10,20,23,34)(15,39,29,26)(17,28,31,41)(22,43,36,33)(24,35,38,45)(30,47,42,40)(37,48,46,44)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,8)(5,9)(6,24)(10,17)(11,18)(12,19)(13,35)(14,21)(15,37)(16,38)(20,28)(22,30)(23,31)(25,32)(26,44)(27,45)(29,46)(33,40)(34,41)(36,42)(39,48)(43,47)",
+            perm"(1,3,5,12)(2,7,9,19)(4,25,14,11)(6,13,16,27)(8,32,21,18)(10,20,23,34)(15,39,29,26)(17,28,31,41)(22,43,36,33)(24,35,38,45)(30,47,42,40)(37,48,46,44)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,21)(5,9)(6,24)(8,14)(10,17)(11,32)(12,19)(13,35)(15,46)(16,38)(18,25)(20,28)(22,42)(23,31)(26,48)(27,45)(29,37)(30,36)(33,47)(34,41)(39,44)(40,43)",
+            perm"(1,3,5,12)(2,7,9,19)(4,25,14,11)(6,13,16,27)(8,32,21,18)(10,20,23,34)(15,39,29,26)(17,28,31,41)(22,43,36,33)(24,35,38,45)(30,47,42,40)(37,48,46,44)",
+            perm"(1,4,5,14)(2,8,9,21)(3,11,12,25)(6,15,16,29)(7,18,19,32)(10,22,23,36)(13,26,27,39)(17,30,31,42)(20,33,34,43)(24,37,38,46)(28,40,41,47)(35,44,45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,9)(3,7,12,19)(4,8,14,21)(6,24,16,38)(10,31,23,17)(11,18,25,32)(13,35,27,45)(15,37,29,46)(20,41,34,28)(22,42,36,30)(26,44,39,48)(33,47,43,40)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,21)(5,9)(6,24)(8,14)(10,17)(11,32)(12,19)(13,35)(15,46)(16,38)(18,25)(20,28)(22,42)(23,31)(26,48)(27,45)(29,37)(30,36)(33,47)(34,41)(39,44)(40,43)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4)", perm"(5,6,7)", perm"(8,9,10,11)"]),
+        PermGroup([
+            perm"(1,2)(3,20)(4,8)(5,9)(6,10)(7,13)(11,33)(12,35)(14,21)(15,22)(16,23)(17,24)(18,26)(19,28)(25,44)(27,45)(29,36)(30,37)(31,38)(32,40)(34,41)(39,48)(42,46)(43,47)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5,16)(2,9,23)(3,12,27)(4,14,29)(6,17,31)(7,19,34)(8,21,36)(10,24,38)(11,25,39)(13,28,41)(15,30,42)(18,32,43)(20,35,45)(22,37,46)(26,40,47)(33,44,48)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,17)(7,20)(8,22)(9,24)(11,26)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(23,38)(25,40)(27,41)(29,42)(32,44)(34,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,10)(3,20,13,7)(4,8,15,22)(5,9,17,24)(11,33,26,18)(12,35,28,19)(14,21,30,37)(16,23,31,38)(25,44,40,32)(27,45,41,34)(29,36,42,46)(39,48,47,43)",
+            perm"(1,3,6,13)(2,7,10,20)(4,11,15,26)(5,12,17,28)(8,18,22,33)(9,19,24,35)(14,25,30,40)(16,27,31,41)(21,32,37,44)(23,34,38,45)(29,39,42,47)(36,43,46,48)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5,16)(2,9,23)(3,12,27)(4,14,29)(6,17,31)(7,19,34)(8,21,36)(10,24,38)(11,25,39)(13,28,41)(15,30,42)(18,32,43)(20,35,45)(22,37,46)(26,40,47)(33,44,48)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,17)(7,20)(8,22)(9,24)(11,26)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(23,38)(25,40)(27,41)(29,42)(32,44)(34,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,20)(4,8)(5,9)(6,10)(7,13)(11,33)(12,35)(14,21)(15,22)(16,23)(17,24)(18,26)(19,28)(25,44)(27,45)(29,36)(30,37)(31,38)(32,40)(34,41)(39,48)(42,46)(43,47)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4,6,15)(2,8,10,22)(3,11,13,26)(5,14,17,30)(7,18,20,33)(9,21,24,37)(12,25,28,40)(16,29,31,42)(19,32,35,44)(23,36,38,46)(27,39,41,47)(34,43,45,48)",
+            perm"(1,5,16)(2,9,23)(3,12,27)(4,14,29)(6,17,31)(7,19,34)(8,21,36)(10,24,38)(11,25,39)(13,28,41)(15,30,42)(18,32,43)(20,35,45)(22,37,46)(26,40,47)(33,44,48)",
+            perm"(1,6)(2,10)(3,13)(4,15)(5,17)(7,20)(8,22)(9,24)(11,26)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(23,38)(25,40)(27,41)(29,42)(32,44)(34,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,21)(5,10)(6,9)(8,14)(11,32)(12,20)(13,19)(15,37)(16,36)(17,24)(18,25)(22,30)(23,29)(26,44)(27,43)(28,35)(31,46)(33,40)(34,39)(38,42)(41,48)(45,47)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4,14)(2,8,21)(3,11,25)(5,16,42)(6,31,29)(7,18,32)(9,23,46)(10,38,36)(12,27,47)(13,41,39)(15,30,17)(19,34,48)(20,45,43)(22,37,24)(26,40,28)(33,44,35)",
+            perm"(1,5)(2,9)(3,12)(4,15)(6,17)(7,19)(8,22)(10,24)(11,26)(13,28)(14,29)(16,31)(18,33)(20,35)(21,36)(23,38)(25,39)(27,41)(30,42)(32,43)(34,45)(37,46)(40,47)(44,48)",
+            perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,8)(5,9)(6,10)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(17,24)(25,32)(26,33)(27,34)(28,35)(29,36)(30,37)(31,38)(39,43)(40,44)(41,45)(42,46)(47,48)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4,14)(2,8,21)(3,11,25)(5,16,42)(6,31,29)(7,18,32)(9,23,46)(10,38,36)(12,27,47)(13,41,39)(15,30,17)(19,34,48)(20,45,43)(22,37,24)(26,40,28)(33,44,35)",
+            perm"(1,5)(2,9)(3,12)(4,15)(6,17)(7,19)(8,22)(10,24)(11,26)(13,28)(14,29)(16,31)(18,33)(20,35)(21,36)(23,38)(25,39)(27,41)(30,42)(32,43)(34,45)(37,46)(40,47)(44,48)",
+            perm"(1,6)(2,10)(3,13)(4,16)(5,17)(7,20)(8,23)(9,24)(11,27)(12,28)(14,30)(15,31)(18,34)(19,35)(21,37)(22,38)(25,40)(26,41)(29,42)(32,44)(33,45)(36,46)(39,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2,7)(3,9,32)(4,22,18)(5,11,37)(6,27,20)(8,19,12)(10,21,17)(13,26,48)(14,41,43)(15,39,45)(16,47,33)(23,36,42)(24,46,28)(25,44,30)(29,40,35)(31,38,34)",
+            perm"(1,3)(2,8)(4,12)(5,13)(6,14)(7,18)(9,22)(10,23)(11,24)(15,28)(16,29)(17,30)(19,32)(20,33)(21,34)(25,38)(26,39)(27,40)(31,42)(35,43)(36,44)(37,45)(41,47)(46,48)",
+            perm"(1,4)(2,9)(3,12)(5,15)(6,16)(7,19)(8,22)(10,25)(11,26)(13,28)(14,29)(17,31)(18,32)(20,35)(21,36)(23,38)(24,39)(27,41)(30,42)(33,43)(34,44)(37,46)(40,47)(45,48)",
+            perm"(1,5)(2,10)(3,13)(4,15)(6,17)(7,20)(8,23)(9,25)(11,27)(12,28)(14,30)(16,31)(18,33)(19,35)(21,37)(22,38)(24,40)(26,41)(29,42)(32,43)(34,45)(36,46)(39,47)(44,48)",
+            perm"(1,6)(2,11)(3,14)(4,16)(5,17)(7,21)(8,24)(9,26)(10,27)(12,29)(13,30)(15,31)(18,34)(19,36)(20,37)(22,39)(23,40)(25,41)(28,42)(32,44)(33,45)(35,46)(38,47)(43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,7)(4,8)(5,9)(6,24)(10,17)(11,18)(12,19)(13,35)(14,21)(15,37)(16,38)(20,28)(22,30)(23,31)(25,32)(26,44)(27,45)(29,46)(33,40)(34,41)(36,42)(39,48)(43,47)",
+            perm"(1,3)(2,7)(4,11)(5,12)(6,13)(8,18)(9,19)(10,20)(14,25)(15,26)(16,27)(17,28)(21,32)(22,33)(23,34)(24,35)(29,39)(30,40)(31,41)(36,43)(37,44)(38,45)(42,47)(46,48)",
+            perm"(1,4)(2,8)(3,11)(5,14)(6,15)(7,18)(9,21)(10,22)(12,25)(13,26)(16,29)(17,30)(19,32)(20,33)(23,36)(24,37)(27,39)(28,40)(31,42)(34,43)(35,44)(38,46)(41,47)(45,48)",
+            perm"(1,5)(2,9)(3,12)(4,14)(6,16)(7,19)(8,21)(10,23)(11,25)(13,27)(15,29)(17,31)(18,32)(20,34)(22,36)(24,38)(26,39)(28,41)(30,42)(33,43)(35,45)(37,46)(40,47)(44,48)",
+            perm"(1,6,17)(2,10,24)(3,13,28)(4,15,30)(5,16,31)(7,20,35)(8,22,37)(9,23,38)(11,26,40)(12,27,41)(14,29,42)(18,33,44)(19,34,45)(21,36,46)(25,39,47)(32,43,48)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4)",
+            perm"(5,6)",
+            perm"(7,8)",
+            perm"(9,10,11)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49)",
+        ]),
+        PermGroup([perm"(1,2,3,4,5,6,7)", perm"(8,9,10,11,12,13,14)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2)(3,50)(4,30)(5,49)(6,25)(7,48)(8,47)(9,20)(10,46)(11,45)(12,16)(13,44)(14,43)(15,42)(17,41)(18,40)(19,39)(21,38)(22,37)(23,36)(24,35)(26,34)(27,33)(28,32)(29,31)",
+            perm"(1,3,7,13,21,4,8,14,22,31,9,15,23,32,39,16,24,33,40,45,25,34,41,46,49)(2,5,10,17,26,6,11,18,27,35,12,19,28,36,42,20,29,37,43,47,30,38,44,48,50)",
+            perm"(1,4,9,16,25)(2,6,12,20,30)(3,8,15,24,34)(5,11,19,29,38)(7,14,23,33,41)(10,18,28,37,44)(13,22,32,40,46)(17,27,36,43,48)(21,31,39,45,49)(26,35,42,47,50)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,5)(4,30)(6,25)(7,10)(8,38)(9,20)(11,34)(12,16)(13,17)(14,44)(15,29)(18,41)(19,24)(21,26)(22,48)(23,37)(27,46)(28,33)(31,50)(32,43)(35,49)(36,40)(39,47)(42,45)",
+            perm"(1,3,7,13,21)(2,5,10,17,26)(4,8,14,22,31)(6,11,18,27,35)(9,15,23,32,39)(12,19,28,36,42)(16,24,33,40,45)(20,29,37,43,47)(25,34,41,46,49)(30,38,44,48,50)",
+            perm"(1,4,9,16,25)(2,6,12,20,30)(3,8,15,24,34)(5,11,19,29,38)(7,14,23,33,41)(10,18,28,37,44)(13,22,32,40,46)(17,27,36,43,48)(21,31,39,45,49)(26,35,42,47,50)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,26)(4,30)(5,21)(6,25)(7,17)(8,50)(9,20)(10,13)(11,49)(12,16)(14,48)(15,47)(18,46)(19,45)(22,44)(23,43)(24,42)(27,41)(28,40)(29,39)(31,38)(32,37)(33,36)(34,35)",
+            perm"(1,3,7,13,21)(2,5,10,17,26)(4,8,14,22,31)(6,11,18,27,35)(9,15,23,32,39)(12,19,28,36,42)(16,24,33,40,45)(20,29,37,43,47)(25,34,41,46,49)(30,38,44,48,50)",
+            perm"(1,4,9,16,25)(2,6,12,20,30)(3,8,15,24,34)(5,11,19,29,38)(7,14,23,33,41)(10,18,28,37,44)(13,22,32,40,46)(17,27,36,43,48)(21,31,39,45,49)(26,35,42,47,50)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5,6,7)", perm"(8,9,10,11,12)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3)",
+            perm"(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,5)(4,50,7,52)(6,51,9,48)(8,46,11,49)(10,47,13,44)(12,42,15,45)(14,43,17,40)(16,38,19,41)(18,39,21,36)(20,34,23,37)(22,35,25,32)(24,30,27,33)(26,31,29,28)",
+            perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,37)(36,39)(38,41)(40,43)(42,45)(44,47)(46,49)(48,51)(50,52)",
+            perm"(1,4,8,12,16,20,24,28,32,36,40,44,48)(2,6,10,14,18,22,26,30,34,38,42,46,50)(3,7,11,15,19,23,27,31,35,39,43,47,51)(5,9,13,17,21,25,29,33,37,41,45,49,52)",
+        ]),
+        PermGroup([perm"(1,2,3,4)", perm"(5,6,7,8,9,10,11,12,13,14,15,16,17)"]),
+        PermGroup([
+            perm"(1,2,3,5)(4,34,51,25)(6,35,52,20)(7,37,48,22)(8,14,47,45)(9,32,50,23)(10,15,49,40)(11,17,44,42)(12,46,43,13)(16,26,39,33)(18,27,41,28)(19,29,36,30)(21,24,38,31)",
+            perm"(1,3)(2,5)(4,51)(6,52)(7,48)(8,47)(9,50)(10,49)(11,44)(12,43)(13,46)(14,45)(15,40)(16,39)(17,42)(18,41)(19,36)(20,35)(21,38)(22,37)(23,32)(24,31)(25,34)(26,33)(27,28)(29,30)",
+            perm"(1,4,8,12,16,20,24,28,32,36,40,44,48)(2,6,10,14,18,22,26,30,34,38,42,46,50)(3,7,11,15,19,23,27,31,35,39,43,47,51)(5,9,13,17,21,25,29,33,37,41,45,49,52)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,5)(4,50)(6,48)(7,52)(8,46)(9,51)(10,44)(11,49)(12,42)(13,47)(14,40)(15,45)(16,38)(17,43)(18,36)(19,41)(20,34)(21,39)(22,32)(23,37)(24,30)(25,35)(26,28)(27,33)(29,31)",
+            perm"(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,37)(36,39)(38,41)(40,43)(42,45)(44,47)(46,49)(48,51)(50,52)",
+            perm"(1,4,8,12,16,20,24,28,32,36,40,44,48)(2,6,10,14,18,22,26,30,34,38,42,46,50)(3,7,11,15,19,23,27,31,35,39,43,47,51)(5,9,13,17,21,25,29,33,37,41,45,49,52)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4)",
+            perm"(5,6,7,8,9,10,11,12,13,14,15,16,17)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2)(3,28)(4,33)(5,20)(6,21)(7,26)(8,14)(9,16)(10,15)(11,51)(12,19)(13,18)(17,48)(22,45)(23,50)(24,43)(25,42)(27,46)(29,39)(30,47)(31,37)(32,36)(34,40)(35,44)(38,41)(49,54)(52,53)",
+            perm"(1,3,9,26,38,47,13,24,36,5,11,22,40,49,53,27,39,48,14,25,37,12,23,35,4,10,21)(2,6,15,33,44,50,19,31,42,8,17,29,46,52,54,34,45,51,20,32,43,18,30,41,7,16,28)",
+            perm"(1,4,12,14,27,40,5,13,26)(2,7,18,20,34,46,8,19,33)(3,10,23,25,39,49,11,24,38)(6,16,30,32,45,52,17,31,44)(9,21,35,37,48,53,22,36,47)(15,28,41,43,51,54,29,42,50)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,33)(5,20)(7,26)(8,14)(9,15)(10,44)(11,32)(12,19)(13,18)(16,38)(17,25)(21,50)(22,43)(23,31)(24,30)(27,46)(28,47)(29,37)(34,40)(35,42)(36,41)(39,52)(45,49)(48,54)(51,53)",
+            perm"(1,3,9)(2,6,15)(4,10,21)(5,11,22)(7,16,28)(8,17,29)(12,23,35)(13,24,36)(14,25,37)(18,30,41)(19,31,42)(20,32,43)(26,38,47)(27,39,48)(33,44,50)(34,45,51)(40,49,53)(46,52,54)",
+            perm"(1,4,12,14,27,40,5,13,26)(2,7,18,20,34,46,8,19,33)(3,10,23,25,39,49,11,24,38)(6,16,30,32,45,52,17,31,44)(9,21,35,37,48,53,22,36,47)(15,28,41,43,51,54,29,42,50)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,20)(8,14)(9,15)(10,16)(11,32)(12,18)(13,34)(17,25)(19,27)(21,28)(22,43)(23,30)(24,45)(26,46)(29,37)(31,39)(33,40)(35,41)(36,51)(38,52)(42,48)(44,49)(47,54)(50,53)",
+            perm"(1,3,9,4,10,21,12,23,35)(2,6,15,7,16,28,18,30,41)(5,11,22,13,24,36,26,38,47)(8,17,29,19,31,42,33,44,50)(14,25,37,27,39,48,40,49,53)(20,32,43,34,45,51,46,52,54)",
+            perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,18)(5,20)(7,12)(8,14)(9,15)(10,30)(11,32)(13,46)(16,23)(17,25)(19,40)(21,41)(22,43)(24,52)(26,34)(27,33)(28,35)(29,37)(31,49)(36,54)(38,45)(39,44)(42,53)(47,51)(48,50)",
+            perm"(1,3,9)(2,6,15)(4,24,48)(5,11,22)(7,31,51)(8,17,29)(10,36,27)(12,49,47)(13,39,21)(14,25,37)(16,42,34)(18,52,50)(19,45,28)(20,32,43)(23,53,26)(30,54,33)(35,40,38)(41,46,44)",
+            perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,33)(5,20)(7,26)(8,14)(9,15)(10,44)(11,32)(12,19)(13,18)(16,38)(17,25)(21,50)(22,43)(23,31)(24,30)(27,46)(28,47)(29,37)(34,40)(35,42)(36,41)(39,52)(45,49)(48,54)(51,53)",
+            perm"(1,3,9)(2,6,15)(4,24,48)(5,11,22)(7,31,51)(8,17,29)(10,36,27)(12,49,47)(13,39,21)(14,25,37)(16,42,34)(18,52,50)(19,45,28)(20,32,43)(23,53,26)(30,54,33)(35,40,38)(41,46,44)",
+            perm"(1,4,12,14,27,40,5,13,26)(2,7,18,20,34,46,8,19,33)(3,10,23,25,39,49,11,24,38)(6,16,30,32,45,52,17,31,44)(9,21,35,37,48,53,22,36,47)(15,28,41,43,51,54,29,42,50)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,29)(4,18)(5,20)(6,22)(7,12)(8,14)(9,17)(10,50)(11,15)(13,46)(16,47)(19,40)(21,44)(23,42)(24,41)(25,43)(26,34)(27,33)(28,38)(30,36)(31,35)(32,37)(39,54)(45,53)(48,52)(49,51)",
+            perm"(1,3,9,14,25,37,5,11,22)(2,6,15,20,32,43,8,17,29)(4,10,21,27,39,48,13,24,36)(7,16,28,34,45,51,19,31,42)(12,23,35,40,49,53,26,38,47)(18,30,41,46,52,54,33,44,50)",
+            perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,15)(4,18)(5,8)(6,9)(7,12)(10,41)(11,29)(13,33)(14,20)(16,35)(17,22)(19,26)(21,30)(23,28)(24,50)(25,43)(27,46)(31,47)(32,37)(34,40)(36,44)(38,42)(39,54)(45,53)(48,52)(49,51)",
+            perm"(1,3,9)(2,6,15)(4,24,48)(5,11,22)(7,31,51)(8,17,29)(10,36,27)(12,49,47)(13,39,21)(14,25,37)(16,42,34)(18,52,50)(19,45,28)(20,32,43)(23,53,26)(30,54,33)(35,40,38)(41,46,44)",
+            perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8,9,10,11,12,13,14)"]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,8)(9,15)(10,16)(11,17)(12,18)(13,19)(14,20)(21,28)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(35,41)(36,42)(37,43)(38,44)(39,45)(40,46)(47,50)(48,51)(49,52)(53,54)",
+            perm"(1,3,9)(2,6,15)(4,24,48)(5,11,22)(7,31,51)(8,17,29)(10,36,27)(12,49,47)(13,39,21)(14,25,37)(16,42,34)(18,52,50)(19,45,28)(20,32,43)(23,53,26)(30,54,33)(35,40,38)(41,46,44)",
+            perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,8)(9,15)(10,16)(11,17)(12,18)(13,19)(14,20)(21,28)(22,29)(23,30)(24,31)(25,32)(26,33)(27,34)(35,41)(36,42)(37,43)(38,44)(39,45)(40,46)(47,50)(48,51)(49,52)(53,54)",
+            perm"(1,3,9,5,11,22,14,25,37)(2,6,15,8,17,29,20,32,43)(4,24,48,13,39,21,27,10,36)(7,31,51,19,45,28,34,16,42)(12,49,47,26,23,53,40,38,35)(18,52,50,33,30,54,46,44,41)",
+            perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,20)(8,14)(9,15)(10,16)(11,32)(12,18)(13,34)(17,25)(19,27)(21,28)(22,43)(23,30)(24,45)(26,46)(29,37)(31,39)(33,40)(35,41)(36,51)(38,52)(42,48)(44,49)(47,54)(50,53)",
+            perm"(1,3,9)(2,6,15)(4,10,21)(5,11,22)(7,16,28)(8,17,29)(12,23,35)(13,24,36)(14,25,37)(18,30,41)(19,31,42)(20,32,43)(26,38,47)(27,39,48)(33,44,50)(34,45,51)(40,49,53)(46,52,54)",
+            perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,18)(5,20)(7,12)(8,14)(9,15)(10,30)(11,32)(13,46)(16,23)(17,25)(19,40)(21,41)(22,43)(24,52)(26,34)(27,33)(28,35)(29,37)(31,49)(36,54)(38,45)(39,44)(42,53)(47,51)(48,50)",
+            perm"(1,3,9)(2,6,15)(4,10,21)(5,11,22)(7,16,28)(8,17,29)(12,23,35)(13,24,36)(14,25,37)(18,30,41)(19,31,42)(20,32,43)(26,38,47)(27,39,48)(33,44,50)(34,45,51)(40,49,53)(46,52,54)",
+            perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,15)(4,18)(5,20)(6,9)(7,12)(8,14)(10,41)(11,43)(13,46)(16,35)(17,37)(19,40)(21,30)(22,32)(23,28)(24,54)(25,29)(26,34)(27,33)(31,53)(36,52)(38,51)(39,50)(42,49)(44,48)(45,47)",
+            perm"(1,3,9)(2,6,15)(4,10,21)(5,11,22)(7,16,28)(8,17,29)(12,23,35)(13,24,36)(14,25,37)(18,30,41)(19,31,42)(20,32,43)(26,38,47)(27,39,48)(33,44,50)(34,45,51)(40,49,53)(46,52,54)",
+            perm"(1,4,12)(2,7,18)(3,10,23)(5,13,26)(6,16,30)(8,19,33)(9,21,35)(11,24,38)(14,27,40)(15,28,41)(17,31,44)(20,34,46)(22,36,47)(25,39,49)(29,42,50)(32,45,52)(37,48,53)(43,51,54)",
+            perm"(1,5,14)(2,8,20)(3,11,25)(4,13,27)(6,17,32)(7,19,34)(9,22,37)(10,24,39)(12,26,40)(15,29,43)(16,31,45)(18,33,46)(21,36,48)(23,38,49)(28,42,51)(30,44,52)(35,47,53)(41,50,54)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5)", perm"(6,7,8)", perm"(9,10,11)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,4,7,11)(3,19,28,51,26)(5,23,32,53,10)(6,39,52,42,41)(8,27,36,40,14)(9,43,54,46,25)(12,31,20,44,18)(13,47,55,30,29)(15,24,48,22,16)(17,50,45,34,33)(21,35,49,38,37)",
+            perm"(1,3,6,10,15,20,25,30,35,40,45)(2,5,9,14,19,24,29,34,39,44,49)(4,8,13,18,23,28,33,38,43,48,52)(7,12,17,22,27,32,37,42,47,51,54)(11,16,21,26,31,36,41,46,50,53,55)",
+        ]),
+        PermGroup([perm"(1,2,3,4,5)", perm"(6,7,8,9,10,11,12,13,14,15,16)"]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,6,4,7,9,13)(5,48,10,53,11,54,17,56)(8,50,14,51,15,55,21,44)(12,40,18,46,19,47,25,52)(16,42,22,43,23,49,29,36)(20,32,26,38,27,39,33,45)(24,34,30,35,31,41,37,28)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,37)(28,34,35,41)(32,38,39,45)(36,42,43,49)(40,46,47,52)(44,50,51,55)(48,53,54,56)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)",
+            perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)",
+        ]),
+        PermGroup([perm"(1,2,3,4,5,6,7)", perm"(8,9,10,11,12,13,14,15)"]),
+        PermGroup([
+            perm"(1,2,4,7)(3,13,9,6)(5,48,11,54)(8,51,15,44)(10,56,17,53)(12,40,19,47)(14,50,21,55)(16,43,23,36)(18,52,25,46)(20,32,27,39)(22,42,29,49)(24,35,31,28)(26,45,33,38)(30,34,37,41)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,37)(28,34,35,41)(32,38,39,45)(36,42,43,49)(40,46,47,52)(44,50,51,55)(48,53,54,56)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)",
+            perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,48)(8,44)(9,13)(10,53)(11,54)(12,40)(14,50)(15,51)(16,36)(17,56)(18,46)(19,47)(20,32)(21,55)(22,42)(23,43)(24,28)(25,52)(26,38)(27,39)(29,49)(30,34)(31,35)(33,45)(37,41)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,37)(28,34,35,41)(32,38,39,45)(36,42,43,49)(40,46,47,52)(44,50,51,55)(48,53,54,56)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)",
+            perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,13)(4,7)(5,48)(6,9)(8,44)(10,56)(11,54)(12,40)(14,55)(15,51)(16,36)(17,53)(18,52)(19,47)(20,32)(21,50)(22,49)(23,43)(24,28)(25,46)(26,45)(27,39)(29,42)(30,41)(31,35)(33,38)(34,37)",
+            perm"(1,3,4,9)(2,6,7,13)(5,10,11,17)(8,14,15,21)(12,18,19,25)(16,22,23,29)(20,26,27,33)(24,30,31,37)(28,34,35,41)(32,38,39,45)(36,42,43,49)(40,46,47,52)(44,50,51,55)(48,53,54,56)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)",
+            perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,7)(3,6,9,13)(5,48,11,54)(8,51,15,44)(10,53,17,56)(12,40,19,47)(14,55,21,50)(16,43,23,36)(18,46,25,52)(20,32,27,39)(22,49,29,42)(24,35,31,28)(26,38,33,45)(30,41,37,34)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,37)(32,38)(35,41)(36,42)(39,45)(40,46)(43,49)(44,50)(47,52)(48,53)(51,55)(54,56)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)",
+            perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,13)(4,7)(5,48)(6,9)(8,44)(10,56)(11,54)(12,40)(14,55)(15,51)(16,36)(17,53)(18,52)(19,47)(20,32)(21,50)(22,49)(23,43)(24,28)(25,46)(26,45)(27,39)(29,42)(30,41)(31,35)(33,38)(34,37)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,37)(32,38)(35,41)(36,42)(39,45)(40,46)(43,49)(44,50)(47,52)(48,53)(51,55)(54,56)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)",
+            perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)",
+        ]),
+        PermGroup([perm"(1,2)", perm"(3,4,5,6)", perm"(7,8,9,10,11,12,13)"]),
+        PermGroup([
+            perm"(1,2)(3,14)(4,7)(5,8)(6,10)(9,22)(11,15)(12,16)(13,18)(17,30)(19,23)(20,24)(21,26)(25,38)(27,31)(28,32)(29,34)(33,46)(35,39)(36,40)(37,42)(41,53)(43,47)(44,48)(45,50)(49,56)(51,54)(52,55)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,37)(32,38)(35,41)(36,42)(39,45)(40,46)(43,49)(44,50)(47,52)(48,53)(51,55)(54,56)",
+            perm"(1,4,11,19,27,35,43)(2,7,15,23,31,39,47)(3,9,17,25,33,41,49)(5,12,20,28,36,44,51)(6,13,21,29,37,45,52)(8,16,24,32,40,48,54)(10,18,26,34,42,50,55)(14,22,30,38,46,53,56)",
+            perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,20)(13,22)(15,24)(17,26)(19,28)(21,30)(23,32)(25,34)(27,36)(29,38)(31,40)(33,42)(35,44)(37,46)(39,48)(41,50)(43,51)(45,53)(47,54)(49,55)(52,56)",
+        ]),
+        PermGroup([
+            perm"(1,2,5,8)(3,14,10,6)(4,7,12,16)(9,22,18,13)(11,15,20,24)(17,30,26,21)(19,23,28,32)(25,38,34,29)(27,31,36,40)(33,46,42,37)(35,39,44,48)(41,53,50,45)(43,47,51,54)(49,56,55,52)",
+            perm"(1,3,5,10)(2,6,8,14)(4,9,12,18)(7,13,16,22)(11,17,20,26)(15,21,24,30)(19,25,28,34)(23,29,32,38)(27,33,36,42)(31,37,40,46)(35,41,44,50)(39,45,48,53)(43,49,51,55)(47,52,54,56)",
+            perm"(1,4,11,19,27,35,43)(2,7,15,23,31,39,47)(3,9,17,25,33,41,49)(5,12,20,28,36,44,51)(6,13,21,29,37,45,52)(8,16,24,32,40,48,54)(10,18,26,34,42,50,55)(14,22,30,38,46,53,56)",
+            perm"(1,5)(2,8)(3,10)(4,12)(6,14)(7,16)(9,18)(11,20)(13,22)(15,24)(17,26)(19,28)(21,30)(23,32)(25,34)(27,36)(29,38)(31,40)(33,42)(35,44)(37,46)(39,48)(41,50)(43,51)(45,53)(47,54)(49,55)(52,56)",
+        ]),
+        PermGroup([
+            perm"(1,2,6,13,21,29,37)(3,8,16,34,51,48,54)(4,9,26,44,41,50,45)(5,18,36,33,43,38,46)(7,15,24,42,55,52,12)(10,19,14,23,32,49,56)(11,28,25,35,30,39,47)(17,27,22,31,40,53,20)",
+            perm"(1,3)(2,7)(4,10)(5,11)(6,14)(8,17)(9,18)(12,20)(13,22)(15,25)(16,26)(19,28)(21,30)(23,33)(24,34)(27,36)(29,38)(31,41)(32,42)(35,44)(37,45)(39,48)(40,49)(43,51)(46,52)(47,53)(50,55)(54,56)",
+            perm"(1,4)(2,8)(3,10)(5,12)(6,15)(7,17)(9,19)(11,20)(13,23)(14,25)(16,27)(18,28)(21,31)(22,33)(24,35)(26,36)(29,39)(30,41)(32,43)(34,44)(37,46)(38,48)(40,50)(42,51)(45,52)(47,54)(49,55)(53,56)",
+            perm"(1,5)(2,9)(3,11)(4,12)(6,16)(7,18)(8,19)(10,20)(13,24)(14,26)(15,27)(17,28)(21,32)(22,34)(23,35)(25,36)(29,40)(30,42)(31,43)(33,44)(37,47)(38,49)(39,50)(41,51)(45,53)(46,54)(48,55)(52,56)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,48)(8,44)(9,13)(10,53)(11,54)(12,40)(14,50)(15,51)(16,36)(17,56)(18,46)(19,47)(20,32)(21,55)(22,42)(23,43)(24,28)(25,52)(26,38)(27,39)(29,49)(30,34)(31,35)(33,45)(37,41)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,13)(8,14)(11,17)(12,18)(15,21)(16,22)(19,25)(20,26)(23,29)(24,30)(27,33)(28,34)(31,37)(32,38)(35,41)(36,42)(39,45)(40,46)(43,49)(44,50)(47,52)(48,53)(51,55)(54,56)",
+            perm"(1,4)(2,7)(3,9)(5,11)(6,13)(8,15)(10,17)(12,19)(14,21)(16,23)(18,25)(20,27)(22,29)(24,31)(26,33)(28,35)(30,37)(32,39)(34,41)(36,43)(38,45)(40,47)(42,49)(44,51)(46,52)(48,54)(50,55)(53,56)",
+            perm"(1,5,12,20,28,36,44)(2,8,16,24,32,40,48)(3,10,18,26,34,42,50)(4,11,19,27,35,43,51)(6,14,22,30,38,46,53)(7,15,23,31,39,47,54)(9,17,25,33,41,49,55)(13,21,29,37,45,52,56)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4)",
+            perm"(5,6)",
+            perm"(7,8,9,10,11,12,13)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,4)(3,23,37)(5,25,33)(6,44,13)(7,21,35)(8,46,9)(10,42,11)(12,29,22)(14,31,18)(15,50,55)(16,27,20)(17,52,51)(19,48,53)(24,56,40)(26,57,36)(28,54,38)(30,41,49)(32,43,45)(34,39,47)",
+            perm"(1,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54)(2,5,8,11,14,17,20,23,26,29,32,35,38,41,44,47,50,53,56)(4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,55,57)",
+        ]),
+        PermGroup([
+            perm"(1,2,3)",
+            perm"(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2)(3,58)(4,57)(5,56)(6,55)(7,54)(8,53)(9,52)(10,51)(11,50)(12,49)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)",
+            perm"(1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57)(2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,4,7)(3,6,10,15)(5,18,12,30)(8,24,17,13)(9,14,20,26)(11,29,22,42)(16,36,28,23)(19,25,32,38)(21,41,34,52)(27,47,40,35)(31,37,43,48)(33,51,45,58)(39,55,50,46)(44,57,53,60)(49,59,56,54)",
+            perm"(1,3,9,19,31)(2,6,14,25,37)(4,10,20,32,43)(5,11,21,33,44)(7,15,26,38,48)(8,16,27,39,49)(12,22,34,45,53)(13,23,35,46,54)(17,28,40,50,56)(18,29,41,51,57)(24,36,47,55,59)(30,42,52,58,60)",
+            perm"(1,4)(2,7)(3,10)(5,12)(6,15)(8,17)(9,20)(11,22)(13,24)(14,26)(16,28)(18,30)(19,32)(21,34)(23,36)(25,38)(27,40)(29,42)(31,43)(33,45)(35,47)(37,48)(39,50)(41,52)(44,53)(46,55)(49,56)(51,58)(54,59)(57,60)",
+            perm"(1,5,13)(2,8,18)(3,11,23)(4,12,24)(6,16,29)(7,17,30)(9,21,35)(10,22,36)(14,27,41)(15,28,42)(19,33,46)(20,34,47)(25,39,51)(26,40,52)(31,44,54)(32,45,55)(37,49,57)(38,50,58)(43,53,59)(48,56,60)",
+        ]),
+        PermGroup([
+            perm"(1,2,4,7)(3,6,10,15)(5,42,12,52)(8,47,17,36)(9,14,19,25)(11,51,21,58)(13,30,23,41)(16,55,27,46)(18,35,29,24)(20,57,31,60)(22,40,33,50)(26,59,37,54)(28,45,39,34)(32,49,43,56)(38,53,48,44)",
+            perm"(1,3,9)(2,6,14)(4,10,19)(5,11,20)(7,15,25)(8,16,26)(12,21,31)(13,22,32)(17,27,37)(18,28,38)(23,33,43)(24,34,44)(29,39,48)(30,40,49)(35,45,53)(36,46,54)(41,50,56)(42,51,57)(47,55,59)(52,58,60)",
+            perm"(1,4)(2,7)(3,10)(5,12)(6,15)(8,17)(9,19)(11,21)(13,23)(14,25)(16,27)(18,29)(20,31)(22,33)(24,35)(26,37)(28,39)(30,41)(32,43)(34,45)(36,47)(38,48)(40,50)(42,52)(44,53)(46,55)(49,56)(51,58)(54,59)(57,60)",
+            perm"(1,5,13,24,36)(2,8,18,30,42)(3,11,22,34,46)(4,12,23,35,47)(6,16,28,40,51)(7,17,29,41,52)(9,20,32,44,54)(10,21,33,45,55)(14,26,38,49,57)(15,27,39,50,58)(19,31,43,53,59)(25,37,48,56,60)",
+        ]),
+        PermGroup([
+            perm"(1,2,3,6)(4,16,9,25)(5,42,10,50)(7,19,14,11)(8,45,15,36)(12,58,20,60)(13,30,21,39)(17,59,26,55)(18,33,27,24)(22,52,31,57)(23,51,32,56)(28,54,37,47)(29,53,38,46)(34,41,43,49)(35,40,44,48)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,25)(17,26)(18,27)(22,31)(23,32)(24,33)(28,37)(29,38)(30,39)(34,43)(35,44)(36,45)(40,48)(41,49)(42,50)(46,53)(47,54)(51,56)(52,57)(55,59)(58,60)",
+            perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,25)(8,17,28)(10,20,31)(13,23,34)(15,26,37)(18,29,40)(21,32,43)(24,35,46)(27,38,48)(30,41,51)(33,44,53)(36,47,55)(39,49,56)(42,52,58)(45,54,59)(50,57,60)",
+            perm"(1,5,13,24,36)(2,8,18,30,42)(3,10,21,33,45)(4,12,23,35,47)(6,15,27,39,50)(7,17,29,41,52)(9,20,32,44,54)(11,22,34,46,55)(14,26,38,49,57)(16,28,40,51,58)(19,31,43,53,59)(25,37,48,56,60)",
+        ]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6,7)", perm"(8,9,10,11,12)"]),
+        PermGroup([perm"(1,2,3,4,5)", perm"(1,2,3)"]),
+        PermGroup([
+            perm"(1,2,4,7)(3,6,10,15)(5,18,47,41)(8,23,52,24)(9,14,19,25)(11,28,55,50)(12,29,36,30)(13,42,35,17)(16,33,58,34)(20,38,59,56)(21,39,46,40)(22,51,45,27)(26,43,60,44)(31,48,54,49)(32,57,53,37)",
+            perm"(1,3,9)(2,6,14)(4,10,19)(5,11,20)(7,15,25)(8,16,26)(12,21,31)(13,22,32)(17,27,37)(18,28,38)(23,33,43)(24,34,44)(29,39,48)(30,40,49)(35,45,53)(36,46,54)(41,50,56)(42,51,57)(47,55,59)(52,58,60)",
+            perm"(1,4)(2,7)(3,10)(5,47)(6,15)(8,52)(9,19)(11,55)(12,36)(13,35)(14,25)(16,58)(17,42)(18,41)(20,59)(21,46)(22,45)(23,24)(26,60)(27,51)(28,50)(29,30)(31,54)(32,53)(33,34)(37,57)(38,56)(39,40)(43,44)(48,49)",
+            perm"(1,5,13,24,36)(2,8,18,30,42)(3,11,22,34,46)(4,12,23,35,47)(6,16,28,40,51)(7,17,29,41,52)(9,20,32,44,54)(10,21,33,45,55)(14,26,38,49,57)(15,27,39,50,58)(19,31,43,53,59)(25,37,48,56,60)",
+        ]),
+        PermGroup([
+            perm"(1,2,3,6)(4,16,9,25)(5,30,45,27)(7,19,14,11)(8,33,50,13)(10,39,36,18)(12,51,54,48)(15,24,42,21)(17,53,57,34)(20,56,47,40)(22,41,59,38)(23,28,44,60)(26,46,52,43)(29,31,49,55)(32,37,35,58)",
+            perm"(1,3)(2,6)(4,9)(5,45)(7,14)(8,50)(10,36)(11,19)(12,54)(13,33)(15,42)(16,25)(17,57)(18,39)(20,47)(21,24)(22,59)(23,44)(26,52)(27,30)(28,60)(29,49)(31,55)(32,35)(34,53)(37,58)(38,41)(40,56)(43,46)(48,51)",
+            perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,25)(8,17,28)(10,20,31)(13,23,34)(15,26,37)(18,29,40)(21,32,43)(24,35,46)(27,38,48)(30,41,51)(33,44,53)(36,47,55)(39,49,56)(42,52,58)(45,54,59)(50,57,60)",
+            perm"(1,5,13,24,36)(2,8,18,30,42)(3,10,21,33,45)(4,12,23,35,47)(6,15,27,39,50)(7,17,29,41,52)(9,20,32,44,54)(11,22,34,46,55)(14,26,38,49,57)(16,28,40,51,58)(19,31,43,53,59)(25,37,48,56,60)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,42)(8,36)(9,14)(10,50)(11,16)(12,52)(13,30)(15,45)(17,47)(18,24)(19,25)(20,57)(21,39)(22,58)(23,41)(26,54)(27,33)(28,55)(29,35)(31,60)(32,49)(34,51)(37,59)(38,44)(40,46)(43,56)(48,53)",
+            perm"(1,3)(2,6)(4,19)(5,10)(7,25)(8,15)(9,11)(12,31)(13,21)(14,16)(17,37)(18,27)(20,22)(23,43)(24,33)(26,28)(29,48)(30,39)(32,34)(35,53)(36,45)(38,40)(41,56)(42,50)(44,46)(47,59)(49,51)(52,60)(54,55)(57,58)",
+            perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,25)(8,17,28)(10,20,31)(13,23,34)(15,26,37)(18,29,40)(21,32,43)(24,35,46)(27,38,48)(30,41,51)(33,44,53)(36,47,55)(39,49,56)(42,52,58)(45,54,59)(50,57,60)",
+            perm"(1,5,13,24,36)(2,8,18,30,42)(3,10,21,33,45)(4,12,23,35,47)(6,15,27,39,50)(7,17,29,41,52)(9,20,32,44,54)(11,22,34,46,55)(14,26,38,49,57)(16,28,40,51,58)(19,31,43,53,59)(25,37,48,56,60)",
+        ]),
+        PermGroup([
+            perm"(1,2,6)(3,7,14)(4,9,28)(5,20,15)(8,16,13)(10,17,25)(11,19,40)(12,32,26)(18,27,24)(21,29,37)(22,31,51)(23,44,38)(30,39,36)(33,41,48)(34,43,58)(35,54,49)(42,50,47)(45,53,60)(46,59,56)(52,57,55)",
+            perm"(1,3,10,21,33)(2,7,17,29,41)(4,11,22,34,45)(5,12,23,35,46)(6,14,25,37,48)(8,18,30,42,52)(9,19,31,43,53)(13,24,36,47,55)(15,26,38,49,56)(16,27,39,50,57)(20,32,44,54,59)(28,40,51,58,60)",
+            perm"(1,4)(2,8)(3,11)(5,13)(6,15)(7,18)(9,20)(10,22)(12,24)(14,26)(16,28)(17,30)(19,32)(21,34)(23,36)(25,38)(27,40)(29,42)(31,44)(33,45)(35,47)(37,49)(39,51)(41,52)(43,54)(46,55)(48,56)(50,58)(53,59)(57,60)",
+            perm"(1,5)(2,9)(3,12)(4,13)(6,16)(7,19)(8,20)(10,23)(11,24)(14,27)(15,28)(17,31)(18,32)(21,35)(22,36)(25,39)(26,40)(29,43)(30,44)(33,46)(34,47)(37,50)(38,51)(41,53)(42,54)(45,55)(48,57)(49,58)(52,59)(56,60)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,42)(8,36)(9,14)(10,50)(11,16)(12,52)(13,30)(15,45)(17,47)(18,24)(19,25)(20,57)(21,39)(22,58)(23,41)(26,54)(27,33)(28,55)(29,35)(31,60)(32,49)(34,51)(37,59)(38,44)(40,46)(43,56)(48,53)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,25)(17,26)(18,27)(22,31)(23,32)(24,33)(28,37)(29,38)(30,39)(34,43)(35,44)(36,45)(40,48)(41,49)(42,50)(46,53)(47,54)(51,56)(52,57)(55,59)(58,60)",
+            perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,25)(8,17,28)(10,20,31)(13,23,34)(15,26,37)(18,29,40)(21,32,43)(24,35,46)(27,38,48)(30,41,51)(33,44,53)(36,47,55)(39,49,56)(42,52,58)(45,54,59)(50,57,60)",
+            perm"(1,5,13,24,36)(2,8,18,30,42)(3,10,21,33,45)(4,12,23,35,47)(6,15,27,39,50)(7,17,29,41,52)(9,20,32,44,54)(11,22,34,46,55)(14,26,38,49,57)(16,28,40,51,58)(19,31,43,53,59)(25,37,48,56,60)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,7)(5,18)(8,13)(9,14)(10,27)(11,16)(12,30)(15,21)(17,24)(19,25)(20,39)(22,28)(23,42)(26,33)(29,36)(31,37)(32,50)(34,40)(35,52)(38,45)(41,47)(43,48)(44,57)(46,58)(49,54)(51,55)(53,60)(56,59)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,25)(17,26)(18,27)(22,31)(23,32)(24,33)(28,37)(29,38)(30,39)(34,43)(35,44)(36,45)(40,48)(41,49)(42,50)(46,53)(47,54)(51,56)(52,57)(55,59)(58,60)",
+            perm"(1,4,11,22,34)(2,7,16,28,40)(3,9,19,31,43)(5,12,23,35,46)(6,14,25,37,48)(8,17,29,41,51)(10,20,32,44,53)(13,24,36,47,55)(15,26,38,49,56)(18,30,42,52,58)(21,33,45,54,59)(27,39,50,57,60)",
+            perm"(1,5,13)(2,8,18)(3,10,21)(4,12,24)(6,15,27)(7,17,30)(9,20,33)(11,23,36)(14,26,39)(16,29,42)(19,32,45)(22,35,47)(25,38,50)(28,41,52)(31,44,54)(34,46,55)(37,49,57)(40,51,58)(43,53,59)(48,56,60)",
+        ]),
+        PermGroup([
+            perm"(1,2)(3,6)(4,16)(5,42)(7,11)(8,36)(9,25)(10,50)(12,58)(13,30)(14,19)(15,45)(17,55)(18,24)(20,60)(21,39)(22,52)(23,51)(26,59)(27,33)(28,47)(29,46)(31,57)(32,56)(34,41)(35,40)(37,54)(38,53)(43,49)(44,48)",
+            perm"(1,3)(2,6)(4,9)(5,10)(7,14)(8,15)(11,19)(12,20)(13,21)(16,25)(17,26)(18,27)(22,31)(23,32)(24,33)(28,37)(29,38)(30,39)(34,43)(35,44)(36,45)(40,48)(41,49)(42,50)(46,53)(47,54)(51,56)(52,57)(55,59)(58,60)",
+            perm"(1,4,11)(2,7,16)(3,9,19)(5,12,22)(6,14,25)(8,17,28)(10,20,31)(13,23,34)(15,26,37)(18,29,40)(21,32,43)(24,35,46)(27,38,48)(30,41,51)(33,44,53)(36,47,55)(39,49,56)(42,52,58)(45,54,59)(50,57,60)",
+            perm"(1,5,13,24,36)(2,8,18,30,42)(3,10,21,33,45)(4,12,23,35,47)(6,15,27,39,50)(7,17,29,41,52)(9,20,32,44,54)(11,22,34,46,55)(14,26,38,49,57)(16,28,40,51,58)(19,31,43,53,59)(25,37,48,56,60)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4)",
+            perm"(5,6,7)",
+            perm"(8,9,10,11,12)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2)(3,62)(4,61)(5,60)(6,59)(7,58)(8,57)(9,56)(10,55)(11,54)(12,53)(13,52)(14,51)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)",
+            perm"(1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61)(2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62)",
+        ]),
+        PermGroup([
+            perm"(1,2)",
+            perm"(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33)",
+        ]),
+    ],
+    [
+        PermGroup([
+            perm"(1,2,5,3,6,11,8,13,19)(4,15,39,9,23,47,16,31,54)(7,21,35,14,29,43,22,37,27)(10,33,12,17,41,20,25,49,28)(18,51,48,26,58,55,34,62,60)(24,56,44,32,61,52,40,63,36)(30,53,50,38,59,57,46,45,42)",
+            perm"(1,3,8)(2,6,13)(4,9,16)(5,11,19)(7,14,22)(10,17,25)(12,20,28)(15,23,31)(18,26,34)(21,29,37)(24,32,40)(27,35,43)(30,38,46)(33,41,49)(36,44,52)(39,47,54)(42,50,57)(45,53,59)(48,55,60)(51,58,62)(56,61,63)",
+            perm"(1,4,10,18,27,36,45)(2,7,15,24,33,42,51)(3,9,17,26,35,44,53)(5,12,21,30,39,48,56)(6,14,23,32,41,50,58)(8,16,25,34,43,52,59)(11,20,29,38,47,55,61)(13,22,31,40,49,57,62)(19,28,37,46,54,60,63)",
+        ]),
+        PermGroup([perm"(1,2,3,4,5,6,7)", perm"(8,9,10,11,12,13,14,15,16)"]),
+        PermGroup([
+            perm"(1,2,5)(3,6,11)(4,15,39)(7,21,27)(8,13,19)(9,23,47)(10,33,12)(14,29,35)(16,31,54)(17,41,20)(18,51,48)(22,37,43)(24,56,36)(25,49,28)(26,58,55)(30,45,42)(32,61,44)(34,62,60)(38,53,50)(40,63,52)(46,59,57)",
+            perm"(1,3,8)(2,6,13)(4,9,16)(5,11,19)(7,14,22)(10,17,25)(12,20,28)(15,23,31)(18,26,34)(21,29,37)(24,32,40)(27,35,43)(30,38,46)(33,41,49)(36,44,52)(39,47,54)(42,50,57)(45,53,59)(48,55,60)(51,58,62)(56,61,63)",
+            perm"(1,4,10,18,27,36,45)(2,7,15,24,33,42,51)(3,9,17,26,35,44,53)(5,12,21,30,39,48,56)(6,14,23,32,41,50,58)(8,16,25,34,43,52,59)(11,20,29,38,47,55,61)(13,22,31,40,49,57,62)(19,28,37,46,54,60,63)",
+        ]),
+        PermGroup([perm"(1,2,3)", perm"(4,5,6)", perm"(7,8,9,10,11,12,13)"]),
+    ],
+]