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AbstractGroupData.wl
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AbstractGroupData.wl
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(* ::Package:: *)
(*Character tables of abstract groups*)
BeginPackage["AbstractGroupData`"]
Unprotect@@Names["AbstractGroupData`*"];
ClearAll@@Names["AbstractGroupData`*"];
AGCharTab::usage="AGCharTab[m,n] returns the character table of the abstract group \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\).";
AGClasses::usage="AGClasses[m,n] returns the elements in each class of the abstract group \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\), in which each element is given by its powers of generators.";
allAGindex::usage="allAGindex is a list of {m,n} for all abstract groups that will be used.";
checkAGCharTab::usage="checkAGCharTab[m,n] checks if the character table of \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\) fulfills orthonormality.";
showAGCharTab::usage="showAGCharTab[m,n] shows the character table and classes of \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\).";
getAGClassesByGen::usage="getAGClassesByGen[m,n,gens,mul] uses the generators gens and the binary function mul as the multiplication to get the classes of the abstract group \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\).";
showAGCharTabByGen::usage="showAGCharTabByGen[m,n,gens,mul] shows the the classes and character table of the abstract group \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\) using the specified generators gens and the binary function mul as the multiplication.";
AGIrepGen::usage="AGIrepGen[m,n] returns the generators of all irreps in \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\)."
showAGIrepGen::usage="showAGIrepGen[m,n] shows the data of AGIrepGen[m,n] in a table form."
getAGIrepMat::usage="getAGIrepMat[m,n,iR,powers] gives the matrix of the iR-th irep of the group element described by the powers of generators in \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\)."
getAGIrepClassMat::usage="getAGIrepClassMat[m,n,iR,ic] gives all the matrices of the iR-th irep in the ic-th class in \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\)."
checkAGIrepMat::usage="checkAGIrepMat[m,n] checks if the data in AGCharTab, AGClasses, and AGIrepGen for \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\) are compatible with each other."
checkAGGen::usage="checkAGGen[m,n,gens,ie,times,myequal(optional)] checks if the generators gens generate the abstract group \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\)."
checkAGGenRelations::usage="checkAGGenRelations[m,n,relat] checks if the representation matrices of the generators satisfy the realtions between the generators "<>
"of the abstract group \!\(\*SubsuperscriptBox[\(G\), \(m\), \(n\)]\). relat is a list of (string) relations, e.g. {\"Q2=E\",\"QP3=P3Q\",\"TS=P3ST\"}.";
Begin["`Private`"]
allAGindex={{1,1}, {2,1}, {3,1}, {4,1}, {4,2}, {6,1}, {6,2}, {8,1}, {8,2}, {8,3},
{8,4}, {8,5}, {12,1}, {12,2}, {12,3}, {12,4}, {12,5}, {12,6}, {16,1}, {16,2},
{16,3}, {16,4}, {16,5}, {16,6}, {16,7}, {16,8}, {16,9}, {16,10}, {16,11}, {16,12},
{16,13}, {16,14}, {24,1}, {24,2}, {24,3}, {24,4}, {24,5}, {24,6}, {24,7}, {24,8},
{24,9}, {24,10}, {24,11}, {24,12}, {32,1}, {32,2}, {32,3}, {32,4}, {32,5}, {32,6},
{32,7}, {32,8}, {32,9}, {32,10}, {32,11}, {32,12}, {32,13}, {32,14}, {32,15}, {32,16},
{32,17}, {48,1}, {48,2}, {48,3}, {48,4}, {48,5}, {48,6}, {48,7}, {48,8}, {48,9},
{48,10}, {48,11}, {48,12}, {48,13}, {48,14}, {48,15}, {64,1}, {64,2}, {64,3}, {64,4},
{64,5}, {96,1}, {96,2}, {96,3}, {96,4}, {96,5}, {96,6}, {96,7}, {96,8}, {96,9},
{96,10}, {192,1}, {192,2}};
(* ::Section:: *)
(*Character tables and classes of abstract groups*)
(* ::Subsection:: *)
(*Data definition for AGCharTab and AGClasses*)
(* Parameters *)
\[Omega]=Exp[I 2\[Pi]/3];
\[Theta]=(1+I)/Sqrt[2];
\[Sigma]=Exp[I \[Pi]/8];
(* Construct character table of a direct product group from its normal subgroup *)
otimesG21[ct_]:=ArrayFlatten[{{ct,ct},{ct,-ct}}];
otimesG41[ct_]:=ArrayFlatten[{{ct,ct,ct,ct},{ct,I*ct,-ct,-I*ct},{ct,-ct,ct,-ct},{ct,-I*ct,-ct,I*ct}}];
otimesG42[ct_]:=ArrayFlatten[{{ct,ct,ct,ct},{ct,-ct,ct,-ct},{ct,ct,-ct,-ct},{ct,-ct,-ct,ct}}];
AGCharTab[1,1]={{1}};
AGClasses[1,1]={{{0}}};
AGCharTab[2,1]={{1,1},{1,-1}};
AGClasses[2,1]={{{0}},{{1}}};
AGCharTab[3,1]={{1,1,1},{1,\[Omega],\[Omega]\[Conjugate]},{1,\[Omega]\[Conjugate],\[Omega]}};
AGClasses[3,1]={{{0}},{{1}},{{2}}};
AGCharTab[4,1]={{1,1,1,1},{1,I,-1,-I},{1,-1,1,-1},{1,-I,-1,I}};
AGClasses[4,1]={{{0}},{{1}},{{2}},{{3}}};
AGCharTab[4,2]={{1,1,1,1},{1,1,-1,-1},{1,-1,1,-1},{1,-1,-1,1}};
AGClasses[4,2]={{{0,0}},{{1,0}},{{0,1}},{{1,1}}};
AGCharTab[6,1]={{1,1,1,1,1,1},{1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega]},{1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate]},
{1,-1,1,-1,1,-1},{1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega]},{1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate]}};
AGClasses[6,1]={{{0}},{{1}},{{2}},{{3}},{{4}},{{5}}};
AGCharTab[6,2]={{1,1,1},{1,1,-1},{2,-1,0}};
AGClasses[6,2]={{{0,0}},{{1,0},{2,0}},{{0,1},{1,1},{2,1}}};
AGCharTab[8,1]={{1,1,1,1,1,1,1,1},{1,\[Theta],I,-\[Theta]\[Conjugate],-1,-\[Theta],-I,\[Theta]\[Conjugate]},
{1,I,-1,-I,1,I,-1,-I},{1,-\[Theta]\[Conjugate],-I,\[Theta],-1,\[Theta]\[Conjugate],I,-\[Theta]},
{1,-1,1,-1,1,-1,1,-1},{1,-\[Theta],I,\[Theta]\[Conjugate],-1,\[Theta],-I,-\[Theta]\[Conjugate]},
{1,-I,-1,I,1,-I,-1,I},{1,\[Theta]\[Conjugate],-I,-\[Theta],-1,-\[Theta]\[Conjugate],I,\[Theta]}};
AGClasses[8,1]={{{0}},{{1}},{{2}},{{3}},{{4}},{{5}},{{6}},{{7}}};
AGCharTab[8,2]={{1,1,1,1,1,1,1,1},{1,I,-1,-I,1,I,-1,-I},
{1,-1,1,-1,1,-1,1,-1},{1,-I,-1,I,1,-I,-1,I},
{1,1,1,1,-1,-1,-1,-1},{1,I,-1,-I,-1,-I,1,I},
{1,-1,1,-1,-1,1,-1,1},{1,-I,-1,I,-1,I,1,-I}};
AGClasses[8,2]={{{0,0}},{{1,0}},{{2,0}},{{3,0}},{{0,1}},{{1,1}},{{2,1}},{{3,1}}};
AGCharTab[8,3]={{1,1,1,1,1,1,1,1},{1,-1,1,-1,1,-1,1,-1},
{1,1,-1,-1,1,1,-1,-1},{1,-1,-1,1,1,-1,-1,1},
{1,1,1,1,-1,-1,-1,-1},{1,-1,1,-1,-1,1,-1,1},
{1,1,-1,-1,-1,-1,1,1},{1,-1,-1,1,-1,1,1,-1}};
AGClasses[8,3]={{{0,0,0}},{{1,0,0}},{{0,1,0}},{{1,1,0}},{{0,0,1}},{{1,0,1}},{{0,1,1}},{{1,1,1}}};
AGCharTab[8,4]={{1,1,1,1,1},{1,1,1,-1,-1},{1,1,-1,1,-1},{1,1,-1,-1,1},{2,-2,0,0,0}};
AGClasses[8,4]={{{0,0}},{{2,0}},{{1,0},{3,0}},{{0,1},{2,1}},{{1,1},{3,1}}};
AGCharTab[8,5]={{1,1,1,1,1},{1,1,1,-1,-1},{1,1,-1,1,-1},{1,1,-1,-1,1},{2,-2,0,0,0}};
AGClasses[8,5]={{{0,0}},{{2,0}},{{1,0},{3,0}},{{0,1},{2,1}},{{1,1},{3,1}}};
AGCharTab[12,1]={{1,1,1,1,1,1,1,1,1,1,1,1},{1,-I \[Omega],-\[Omega]\[Conjugate],I,\[Omega],-I \[Omega]\[Conjugate],-1,I \[Omega],\[Omega]\[Conjugate],-I,-\[Omega],I \[Omega]\[Conjugate]},
{1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega],1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega]},{1,I,-1,-I,1,I,-1,-I,1,I,-1,-I},
{1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate]},{1,-I \[Omega]\[Conjugate],-\[Omega],I,\[Omega]\[Conjugate],-I \[Omega],-1,I \[Omega]\[Conjugate],\[Omega],-I,-\[Omega]\[Conjugate],I \[Omega]},
{1,-1,1,-1,1,-1,1,-1,1,-1,1,-1},{1,I \[Omega],-\[Omega]\[Conjugate],-I ,\[Omega],I \[Omega]\[Conjugate],-1,-I \[Omega],\[Omega]\[Conjugate],I,-\[Omega],-I \[Omega]\[Conjugate]},
{1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega]},{1,-I,-1,I,1,-I,-1,I,1,-I,-1,I},
{1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate],1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate]},{1,I \[Omega]\[Conjugate],-\[Omega],-I,\[Omega]\[Conjugate],I \[Omega],-1,-I \[Omega]\[Conjugate],\[Omega],I,-\[Omega]\[Conjugate],-I \[Omega]}};
AGClasses[12,1]={{{0}},{{1}},{{2}},{{3}},{{4}},{{5}},{{6}},{{7}},{{8}},{{9}},{{10}},{{11}}};
AGCharTab[12,2]={{1,1,1,1,1,1,1,1,1,1,1,1},{1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate]},
{1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega]},{1,1,1,-1,-1,-1,1,1,1,-1,-1,-1},
{1,\[Omega],\[Omega]\[Conjugate],-1,-\[Omega],-\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],-1,-\[Omega],-\[Omega]\[Conjugate]},{1,\[Omega]\[Conjugate],\[Omega],-1,-\[Omega]\[Conjugate],-\[Omega],1,\[Omega]\[Conjugate],\[Omega],-1,-\[Omega]\[Conjugate],-\[Omega]},
{1,1,1,1,1,1,-1,-1,-1,-1,-1,-1},{1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],-1,-\[Omega],-\[Omega]\[Conjugate],-1,-\[Omega],-\[Omega]\[Conjugate]},
{1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],-1,-\[Omega]\[Conjugate],-\[Omega],-1,-\[Omega]\[Conjugate],-\[Omega]},{1,1,1,-1,-1,-1,-1,-1,-1,1,1,1},
{1,\[Omega],\[Omega]\[Conjugate],-1,-\[Omega],-\[Omega]\[Conjugate],-1,-\[Omega],-\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate]},{1,\[Omega]\[Conjugate],\[Omega],-1,-\[Omega]\[Conjugate],-\[Omega],-1,-\[Omega]\[Conjugate],-\[Omega],1,\[Omega]\[Conjugate],\[Omega]}};
AGClasses[12,2]={{{0,0,0}},{{1,0,0}},{{2,0,0}},{{0,1,0}},{{1,1,0}},{{2,1,0}},
{{0,0,1}},{{1,0,1}},{{2,0,1}},{{0,1,1}},{{1,1,1}},{{2,1,1}}};
AGCharTab[12,3]={{1,1,1,1,1,1},{1,1,1,1,-1,-1},{1,-1,-1,1,1,-1},
{1,-1,-1,1,-1,1},{2,2,-1,-1,0,0},{2,-2,1,-1,0,0}};
AGClasses[12,3]={{{0,0}},{{3,0}},{{1,0},{5,0}},{{2,0},{4,0}},{{0,1},{2,1},{4,1}},{{1,1},{3,1},{5,1}}};
AGCharTab[12,4]={{1,1,1,1,1,1},{1,1,1,1,-1,-1},{1,-1,-1,1,I,-I},
{1,-1,-1,1,-I,I},{2,2,-1,-1,0,0},{2,-2,1,-1,0,0}};
AGClasses[12,4]={{{0,0}},{{3,0}},{{1,0},{5,0}},{{2,0},{4,0}},{{0,1},{2,1},{4,1}},{{1,1},{3,1},{5,1}}};
AGCharTab[12,5]={{1,1,1,1},{1,1,\[Omega],\[Omega]\[Conjugate]},{1,1,\[Omega]\[Conjugate],\[Omega]},{3,-1,0,0}};
AGClasses[12,5]={{{0,0,0}},{{0,1,0},{0,0,1},{0,1,1}},{{1,0,0},{1,1,0},{1,0,1},{1,1,1}},
{{2,0,0},{2,1,0},{2,0,1},{2,1,1}}};
AGCharTab[12,6]={{1,1,1,1,1,1,1,1,1,1,1,1},{1,- \[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega],1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega]},
{1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate]},{1,-1,1,-1,1,-1,1,-1,1,-1,1,-1},
{1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega]},{1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate],1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate]},
{1,1,1,1,1,1,-1,-1,-1,-1,-1,-1},{1,- \[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega],-1,\[Omega]\[Conjugate],-\[Omega],1,-\[Omega]\[Conjugate],\[Omega]},
{1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],-1,-\[Omega],-\[Omega]\[Conjugate],-1,-\[Omega],-\[Omega]\[Conjugate]},{1,-1,1,-1,1,-1,-1,1,-1,1,-1,1},
{1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],-1,-\[Omega]\[Conjugate],-\[Omega],-1,-\[Omega]\[Conjugate],-\[Omega]},{1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate],1,-\[Omega],\[Omega]\[Conjugate]}};
AGClasses[12,6]={{{0,0}},{{1,0}},{{2,0}},{{3,0}},{{4,0}},{{5,0}},{{0,1}},
{{1,1}},{{2,1}},{{3,1}},{{4,1}},{{5,1}}};
AGCharTab[16,1]=Table[Table[\[Sigma]^((s-1)(t-1)),{s,1,16}],{t,1,16}];
AGClasses[16,1]=Table[{{s-1}},{s,1,16}];
AGCharTab[16,2]=otimesG21[AGCharTab[8,1]];
AGClasses[16,2]={{{0,0}},{{1,0}},{{2,0}},{{3,0}},{{4,0}},{{5,0}},{{6,0}},{{7,0}},
{{0,1}},{{1,1}},{{2,1}},{{3,1}},{{4,1}},{{5,1}},{{6,1}},{{7,1}}};
AGCharTab[16,3]=otimesG41[AGCharTab[4,1]];
AGClasses[16,3]={{{0,0}},{{1,0}},{{2,0}},{{3,0}},{{0,1}},{{1,1}},{{2,1}},{{3,1}},
{{0,2}},{{1,2}},{{2,2}},{{3,2}},{{0,3}},{{1,3}},{{2,3}},{{3,3}}};
AGCharTab[16,4]=otimesG21[AGCharTab[8,2]];
AGClasses[16,4]={{{0,0,0}},{{1,0,0}},{{2,0,0}},{{3,0,0}},
{{0,1,0}},{{1,1,0}},{{2,1,0}},{{3,1,0}},
{{0,0,1}},{{1,0,1}},{{2,0,1}},{{3,0,1}},
{{0,1,1}},{{1,1,1}},{{2,1,1}},{{3,1,1}}};
AGCharTab[16,5]=otimesG21[AGCharTab[8,3]];
AGClasses[16,5]={{{0,0,0,0}},{{1,0,0,0}},{{0,1,0,0}},{{1,1,0,0}},
{{0,0,1,0}},{{1,0,1,0}},{{0,1,1,0}},{{1,1,1,0}},
{{0,0,0,1}},{{1,0,0,1}},{{0,1,0,1}},{{1,1,0,1}},
{{0,0,1,1}},{{1,0,1,1}},{{0,1,1,1}},{{1,1,1,1}}};
AGCharTab[16,6]={{1,1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,-1,-1,-1,-1},
{1,1,1,1,-1,-1,1,1,-1,-1},{1,1,1,1,-1,-1,-1,-1,1,1},
{1,-1,1,-1,I,-I,1,-1,I,-I},{1,-1,1,-1,I,-I,-1,1,-I,I},
{1,-1,1,-1,-I,I,1,-1,-I,I},{1,-1,1,-1,-I,I,-1,1,I,-I},
{2,2I,-2,-2I,0,0,0,0,0,0},{2,-2I,-2,2I,0,0,0,0,0,0}};
AGClasses[16,6]={{{0,0}},{{2,0}},{{4,0}},{{6,0}},{{1,0},{5,0}},{{3,0},{7,0}},
{{0,1},{4,1}},{{2,1},{6,1}},{{1,1},{5,1}},{{3,1},{7,1}}};
AGCharTab[16,7]={{1,1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,-1,-1,-1,-1},
{1,1,1,1,-1,-1,1,1,-1,-1},{1,1,1,1,-1,-1,-1,-1,1,1},
{1,-1,1,-1,1,-1,1,-1,1,-1},{1,-1,1,-1,1,-1,-1,1,-1,1},
{1,-1,1,-1,-1,1,1,-1,-1,1},{1,-1,1,-1,-1,1,-1,1,1,-1},
{2,2I,-2,-2I,0,0,0,0,0,0},{2,-2I,-2,2I,0,0,0,0,0,0}};
AGClasses[16,7]={{{0,0,0}},{{1,0,0}},{{2,0,0}},{{3,0,0}},
{{0,1,0},{2,1,0}},{{1,1,0},{3,1,0}},
{{0,0,1},{2,0,1}},{{1,0,1},{3,0,1}},
{{0,1,1},{2,1,1}},{{1,1,1},{3,1,1}}};
AGCharTab[16,8]={{1,1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,-1,-1,-1,-1},
{1,1,1,1,-1,-1,1,-1,1,-1},{1,1,1,1,-1,-1,-1,1,-1,1},
{1,1,-1,-1,-1,1,I,-I,-I,I},{1,1,-1,-1,-1,1,-I,I,I,-I},
{1,1,-1,-1,1,-1,-I,-I,I,I},{1,1,-1,-1,1,-1,I,I,-I,-I},
{2,-2,2,-2,0,0,0,0,0,0},{2,-2,-2,2,0,0,0,0,0,0}};
AGClasses[16,8]={{{0,0}},{{2,0}},{{0,2}},{{2,2}},{{1,0},{3,0}},{{1,2},{3,2}},
{{0,1},{2,1}},{{1,1},{3,1}},{{0,3},{2,3}},{{1,3},{3,3}}};
AGCharTab[16,9]=otimesG21[AGCharTab[8,4]];
AGClasses[16,9]={{{0,0,0}},{{2,0,0}},{{1,0,0},{3,0,0}},
{{0,1,0},{2,1,0}},{{1,1,0},{3,1,0}},
{{0,0,1}},{{2,0,1}},{{1,0,1},{3,0,1}},
{{0,1,1},{2,1,1}},{{1,1,1},{3,1,1}}};
AGCharTab[16,10]={{1,1,1,1,1,1,1,1,1,1},{1,1,1,1,-1,-1,-1,-1,1,1},
{1,1,1,1,1,1,-1,-1,-1,-1},{1,1,1,1,-1,-1,1,1,-1,-1},
{1,1,-1,-1,1,-1,I,-I,I,-I},{1,1,-1,-1,1,-1,-I,I,-I,I},
{1,1,-1,-1,-1,1,-I,I,I,-I},{1,1,-1,-1,-1,1,I,-I,-I,I},
{2,-2,2,-2,0,0,0,0,0,0},{2,-2,-2,2,0,0,0,0,0,0}};
AGClasses[16,10]={{{0,0,0}},{{0,1,0}},{{2,0,0}},{{2,1,0}},{{0,0,1},{0,1,1}},{{2,0,1},{2,1,1}},
{{1,0,0},{1,1,0}},{{3,0,0},{3,1,0}},{{1,0,1},{1,1,1}},{{3,0,1},{3,1,1}}};
AGCharTab[16,11]=otimesG21[AGCharTab[8,5]];
AGClasses[16,11]={{{0,0,0}},{{2,0,0}},{{1,0,0},{3,0,0}},{{0,1,0},{2,1,0}},{{1,1,0},{3,1,0}},
{{0,0,1}},{{2,0,1}},{{1,0,1},{3,0,1}},{{0,1,1},{2,1,1}},{{1,1,1},{3,1,1}}};
AGCharTab[16,12]={{1,1,1,1,1,1,1},{1,1,1,1,1,-1,-1},{1,1,1,-1,-1,1,-1},{1,1,1,-1,-1,-1,1},
{2,2,-2,0,0,0,0},{2,-2,0,Sqrt[2],-Sqrt[2],0,0},{2,-2,0,-Sqrt[2],Sqrt[2],0,0}};
AGClasses[16,12]={{{0,0}},{{4,0}},{{2,0},{6,0}},{{1,0},{7,0}},{{3,0},{5,0}},
{{0,1},{2,1},{4,1},{6,1}},{{1,1},{3,1},{5,1},{7,1}}};
AGCharTab[16,13]={{1,1,1,1,1,1,1},{1,1,1,1,1,-1,-1},{1,1,1,-1,-1,1,-1},{1,1,1,-1,-1,-1,1},
{2,2,-2,0,0,0,0},{2,-2,0,I Sqrt[2],-I Sqrt[2],0,0},{2,-2,0,-I Sqrt[2],I Sqrt[2],0,0}};
AGClasses[16,13]={{{0,0}},{{4,0}},{{2,0},{6,0}},{{1,0},{3,0}},{{5,0},{7,0}},
{{0,1},{2,1},{4,1},{6,1}},{{1,1},{3,1},{5,1},{7,1}}};
AGCharTab[16,14]={{1,1,1,1,1,1,1},{1,1,1,1,1,-1,-1},{1,1,1,-1,-1,1,-1},{1,1,1,-1,-1,-1,1},
{2,2,-2,0,0,0,0},{2,-2,0,Sqrt[2],-Sqrt[2],0,0},{2,-2,0,-Sqrt[2],Sqrt[2],0,0}};
AGClasses[16,14]={{{0,0}},{{4,0}},{{2,0},{6,0}},{{1,0},{7,0}},{{3,0},{5,0}},
{{0,1},{2,1},{4,1},{6,1}},{{1,1},{3,1},{5,1},{7,1}}};
AGCharTab[24,1]={{1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,1,-1,-1},{1,1,1,1,-1,-1,-1,1,-1},
{1,1,1,1,-1,-1,-1,-1,1},{2,2,-1,-1,-2,1,1,0,0},{2,2,-1,-1,2,-1,-1,0,0},
{2,-2,-1,1,0,I Sqrt[3],-I Sqrt[3],0,0},{2,-2,-1,1,0,-I Sqrt[3],I Sqrt[3],0,0},{2,-2,2,-2,0,0,0,0,0}};
AGClasses[24,1]={{{0,0,0}},{{2,0,0}},{{0,1,0},{0,2,0}},{{2,1,0},{2,2,0}},
{{0,0,1},{2,0,1}},{{0,2,1},{2,1,1}},{{0,1,1},{2,2,1}},
{{1,0,0},{1,1,0},{1,2,0},{3,0,0},{3,1,0},{3,2,0}},
{{1,0,1},{1,1,1},{1,2,1},{3,0,1},{3,1,1},{3,2,1}}};
AGCharTab[24,2]={{1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,1,-1,-1},{1,1,1,1,-1,-1,-1,1,-1},
{1,1,1,1,-1,-1,-1,-1,1},{2,2,-1,-1,-2,1,1,0,0},{2,2,-1,-1,2,-1,-1,0,0},
{2,-2,-1,1,0,Sqrt[3],-Sqrt[3],0,0},{2,-2,-1,1,0,-Sqrt[3],Sqrt[3],0,0},{2,-2,2,-2,0,0,0,0,0}};
AGClasses[24,2]={{{0,0}},{{6,0}},{{4,0},{8,0}},{{2,0},{10,0}},{{3,0},{9,0}},
{{1,0},{11,0}},{{5,0},{7,0}},{{0,1},{2,1},{4,1},{6,1},{8,1},{10,1}},
{{1,1},{3,1},{5,1},{7,1},{9,1},{11,1}}};
AGCharTab[24,3]=otimesG21[AGCharTab[12,4]];
AGClasses[24,3]={{{0,0,0}},{{3,0,0}},{{1,0,0},{5,0,0}},{{2,0,0},{4,0,0}},
{{0,1,0},{2,1,0},{4,1,0}},{{1,1,0},{3,1,0},{5,1,0}},{{0,0,1}},
{{3,0,1}},{{1,0,1},{5,0,1}},{{2,0,1},{4,0,1}},{{0,1,1},{2,1,1},
{4,1,1}},{{1,1,1},{3,1,1},{5,1,1}}};
AGCharTab[24,4]=otimesG41[AGCharTab[6,2]];
AGClasses[24,4]={{{0,0,0}},{{1,0,0},{2,0,0}},{{0,1,0},{1,1,0},{2,1,0}},{{0,0,1}},
{{1,0,1},{2,0,1}},{{0,1,1},{1,1,1},{2,1,1}},{{0,0,2}},{{1,0,2},{2,0,2}},
{{0,1,2},{1,1,2},{2,1,2}},{{0,0,3}},{{1,0,3},{2,0,3}},{{0,1,3},{1,1,3},{2,1,3}}};
AGCharTab[24,5]=otimesG42[AGCharTab[6,2]];
AGClasses[24,5]={{{0,0,0,0}},{{1,0,0,0},{2,0,0,0}},{{0,1,0,0},{1,1,0,0},{2,1,0,0}},
{{0,0,1,0}},{{1,0,1,0},{2,0,1,0}},{{0,1,1,0},{1,1,1,0},{2,1,1,0}},
{{0,0,0,1}},{{1,0,0,1},{2,0,0,1}},{{0,1,0,1},{1,1,0,1},{2,1,0,1}},
{{0,0,1,1}},{{1,0,1,1},{2,0,1,1}},{{0,1,1,1},{1,1,1,1},{2,1,1,1}}};
AGCharTab[24,6]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1},
{1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega],1,\[Omega],\[Omega]\[Conjugate],1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega]},
{1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega],1,\[Omega],\[Omega]\[Conjugate],-1,\[Omega]\[Conjugate],-\[Omega],1,-\[Omega]\[Conjugate],\[Omega]},
{1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate]},
{1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],-1,-\[Omega],-\[Omega]\[Conjugate],-1,-\[Omega],-\[Omega]\[Conjugate]},
{1,-1,1,-1,1,-1,1,1,1,1,-1,1,-1,1,-1},
{1,-1,1,-1,1,-1,1,1,1,-1,1,-1,1,-1,1},
{1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega]},
{1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega],\[Omega]\[Conjugate],-1,-\[Omega]\[Conjugate],-\[Omega],-1,-\[Omega]\[Conjugate],-\[Omega]},
{1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate]},
{1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],-1,\[Omega],-\[Omega]\[Conjugate],1,-\[Omega],\[Omega]\[Conjugate]},
{2,0,-2\[Omega]\[Conjugate],0,2\[Omega],0,-2,2\[Omega]\[Conjugate],-2\[Omega],0,0,0,0,0,0},
{2,0,-2,0,2,0,-2,2,-2,0,0,0,0,0,0},
{2,0,-2\[Omega],0,2\[Omega]\[Conjugate],0,-2,2\[Omega],-2\[Omega]\[Conjugate],0,0,0,0,0,0}};
AGClasses[24,6]={{{0,0}},{{1,0},{7,0}},{{2,0}},{{3,0},{9,0}},{{4,0}},{{5,0},{11,0}},
{{6,0}},{{8,0}},{{10,0}},{{0,1},{6,1}},{{1,1},{7,1}},{{2,1},{8,1}},
{{3,1},{9,1}},{{4,1},{10,1}},{{5,1},{11,1}}};
AGCharTab[24,7]={{1,1,1,1,1},{1,1,-1,-1,1},{2,2,0,0,-1},{3,-1,1,-1,0},{3,-1,-1,1,0}};
AGClasses[24,7]={{{0,0,0,0}},{{0,0,1,0},{0,1,0,0},{0,1,1,0}},
{{1,0,0,1},{0,0,1,1},{2,0,0,1},{1,1,1,1},{0,1,1,1},{2,0,1,1}},
{{0,0,0,1},{0,1,0,1},{1,1,0,1},{1,0,1,1},{2,1,1,1},{2,1,0,1}},
{{1,0,0,0},{2,0,0,0},{1,1,0,0},{1,0,1,0},{1,1,1,0},{2,1,1,0},{2,0,1,0},{2,1,0,0}}};
AGCharTab[24,8]={{1,1,1,1,1,1,1,1},{1,1,1,1,\[Omega],\[Omega],\[Omega]\[Conjugate],\[Omega]\[Conjugate]},
{1,1,1,1,\[Omega]\[Conjugate],\[Omega]\[Conjugate],\[Omega],\[Omega]},{1,-1,-1,1,1,-1,1,-1},
{1,-1,-1,1,\[Omega],-\[Omega],\[Omega]\[Conjugate],-\[Omega]\[Conjugate]},{1,-1,-1,1,\[Omega]\[Conjugate],-\[Omega]\[Conjugate],\[Omega],-\[Omega]},
{3,3,-1,-1,0,0,0,0},{3,-3,1,-1,0,0,0,0}};
AGClasses[24,8]={{{0,0,0}},{{3,0,0}},{{0,1,0},{0,0,1},{3,1,1}},{{3,1,0},{3,0,1},{0,1,1}},
{{1,1,0},{1,0,1},{4,0,0},{4,1,1}},{{4,1,0},{4,0,1},{1,0,0},{1,1,1}},
{{2,0,0},{2,1,1},{5,1,0},{5,0,1}},{{5,0,0},{5,1,1},{2,1,0},{2,0,1}}};
AGCharTab[24,9]={{1,1,1,1,1,1,1},{1,1,1,\[Omega],\[Omega],\[Omega]\[Conjugate],\[Omega]\[Conjugate]},{1,1,1,\[Omega]\[Conjugate],\[Omega]\[Conjugate],\[Omega],\[Omega]},{2,-2,0,1,-1,-1,1},
{2,-2,0,\[Omega],-\[Omega],-\[Omega]\[Conjugate],\[Omega]\[Conjugate]},{2,-2,0,\[Omega]\[Conjugate],-\[Omega]\[Conjugate],-\[Omega],\[Omega]},{3,3,-1,0,0,0,0}};
AGClasses[24,9]={{{0,0,0}},{{3,0,0}},{{0,1,0},{0,0,1},{3,1,0},{3,0,1},{0,1,1},{3,1,1}},
{{1,0,0},{1,1,0},{1,1,1},{1,0,1}},{{4,0,0},{4,1,0},{4,1,1},{4,0,1}},
{{2,0,0},{5,0,1},{5,1,1},{5,1,0}},{{5,0,0},{2,0,1},{2,1,1},{2,1,0}}};
AGCharTab[24,10]={{1,1,1,1,1,1,1,1},{1,1,\[Omega],\[Omega]\[Conjugate],1,1,\[Omega],\[Omega]\[Conjugate]},
{1,1,\[Omega]\[Conjugate],\[Omega],1,1,\[Omega]\[Conjugate],\[Omega]},{3,-1,0,0,3,-1,0,0},
{1,1,1,1,-1,-1,-1,-1},{1,1,\[Omega],\[Omega]\[Conjugate],-1,-1,-\[Omega],-\[Omega]\[Conjugate]},
{1,1,\[Omega]\[Conjugate],\[Omega],-1,-1,-\[Omega]\[Conjugate],-\[Omega]},{3,-1,0,0,-3,1,0,0}};
AGClasses[24,10]={{{0,0,0}},{{0,1,0},{0,0,1},{0,1,1}},{{2,0,0},{2,1,0},{2,0,1},{2,1,1}},
{{4,0,0},{4,1,0},{4,0,1},{4,1,1}},{{3,0,0}},{{3,1,0},{3,0,1},{3,1,1}},
{{5,0,0},{5,1,0},{5,0,1},{5,1,1}},{{1,0,0},{1,1,0},{1,0,1},{1,1,1}}};
AGCharTab[24,11]={{1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,1,-1,-1},
{1,1,-1,-1,1,1,-1,1,-1},{1,1,-1,-1,1,1,-1,-1,1},
{2,2,-1,-1,-1,-1,2,0,0},{2,2,1,1,-1,-1,-2,0,0},
{2,-2,0,0,-2,2,0,0,0},{2,-2,Sqrt[3],-Sqrt[3],1,-1,0,0,0},
{2,-2,-Sqrt[3],Sqrt[3],1,-1,0,0,0}};
AGClasses[24,11]={{{0,0}},{{6,0}},{{1,0},{11,0}},{{5,0},{7,0}},{{2,0},{10,0}},
{{4,0},{8,0}},{{3,0},{9,0}},{{0,1},{2,1},{4,1},{6,1},{8,1},{10,1}},
{{1,1},{3,1},{5,1},{7,1},{9,1},{11,1}}};
AGCharTab[24,12]=otimesG21[AGCharTab[12,1]];
AGClasses[24,12]={{{0,0}},{{1,0}},{{2,0}},{{3,0}},{{4,0}},{{5,0}},{{6,0}},{{7,0}},
{{8,0}},{{9,0}},{{10,0}},{{11,0}},{{0,1}},{{1,1}},{{2,1}},{{3,1}},
{{4,1}},{{5,1}},{{6,1}},{{7,1}},{{8,1}},{{9,1}},{{10,1}},{{11,1}}};
AGCharTab[32,1]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1},
{1,1,1,1,-1,-1,-1,-1, 1, 1, 1,-1,1,-1},{1,1,1,1,-1,-1,-1,-1,1,1,-1,1,-1,1},
{1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1},{1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1},
{1,1,1,1,-1,-1,1,1,-1,-1,1,-1,-1,1},{1,1,1,1,-1,-1,1,1,-1,-1,-1,1,1,-1},
{2,2,-2,-2,0,0,0,0,2,-2,0,0,0,0},{2,-2,2,-2,2,-2,0,0,0,0,0,0,0,0},
{2,-2,2,-2,-2,2,0,0,0,0,0,0,0,0},{2,-2,-2,2,0,0,2I,-2I,0,0,0,0,0,0},
{2,-2,-2,2,0,0,-2I,2I,0,0,0,0,0,0},{2,2,-2,-2,0,0,0,0,-2,2,0,0,0,0}};
AGClasses[32,1]={{{0,0,0}},{{0,2,0}},{{0,0,2}},{{0,2,2}},{{0,0,1},{0,0,3}},{{0,2,1},{0,2,3}},
{{1,0,1},{1,2,3}},{{1,2,1},{1,0,3}},{{1,0,0},{1,2,0}},{{1,0,2},{1,2,2}},
{{1,1,0},{1,3,0},{1,1,2},{1,3,2}},{{1,1,1},{1,1,3},{1,3,1},{1,3,3}},
{{0,1,0},{0,3,0},{0,1,2},{0,3,2}},{{0,3,1},{0,1,1},{0,3,3},{0,1,3}}};
AGCharTab[32,2]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1},
{1,1,1,1,-1,-1,1,1, -1,- 1, 1,-1,1,-1},{1,1,1,1,-1,-1,1,1,-1,-1,-1,1,-1,1},
{1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1},{1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1},
{1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,1},{1,1,1,1,-1,-1,-1,-1,1,1,-1,1,1,-1},
{2,-2,2,-2,2,-2,0,0,0,0,0,0,0,0},{2,2,-2,-2,0,0,2,-2,0,0,0,0,0,0},
{2,-2,-2,2,0,0,0,0,2,-2,0,0,0,0},{2,-2,2,-2,-2,2,0,0,0,0,0,0,0,0},
{2,2,-2,-2,0,0,-2,2,0,0,0,0,0,0},{2,-2,-2,2,0,0,0,0,-2,2,0,0,0,0}};
AGClasses[32,2]={{{0,0,0}},{{0,2,0}},{{2,0,0}},{{2,2,0}},{{3,0,1},{1,0,1}},{{3,2,1},{1,2,1}},
{{0,1,1},{0,3,1}},{{2,3,1},{2,1,1}},{{1,1,0},{3,3,0}},{{1,3,0},{3,1,0}},
{{0,0,1},{2,0,1},{0,2,1},{2,2,1}},{{1,0,0},{3,0,0},{1,2,0},{3,2,0}},
{{0,1,0},{2,1,0},{0,3,0},{2,3,0}},{{1,1,1},{3,1,1},{1,3,1},{3,3,1}}};
AGCharTab[32,3]=otimesG42[AGCharTab[8,4]];
AGClasses[32,3]={{{0,0,0,0}},{{2,0,0,0}},{{1,0,0,0},{3,0,0,0}},{{0,1,0,0},{2,1,0,0}},
{{1,1,0,0},{3,1,0,0}},{{0,0,1,0}},{{2,0,1,0}},{{1,0,1,0},{3,0,1,0}},
{{0,1,1,0},{2,1,1,0}},{{1,1,1,0},{3,1,1,0}},{{0,0,0,1}},{{2,0,0,1}},
{{1,0,0,1},{3,0,0,1}},{{0,1,0,1},{2,1,0,1}},{{1,1,0,1},{3,1,0,1}},
{{0,0,1,1}},{{2,0,1,1}},{{1,0,1,1},{3,0,1,1}},{{0,1,1,1},{2,1,1,1}},
{{1,1,1,1},{3,1,1,1}}};
AGCharTab[32,4]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1},
{1,-1,1,-1,-1,1,I,-I,I,-I,-I,I,-1,1},
{1,-1,1,-1,-1,1,I,-I,I,-I,I,-I,1,-1},
{1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1},
{1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1},
{1,-1,1,-1,-1,1,-I,I,-I,I,I,-I,-1,1},
{1,-1,1,-1,-1,1,-I,I,-I,I,-I,I,1,-1},
{2,2,2,2,-2,-2,0,0,0,0,0,0,0,0},
{2,-2,2,-2,2,-2,0,0,0,0,0,0,0,0},
{2,2I,-2,-2I,0,0,1-I,1+I,-1+I,-1-I,0,0,0,0},
{2,2I,-2,-2I,0,0,-1+I,-1-I,1-I,1+I,0,0,0,0},
{2,-2I,-2,2I,0,0,1+I,1-I,-1-I,-1+I,0,0,0,0},
{2,-2I,-2,2I,0,0,-1-I,-1+I,1+I,1-I,0,0,0,0}};
AGClasses[32,4]={{{0,0,0}},{{0,1,0}},{{0,2,0}},{{0,3,0}},{{2,0,0},{2,2,0}},{{2,1,0},{2,3,0}},
{{1,0,0},{3,3,0}},{{1,1,0},{3,0,0}},{{1,2,0},{3,1,0}},{{1,3,0},{3,2,0}},
{{1,1,1},{3,0,1},{1,3,1},{3,2,1}},{{1,0,1},{1,2,1},{3,1,1},{3,3,1}},
{{0,1,1},{0,3,1},{2,0,1},{2,2,1}},{{0,0,1},{0,2,1},{2,1,1},{2,3,1}}};
AGCharTab[32,5]=otimesG21[AGCharTab[16,10]];
AGClasses[32,5]={{{0,0,0,0}},{{0,1,0,0}},{{2,0,0,0}},{{2,1,0,0}},{{0,0,1,0},{0,1,1,0}},
{{2,0,1,0},{2,1,1,0}},{{1,0,0,0},{1,1,0,0}},{{3,0,0,0},{3,1,0,0}},
{{1,0,1,0},{1,1,1,0}},{{3,0,1,0},{3,1,1,0}},{{0,0,0,1}},{{0,1,0,1}},
{{2,0,0,1}},{{2,1,0,1}},{{0,0,1,1},{0,1,1,1}},{{2,0,1,1},{2,1,1,1}},
{{1,0,0,1},{1,1,0,1}},{{3,0,0,1},{3,1,0,1}},{{1,0,1,1},{1,1,1,1}},
{{3,0,1,1},{3,1,1,1}}};
AGCharTab[32,6]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1},
{1,1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1},
{1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1},
{1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1},
{1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1},
{1,1,-1,-1,1,1,-1,1,1,-1,1,-1,-1,1},
{1,1,-1,-1,1,1,-1,1,1,-1,-1,1,1,-1},
{2,-2,0,0,2,-2,0,2I,-2I,0,0,0,0,0},
{2,-2,0,0,2,-2,0,-2I,2I,0,0,0,0,0},
{2,2,0,0,-2,-2,2,0,0,-2,0,0,0,0},
{2,2,0,0,-2,-2,-2,0,0,2,0,0,0,0},
{2,-2,2I,-2I,-2,2,0,0,0,0,0,0,0,0},
{2,-2,-2I,2I,-2,2,0,0,0,0,0,0,0,0}};
AGClasses[32,6]={{{0,0,0}},{{2,0,0}},{{1,0,0},{3,2,0}},{{3,0,0},{1,2,0}},{{0,2,0}},{{2,2,0}},
{{0,0,1},{2,0,1}},{{1,0,1},{1,2,1}},{{3,0,1},{3,2,1}},{{0,2,1},{2,2,1}},
{{1,3,0},{3,3,0},{1,1,0},{3,1,0}},{{0,1,0},{0,3,0},{2,1,0},{2,3,0}},
{{1,3,1},{3,3,1},{1,1,1},{3,1,1}},{{0,1,1},{0,3,1},{2,1,1},{2,3,1}}};
AGCharTab[32,7]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1},
{1,1,1,1,1,-1,-1,-1,1,1,1,-1,-1,-1},
{1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1},
{1,1,1,1,-1,1,1,-1,1,1,-1,1,1,-1},
{1,1,1,1,-1,1,1,-1,-1,-1,1,-1,-1,1},
{1,1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,1},
{1,1,1,1,-1,-1,-1,1,-1,-1,1,1,1,-1},
{2,-2,2,-2,0,0,0,0,0,0,0,2,-2,0},
{2,-2,2,-2,0,0,0,0,0,0,0,-2,2,0},
{2,-2,-2,2,0,0,0,0,2,-2,0,0,0,0},
{2,-2,-2,2,0,0,0,0,-2,2,0,0,0,0},
{2,2,-2,-2,0,2I,-2I,0,0,0,0,0,0,0},
{2,2,-2,-2,0,-2I,2I,0,0,0,0,0,0,0}};
AGClasses[32,7]={{{0,0,0}},{{2,0,0}},{{0,2,0}},{{2,2,0}},{{1,0,0},{3,0,0},{1,2,0},{3,2,0}},
{{0,1,0},{2,1,0}},{{0,3,0},{2,3,0}},{{1,1,0},{3,1,0},{1,3,0},{3,3,0}},
{{0,0,1},{2,2,1}},{{2,0,1},{0,2,1}},{{1,0,1},{3,0,1},{1,2,1},{3,2,1}},
{{0,1,1},{0,3,1}},{{2,1,1},{2,3,1}},{{1,1,1},{3,1,1},{1,3,1},{3,3,1}}};
AGCharTab[32,8]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,1,1,-1,-1},
{1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1},
{1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,1,1},
{1,-1,1,-1,1,-1,I,-I,I,-I,1,-1,1,-1,1,-1,I,-I,I,-I},
{1,-1,1,-1,-1,1,I,-I,-I,I,1,-1,1,-1,-1,1,I,-I,-I,I},
{1,-1,1,-1,1,-1,-I,I,-I,I,1,-1,1,-1,1,-1,-I,I,-I,I},
{1,-1,1,-1,-1,1,-I,I,I,-I,1,-1,1,-1,-1,1,-I,I,I,-I},
{2,-2 I,-2,2 I,0,0,0,0,0,0,2,-2 I,-2,2 I,0,0,0,0,0,0},
{2,2 I,-2,-2 I,0,0,0,0,0,0,2,2 I,-2,-2 I,0,0,0,0,0,0},
{1,I,-1,-I,I,-1,\[Theta],-\[Theta]\[Conjugate],-\[Theta]\[Conjugate],-\[Theta],-1,-I,1,I,-I,1,-\[Theta],\[Theta]\[Conjugate],\[Theta]\[Conjugate],\[Theta]},
{1,I,-1,-I,I,-1,-\[Theta],\[Theta]\[Conjugate],\[Theta]\[Conjugate],\[Theta],-1,-I,1,I,-I,1,\[Theta],-\[Theta]\[Conjugate],-\[Theta]\[Conjugate],-\[Theta]},
{1,-I,-1,I,I,1,\[Theta]\[Conjugate],-\[Theta],\[Theta],\[Theta]\[Conjugate],-1,I,1,-I,-I,-1,-\[Theta]\[Conjugate],\[Theta],-\[Theta],-\[Theta]\[Conjugate]},
{1,-I,-1,I,I,1,-\[Theta]\[Conjugate],\[Theta],-\[Theta],-\[Theta]\[Conjugate],-1,I,1,-I,-I,-1,\[Theta]\[Conjugate],-\[Theta],\[Theta],\[Theta]\[Conjugate]},
{1,I,-1,-I,-I,1,\[Theta],-\[Theta]\[Conjugate],\[Theta]\[Conjugate],\[Theta],-1,-I,1,I,I,-1,-\[Theta],\[Theta]\[Conjugate],-\[Theta]\[Conjugate],-\[Theta]},
{1,I,-1,-I,-I,1,-\[Theta],\[Theta]\[Conjugate],-\[Theta]\[Conjugate],-\[Theta],-1,-I,1,I,I,-1,\[Theta],-\[Theta]\[Conjugate],\[Theta]\[Conjugate],\[Theta]},
{1,-I,-1,I,-I,-1,\[Theta]\[Conjugate],-\[Theta],-\[Theta],-\[Theta]\[Conjugate],-1,I,1,-I,I,1,-\[Theta]\[Conjugate],\[Theta],\[Theta],\[Theta]\[Conjugate]},
{1,-I,-1,I,-I,-1,-\[Theta]\[Conjugate],\[Theta],\[Theta],\[Theta]\[Conjugate],-1,I,1,-I,I,1,\[Theta]\[Conjugate],-\[Theta],-\[Theta],-\[Theta]\[Conjugate]},
{2,-2,2,-2,0,0,0,0,0,0,-2,2,-2,2,0,0,0,0,0,0},
{2,2,2,2,0,0,0,0,0,0,-2,-2,-2,-2,0,0,0,0,0,0}};
AGClasses[32,8]={{{0,0}},{{6,2}},{{4,0}},{{2,2}},{{0,1},{4,3}},{{6,3},{2,1}},
{{1,0},{5,2}},{{7,2},{3,0}},{{1,1},{5,3}},{{7,3},{3,1}},
{{0,2}},{{6,0}},{{4,2}},{{2,0}},{{0,3},{4,1}},{{6,1},{2,3}},
{{1,2},{5,0}},{{7,0},{3,2}},{{1,3},{5,1}},{{7,1},{3,3}}};
AGCharTab[32,9]=otimesG21[AGCharTab[16,14]];
AGClasses[32,9]={{{0,0,0}},{{4,0,0}},{{2,0,0},{6,0,0}},{{1,0,0},{7,0,0}},{{3,0,0},{5,0,0}},
{{0,1,0},{2,1,0},{4,1,0},{6,1,0}},{{1,1,0},{3,1,0},{5,1,0},{7,1,0}},
{{0,0,1}},{{4,0,1}},{{2,0,1},{6,0,1}},{{1,0,1},{7,0,1}},{{3,0,1},{5,0,1}},
{{0,1,1},{2,1,1},{4,1,1},{6,1,1}},{{1,1,1},{3,1,1},{5,1,1},{7,1,1}}};
AGCharTab[32,10]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1},{1,1,1,1,1,-1,-1,1,1,1,1,1,-1,-1},
{1,1,1,-1,-1,1,-1,1,1,1,-1,-1,1,-1},{1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,1},
{2,2,-2,0,0,0,0,2,2,-2,0,0,0,0},{2,-2,0,Sqrt[2],-Sqrt[2],0,0,2,-2,0,Sqrt[2],-Sqrt[2],0,0},
{2,-2,0,-Sqrt[2],Sqrt[2],0,0,2,-2,0,-Sqrt[2],Sqrt[2],0,0},{1,1,1,1,1,I,I,-1,-1,-1,-1,-1,-I,-I},
{1,1,1,-1,-1,I,-I,-1,-1,-1,1,1,-I,I},{1,1,1,1,1,-I,-I,-1,-1,-1,-1,-1,I,I},
{1,1,1,-1,-1,-I,I,-1,-1,-1,1,1,I,-I},{2,-2,0,Sqrt[2],-Sqrt[2],0,0,-2,2,0,-Sqrt[2],Sqrt[2],0,0},
{2,-2,0,-Sqrt[2],Sqrt[2],0,0,-2,2,0,Sqrt[2],-Sqrt[2],0,0},{2,2,-2,0,0,0,0,-2,-2,2,0,0,0,0}};
AGClasses[32,10]={{{0,0}},{{4,0}},{{2,0},{6,0}},{{1,0},{7,0}},{{3,0},{5,0}},
{{0,1},{2,1},{4,1},{6,1}},{{1,1},{3,1},{5,1},{7,1}},
{{0,2}},{{4,2}},{{2,2},{6,2}},{{1,2},{7,2}},{{3,2},{5,2}},
{{0,3},{2,3},{4,3},{6,3}},{{1,3},{3,3},{5,3},{7,3}}};
AGCharTab[32,11]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1},
{1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1},{1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1},
{2,2,-2,2,2,-2,0,0,0,0,0,0,0,0},{2,-2,0,2,-2,0,I Sqrt[2],I Sqrt[2],-I Sqrt[2],-I Sqrt[2],0,0,0,0},
{2,-2,0,2,-2,0,-I Sqrt[2],-I Sqrt[2],I Sqrt[2],I Sqrt[2],0,0,0,0},{1,1,-1,-1,-1,1,I,-I,I,-I,-1,1,I,-I},
{1,1,-1,-1,-1,1,I,-I,I,-I,1,-1,-I,I},{1,1,-1,-1,-1,1,-I,I,-I,I,1,-1,I,-I},
{1,1,-1,-1,-1,1,-I,I,-I,I,-1,1,-I,I},{2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0},
{2,-2,0,-2,2,0,-Sqrt[2],Sqrt[2],Sqrt[2],-Sqrt[2],0,0,0,0},{2,-2,0,-2,2,0,Sqrt[2],-Sqrt[2],-Sqrt[2],Sqrt[2],0,0,0,0}};
AGClasses[32,11]={{{0,0}},{{4,0}},{{2,0},{6,0}},{{0,2}},{{4,2}},{{2,2},{6,2}},
{{1,0},{3,2}},{{1,2},{3,0}},{{5,0},{7,2}},{{5,2},{7,0}},
{{1,1},{3,3},{5,1},{7,3}},{{1,3},{3,1},{5,3},{7,1}},
{{0,1},{2,3},{4,1},{6,3}},{{0,3},{2,1},{4,3},{6,1}}};
AGCharTab[32,12]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1},
{1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1},
{1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,-1},
{1,1,-1,-1,1,1,-1,-1,1,-1,1,-1,I,-I,I,-I,I,-I,I,-I},
{1,1,-1,-1,1,1,-1,-1,1,-1,1,-1,-I,I,-I,I,-I,I,-I,I},
{1,1,-1,-1,1,1,-1,-1,-1,1,-1,1,-I,I,I,-I,-I,I,I,-I},
{1,1,-1,-1,1,1,-1,-1,-1,1,-1,1,I,-I,-I,I,I,-I,-I,I},
{2,-2,2,-2,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0},
{2,-2,-2,2,2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0},
{1,1,I,I,-1,-1,-I,-I,1,I,-1,-I,\[Theta],-\[Theta]\[Conjugate],\[Theta],-\[Theta]\[Conjugate],-\[Theta],\[Theta]\[Conjugate],-\[Theta],\[Theta]\[Conjugate]},
{1,1,I,I,-1,-1,-I,-I,-1,-I,1,I,-\[Theta],\[Theta]\[Conjugate],\[Theta],-\[Theta]\[Conjugate],\[Theta],-\[Theta]\[Conjugate],-\[Theta],\[Theta]\[Conjugate]},
{1,1,I,I,-1,-1,-I,-I,1,I,-1,-I,-\[Theta],\[Theta]\[Conjugate],-\[Theta],\[Theta]\[Conjugate],\[Theta],-\[Theta]\[Conjugate],\[Theta],-\[Theta]\[Conjugate]},
{1,1,I,I,-1,-1,-I,-I,-1,-I,1,I,\[Theta],-\[Theta]\[Conjugate],-\[Theta],\[Theta]\[Conjugate],-\[Theta],\[Theta]\[Conjugate],\[Theta],-\[Theta]\[Conjugate]},
{1,1,-I,-I,-1,-1,I,I,1,-I,-1,I,-\[Theta]\[Conjugate],\[Theta],-\[Theta]\[Conjugate],\[Theta],\[Theta]\[Conjugate],-\[Theta],\[Theta]\[Conjugate],-\[Theta]},
{1,1,-I,-I,-1,-1,I,I,1,-I,-1,I,\[Theta]\[Conjugate],-\[Theta],\[Theta]\[Conjugate],-\[Theta],-\[Theta]\[Conjugate],\[Theta],-\[Theta]\[Conjugate],\[Theta]},
{1,1,-I,-I,-1,-1,I,I,-1,I,1,-I,\[Theta]\[Conjugate],-\[Theta],-\[Theta]\[Conjugate],\[Theta],-\[Theta]\[Conjugate],\[Theta],\[Theta]\[Conjugate],-\[Theta]},
{1,1,-I,-I,-1,-1,I,I,-1,I,1,-I,-\[Theta]\[Conjugate],\[Theta],\[Theta]\[Conjugate],-\[Theta],\[Theta]\[Conjugate],-\[Theta],-\[Theta]\[Conjugate],\[Theta]},
{2,-2,2 I,-2 I,-2,2,-2 I,2 I,0,0,0,0,0,0,0,0,0,0,0,0},
{2,-2,-2 I,2 I,-2,2,2 I,-2 I,0,0,0,0,0,0,0,0,0,0,0,0}};
AGClasses[32,12]={{{0,0,0}},{{0,1,0}},{{2,0,0}},{{2,1,0}},{{4,0,0}},{{4,1,0}},
{{6,0,0}},{{6,1,0}},{{0,0,1},{0,1,1}},{{2,0,1},{2,1,1}},
{{4,0,1},{4,1,1}},{{6,0,1},{6,1,1}},{{1,0,0},{1,1,0}},
{{3,0,0},{3,1,0}},{{1,0,1},{1,1,1}},{{3,0,1},{3,1,1}},
{{5,0,0},{5,1,0}},{{7,0,0},{7,1,0}},{{5,0,1},{5,1,1}},{{7,0,1},{7,1,1}}};
AGCharTab[32,13]={{1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,1,1, 1,1,-1,-1,-1,-1,-1,-1,-1,-1},
{1,-1,1,-1,1,-1,1,-1,1,1, 1,1,1,-1,1,-1,1,-1,1,-1},
{1,-1,1,-1,1,-1,1,-1,1,1, 1,1,-1,1,-1,1,-1,1,-1,1},
{1,I,-1,-I,I,-1,-I,1,-1,1, -I,I,1,I,-1,-I,I,-1,-I,1},
{1,I,-1,-I,I,-1,-I,1,-1,1, -I,I,-1,-I,1,I,-I,1,I,-1},
{1,-I,-1,I,I,1,-I,-1,-1,1, -I,I,1,-I,-1,I,I,1,-I,-1},
{1,-I,-1,I,I,1,-I,-1,-1,1, -I,I,-1,I,1,-I,-I,-1,I,1},
{1,1,1,1,-1,-1,-1,-1,1,1, -1,-1,1,1,1,1,-1,-1,-1,-1},
{1,1,1,1,-1,-1,-1,-1,1,1, -1,-1,-1,-1,-1,-1,1,1,1,1},
(*Note that the R11-R14 data in the book have errors!*)
{1,-1,1,-1,-1,1,-1,1,1,1, -1,-1,1,-1,1,-1,-1,1,-1,1},
{1,-1,1,-1,-1,1,-1,1,1,1, -1,-1,-1,1,-1,1,1,-1,1,-1},
{1,I,-1,-I,-I,1,I,-1,-1,1, I,-I,1,I,-1,-I,-I,1,I,-1},
{1,I,-1,-I,-I,1,I,-1,-1,1, I,-I,-1,-I,1,I,I,-1,-I,1},
{1,-I,-1,I,-I,-1,I,1,-1,1, I,-I,1,-I,-1,I,-I,-1,I,1},
{1,-I,-1,I,-I,-1,I,1,-1,1, I,-I,-1,I,1,-I,I,1,-I,-1},
{2,0,-2,0,2,0,-2,0,2,-2, 2,-2,0,0,0,0,0,0,0,0},
{2,0,2,0,2 I,0,2 I,0,-2,-2, -2 I,-2 I,0,0,0,0,0,0,0,0},
{2,0,-2,0,-2,0,2,0,2,-2, -2,2,0,0,0,0,0,0,0,00},
{2,0,2,0,-2 I,0,-2 I,0,-2,-2, 2I,2I,0,0,0,0,0,0,0,0}};
AGClasses[32,13]={{{0,0,0}},{{1,0,0},{3,2,0}},{{2,0,0}},{{3,0,0},{1,2,0}},
{{0,1,0}},{{1,1,0},{3,3,0}},{{2,1,0}},{{3,1,0},{1,3,0}},
{{0,2,0}},{{2,2,0}},{{0,3,0}},{{2,3,0}},{{0,0,1},{2,2,1}},
{{1,0,1},{3,2,1}},{{2,0,1},{0,2,1}},{{3,0,1},{1,2,1}},
{{0,1,1},{2,3,1}},{{1,1,1},{3,3,1}},{{2,1,1},{0,3,1}},{{3,1,1},{1,3,1}}};
AGCharTab[32,14]=otimesG21[AGCharTab[16,8]];
AGClasses[32,14]={{{0,0,0}},{{2,0,0}},{{0,2,0}},{{2,2,0}},{{1,0,0},{3,0,0}},{{1,2,0},{3,2,0}},
{{0,1,0},{2,1,0}},{{1,1,0},{3,1,0}},{{0,3,0},{2,3,0}},{{1,3,0},{3,3,0}},
{{0,0,1}},{{2,0,1}},{{0,2,1}},{{2,2,1}},{{1,0,1},{3,0,1}},{{1,2,1},{3,2,1}},
{{0,1,1},{2,1,1}},{{1,1,1},{3,1,1}},{{0,3,1},{2,3,1}},{{1,3,1},{3,3,1}}};
AGCharTab[32,15]=otimesG21[AGCharTab[16,11]];
AGClasses[32,15]={{{0,0,0,0}},{{2,0,0,0}},{{1,0,0,0},{3,0,0,0}},{{0,1,0,0},{2,1,0,0}},
{{1,1,0,0},{3,1,0,0}},{{0,0,1,0}},{{2,0,1,0}},{{1,0,1,0},{3,0,1,0}},
{{0,1,1,0},{2,1,1,0}},{{1,1,1,0},{3,1,1,0}},{{0,0,0,1}},{{2,0,0,1}},
{{1,0,0,1},{3,0,0,1}},{{0,1,0,1},{2,1,0,1}},{{1,1,0,1},{3,1,0,1}},
{{0,0,1,1}},{{2,0,1,1}},{{1,0,1,1},{3,0,1,1}},{{0,1,1,1},{2,1,1,1}},
{{1,1,1,1},{3,1,1,1}}};
AGCharTab[32,16]=otimesG41[AGCharTab[8,5]];
AGClasses[32,16]={{{0,0,0}},{{2,0,0}},{{1,0,0},{3,0,0}},{{0,1,0},{2,1,0}},{{1,1,0},{3,1,0}},
{{0,0,1}},{{2,0,1}},{{1,0,1},{3,0,1}},{{0,1,1},{2,1,1}},{{1,1,1},{3,1,1}},
{{0,0,2}},{{2,0,2}},{{1,0,2},{3,0,2}},{{0,1,2},{2,1,2}},{{1,1,2},{3,1,2}},
{{0,0,3}},{{2,0,3}},{{1,0,3},{3,0,3}},{{0,1,3},{2,1,3}},{{1,1,3},{3,1,3}}};
AGCharTab[32,17]=otimesG41[AGCharTab[8,1]];
AGClasses[32,17]={{{0,0}},{{1,0}},{{2,0}},{{3,0}},{{4,0}},{{5,0}},{{6,0}},{{7,0}},
{{0,1}},{{1,1}},{{2,1}},{{3,1}},{{4,1}},{{5,1}},{{6,1}},{{7,1}},
{{0,2}},{{1,2}},{{2,2}},{{3,2}},{{4,2}},{{5,2}},{{6,2}},{{7,2}},
{{0,3}},{{1,3}},{{2,3}},{{3,3}},{{4,3}},{{5,3}},{{6,3}},{{7,3}}};
AGCharTab[48,1]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},{1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,1,1,-1},
{1,1,-1,1,1,-1,-1,1,1,-1,1,-1,1,-1,1},{1,1,1,1,1,1,-1,-1,-1,1,1,1,1,-1,-1},
{1,1,-1,1,1,-1,-1,1,1,1,-1,1,-1,1,-1},{1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1},
{1,1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,-1,1},{1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1},
{2,2,2,-1,-1,-1,0,0,0,2,2,-1,-1,0,0},{2,2,-2,-1,-1,1,0,0,0,-2,2,1,-1,0,0},
{2,2,-2,-1,-1,1,0,0,0,2,-2,-1,1,0,0},{2,2,2,-1,-1,-1,0,0,0,-2,-2,1,1,0,0},
{2,-2,0,2,-2,0,0,2,-2,0,0,0,0,0,0},{2,-2,0,2,-2,0,0,-2,2,0,0,0,0,0,0},
{4,-4,0,-2,2,0,0,0,0,0,0,0,0,0,0}};
AGClasses[48,1]={{{0,0,0}},{{6,0,0}},{{3,0,1},{9,0,1}},{{4,0,0},{8,0,0}},{{2,0,0},{10,0,0}},
{{1,0,1},{5,0,1},{7,0,1},{11,0,1}},{{1,1,0},{3,1,0},{5,1,0},{7,1,0},{9,1,0},{11,1,0}},
{{0,1,1},{4,1,1},{8,1,1}},{{2,1,1},{6,1,1},{10,1,1}},{{0,0,1},{6,0,1}},
{{3,0,0},{9,0,0}},{{2,0,1},{4,0,1},{8,0,1},{10,0,1}},
{{1,0,0},{5,0,0},{7,0,0},{11,0,0}},
{{0,1,0},{2,1,0},{4,1,0},{6,1,0},{8,1,0},{10,1,0}},
{{1,1,1},{3,1,1},{5,1,1},{7,1,1},{9,1,1},{11,1,1}}};
AGCharTab[48,2]=otimesG21[AGCharTab[24,1]];
AGClasses[48,2]={{{0,0,0,0}},{{2,0,0,0}},{{0,1,0,0},{0,2,0,0}},{{2,1,0,0},{2,2,0,0}},
{{0,0,1,0},{2,0,1,0}},{{0,2,1,0},{2,1,1,0}},{{0,1,1,0},{2,2,1,0}},
{{1,0,0,0},{1,1,0,0},{1,2,0,0},{3,0,0,0},{3,1,0,0},{3,2,0,0}},
{{1,0,1,0},{1,1,1,0},{1,2,1,0},{3,0,1,0},{3,1,1,0},{3,2,1,0}},{{0,0,0,1}},
{{2,0,0,1}},{{0,1,0,1},{0,2,0,1}},{{2,1,0,1},{2,2,0,1}},{{0,0,1,1},{2,0,1,1}},
{{0,2,1,1},{2,1,1,1}},{{0,1,1,1},{2,2,1,1}},
{{1,0,0,1},{1,1,0,1},{1,2,0,1},{3,0,0,1},{3,1,0,1},{3,2,0,1}},
{{1,0,1,1},{1,1,1,1},{1,2,1,1},{3,0,1,1},{3,1,1,1},{3,2,1,1}}};
AGCharTab[48,3]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,\[Omega],\[Omega],\[Omega],\[Omega],\[Omega]\[Conjugate],\[Omega]\[Conjugate],\[Omega]\[Conjugate],\[Omega]\[Conjugate]},
{1,1,1,1,1,1,\[Omega]\[Conjugate],\[Omega]\[Conjugate],\[Omega]\[Conjugate],\[Omega]\[Conjugate],\[Omega],\[Omega],\[Omega],\[Omega]},
{1,-1,1,-1,-1,1,1,-1,1,-1,1,-1,1,-1},
{1,-1,1,-1,-1,1,\[Omega],-\[Omega],\[Omega],-\[Omega],\[Omega]\[Conjugate],-\[Omega]\[Conjugate],\[Omega]\[Conjugate],-\[Omega]\[Conjugate]},
{1,-1,1,-1,-1,1,\[Omega]\[Conjugate],-\[Omega]\[Conjugate],\[Omega]\[Conjugate],-\[Omega]\[Conjugate],\[Omega],-\[Omega],\[Omega],-\[Omega]},
{2,2I,-2,-2I,0,0,-1,-I,1,I,-1,-I,1,I},
{2,2I,-2,-2I,0,0,-\[Omega],-I \[Omega],\[Omega],I \[Omega],-\[Omega]\[Conjugate],-I \[Omega]\[Conjugate],\[Omega]\[Conjugate],I \[Omega]\[Conjugate]},
{2,2I,-2,-2I,0,0,-\[Omega]\[Conjugate],-I \[Omega]\[Conjugate],\[Omega]\[Conjugate],I \[Omega]\[Conjugate],-\[Omega],-I \[Omega],\[Omega],I \[Omega]},
{2,-2I,-2,2I,0,0,-1,I,1,-I,-1,I,1,-I},
{2,-2I,-2,2I,0,0,-\[Omega]\[Conjugate],I \[Omega]\[Conjugate],\[Omega]\[Conjugate],-I \[Omega]\[Conjugate],-\[Omega],I \[Omega],\[Omega],-I \[Omega]},
{2,-2I,-2,2I,0,0,-\[Omega],I \[Omega],\[Omega],-I \[Omega],-\[Omega]\[Conjugate],I \[Omega]\[Conjugate],\[Omega]\[Conjugate],-I \[Omega]\[Conjugate]},
{3,3,3,3,-1,-1,0,0,0,0,0,0,0,0},
{3,-3,3,-3,1,-1,0,0,0,0,0,0,0,0}};
AGClasses[48,3]={{{0,0,0}},{{3,0,0}},{{6,0,0}},{{9,0,0}},
{{0,1,0},{0,0,1},{6,1,0},{6,0,1},{3,1,1},{9,1,1}},
{{0,1,1},{3,1,0},{3,0,1},{6,1,1},{9,1,0},{9,0,1}},{{4,0,0},{1,1,0},{7,0,1},{4,1,1}},
{{7,0,0},{4,1,0},{10,0,1},{7,1,1}},{{10,0,0},{7,1,0},{1,0,1},{10,1,1}},
{{1,0,0},{10,1,0},{4,0,1},{1,1,1}},{{8,0,0},{11,1,0},{5,0,1},{2,1,1}},
{{11,0,0},{2,1,0},{8,0,1},{5,1,1}},{{2,0,0},{5,1,0},{11,0,1},{8,1,1}},
{{5,0,0},{8,1,0},{2,0,1},{11,1,1}}};
AGCharTab[48,4]=otimesG21[AGCharTab[24,9]];
AGClasses[48,4]={{{0,0,0,0}},{{3,0,0,0}},
{{0,1,0,0},{0,0,1,0},{3,1,0,0},{3,0,1,0},{0,1,1,0},{3,1,1,0}},
{{1,0,0,0},{1,1,0,0},{1,1,1,0},{1,0,1,0}},{{4,0,0,0},{4,1,0,0},{4,1,1,0},{4,0,1,0}},
{{2,0,0,0},{5,0,1,0},{5,1,1,0},{5,1,0,0}},{{5,0,0,0},{2,0,1,0},{2,1,1,0},{2,1,0,0}},
{{0,0,0,1}},{{3,0,0,1}},
{{0,1,0,1},{0,0,1,1},{3,1,0,1},{3,0,1,1},{0,1,1,1},{3,1,1,1}},
{{1,0,0,1},{1,1,0,1},{1,1,1,1},{1,0,1,1}},{{4,0,0,1},{4,1,0,1},{4,1,1,1},{4,0,1,1}},
{{2,0,0,1},{5,0,1,1},{5,1,1,1},{5,1,0,1}},{{5,0,0,1},{2,0,1,1},{2,1,1,1},{2,1,0,1}}};
AGCharTab[48,5]=otimesG21[AGCharTab[24,8]];
AGClasses[48,5]={{{0,0,0,0}},{{3,0,0,0}},{{0,1,0,0},{0,0,1,0},{3,1,1,0}},
{{3,1,0,0},{3,0,1,0},{0,1,1,0}},{{1,1,0,0},{1,0,1,0},{4,0,0,0},{4,1,1,0}},
{{4,1,0,0},{4,0,1,0},{1,0,0,0},{1,1,1,0}},{{2,0,0,0},{2,1,1,0},{5,1,0,0},{5,0,1,0}},
{{5,0,0,0},{5,1,1,0},{2,1,0,0},{2,0,1,0}},
{{0,0,0,1}},{{3,0,0,1}},{{0,1,0,1},{0,0,1,1},{3,1,1,1}},
{{3,1,0,1},{3,0,1,1},{0,1,1,1}},{{1,1,0,1},{1,0,1,1},{4,0,0,1},{4,1,1,1}},
{{4,1,0,1},{4,0,1,1},{1,0,0,1},{1,1,1,1}},{{2,0,0,1},{2,1,1,1},{5,1,0,1},{5,0,1,1}},
{{5,0,0,1},{5,1,1,1},{2,1,0,1},{2,0,1,1}}};
AGCharTab[48,6]={{1,1,1,1,1,1,1,1},{1,1,1,1,1,-1,-1,-1},
{2,2,2,-1,-1,0,0,0},{2,-2,0,-1,1,-I Sqrt[2],I Sqrt[2],0},
{2,-2,0,-1,1,I Sqrt[2],-I Sqrt[2],0},{3,3,-1,0,0,1,1,-1},
{3,3,-1,0,0,-1,-1,1},{4,-4,0,1,-1,0,0,0}};
AGClasses[48,6]={{{0,0,0,0}},{{2,0,0,0}},
{{1,0,0,0},{0,1,0,0},{1,1,0,0},{3,0,0,0},{2,1,0,0},{3,1,0,0}},
{{0,0,1,0},{0,0,2,0},{3,0,1,0},{2,1,1,0},{1,1,1,0},{0,1,2,0},{1,0,2,0},{3,1,2,0}},
{{2,0,1,0},{2,0,2,0},{1,0,1,0},{0,1,1,0},{3,1,1,0},{2,1,2,0},{3,0,2,0},{1,1,2,0}},
{{0,1,0,1},{3,0,0,1},{2,1,1,1},{3,1,1,1},{1,0,2,1},{1,1,2,1}},
{{2,1,0,1},{1,0,0,1},{0,1,1,1},{1,1,1,1},{3,0,2,1},{3,1,2,1}},
{{1,1,0,1},{3,1,0,1},{0,0,1,1},{2,0,1,1},{0,0,2,1},{2,0,2,1},
{0,0,0,1},{2,0,0,1},{3,0,1,1},{1,0,1,1},{0,1,2,1},{2,1,2,1}}};
AGCharTab[48,7]={{1,1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,-1,-1,-1,-1},
{1,-1,-1,1,1,-1,-1,1,-1,1},{1,-1,-1,1,1,-1,1,-1,1,-1},
{2,2,2,2,-1,-1,0,0,0,0},{2,-2,-2,2,-1,1,0,0,0,0},
{3,3,-1,-1,0,0,1,1,-1,-1},{3,3,-1,-1,0,0,-1,-1,1,1},
{3,-3,1,-1,0,0,1,-1,-1,1},{3,-3,1,-1,0,0,-1,1,1,-1}};
AGClasses[48,7]={{{0,0,0,0}},{{3,0,0,0}},{{0,1,0,0},{0,0,1,0},{3,1,1,0}},
{{3,1,0,0},{3,0,1,0},{0,1,1,0}},
{{1,0,1,0},{4,0,0,0},{1,1,0,0},{4,1,1,0},{5,1,0,0},{2,0,0,0},{2,1,1,0},{5,0,1,0}},
{{4,0,1,0},{1,0,0,0},{4,1,0,0},{1,1,1,0},{2,1,0,0},{5,0,0,0},{5,1,1,0},{2,0,1,0}},
{{4,0,0,1},{5,1,0,1},{3,1,0,1},{1,0,1,1},{2,0,0,1},{3,0,1,1}},
{{1,0,0,1},{2,1,0,1},{0,1,0,1},{4,0,1,1},{5,0,0,1},{0,0,1,1}},
{{0,0,0,1},{0,1,1,1},{2,1,1,1},{4,1,1,1},{5,0,1,1},{1,1,0,1}},
{{3,0,0,1},{3,1,1,1},{5,1,1,1},{1,1,1,1},{2,0,1,1},{4,1,0,1}}};
AGCharTab[48,8]={{1,1,1,1,1,1,1,1,1,1},{1,1,1,1,1,1,-1,-1,-1,-1},
{1,-1,1,-1,1,-1,I,-I,I,-I},{1,-1,1,-1,1,-1,-I,I,-I,I},
{2,2,-1,-1,2,2,0,0,0,0},{2,-2,-1,1,2,-2,0,0,0,0},
{3,3,0,0,-1,-1,1,1,-1,-1},{3,3,0,0,-1,-1,-1,-1,1,1},
{3,-3,0,0,-1,1,I,-I,-I,I},{3,-3,0,0,-1,1,-I,I,I,-I}};
AGClasses[48,8]={{{0,0,0}},{{0,2,0}},
{{3,1,0},{1,3,0},{0,0,1},{2,2,1},{1,3,1},{2,2,2},{0,0,2},{3,1,1}},
{{3,3,0},{1,1,0},{0,2,1},{2,0,1},{1,1,1},{2,0,2},{0,2,2},{3,3,1}},
{{2,2,0},{3,1,2},{1,3,2}},{{2,0,0},{3,3,2},{1,1,2}},
{{0,1,0},{1,0,1},{0,1,1},{2,3,2},{3,2,2},{0,1,2}},
{{0,3,0},{1,2,1},{0,3,1},{2,1,2},{3,0,2},{0,3,2}},
{{1,0,0},{1,0,2},{2,3,0},{3,2,0},{2,3,1},{3,2,1}},
{{1,2,0},{1,2,2},{2,1,0},{3,0,0},{2,1,1},{3,0,1}}};
AGCharTab[48,9]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1},
{1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1},
{1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1},
{1,1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,I,-I,I,-I},
{1,1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-I,I,-I,I},
{1,1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1,I,-I,-I,I},
{1,1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-I,I,I,-I},
{2,-2,2,-2,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0},
{2,-2,2,-2,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0},
{2,2,-1,-1,2,2,-1,-1,2,2,-1,-1,-1,-1,0,0,0,0},
{2,2,-1,-1,2,2,-1,-1,-2,-2,1,1,1,1,0,0,0,0},
{2,-2,-1,1,2,-2,-1,1,0,0,-I Sqrt[3],-I Sqrt[3],I Sqrt[3],I Sqrt[3],0,0,0,0},
{2,-2,-1,1,2,-2,-1,1,0,0,I Sqrt[3],I Sqrt[3],-I Sqrt[3],-I Sqrt[3],0,0,0,0},
{2,2,-1,-1,-2,-2,1,1,2,-2,-1,1,-1,1,0,0,0,0},
{2,2,-1,-1,-2,-2,1,1,-2,2,1,-1,1,-1,0,0,0,0},
{2,-2,-1,1,-2,2,1,-1,0,0,-I Sqrt[3],I Sqrt[3],I Sqrt[3],-I Sqrt[3],0,0,0,0},
{2,-2,-1,1,-2,2,1,-1,0,0,I Sqrt[3],-I Sqrt[3],-I Sqrt[3],I Sqrt[3],0,0,0,0}};
AGClasses[48,9]={{{0,0,0}},{{3,0,0}},{{2,0,0},{4,0,0}},{{1,0,0},{5,0,0}},{{0,2,0}},{{3,2,0}},
{{2,2,0},{4,2,0}},{{1,2,0},{5,2,0}},{{0,0,1},{3,0,1}},{{0,2,1},{3,2,1}},
{{2,0,1},{1,0,1}},{{2,2,1},{1,2,1}},{{5,0,1},{4,0,1}},{{5,2,1},{4,2,1}},
{{0,1,0},{1,1,0},{2,1,0},{3,1,0},{4,1,0},{5,1,0}},
{{0,3,0},{1,3,0},{2,3,0},{3,3,0},{4,3,0},{5,3,0}},
{{0,1,1},{1,1,1},{2,1,1},{3,1,1},{4,1,1},{5,1,1}},
{{0,3,1},{1,3,1},{2,3,1},{3,3,1},{4,3,1},{5,3,1}}};
AGCharTab[48,10]={{1,1,1,1,1,1,1,1},{1,1,1,1,1,-1,-1,-1},
{2,2,2,-1,-1,0,0,0},{2,-2,0,1,-1,Sqrt[2],-Sqrt[2],0},
{2,-2,0,1,-1,-Sqrt[2],Sqrt[2],0},{3,3,-1,0,0,1,1,-1},
{3,3,-1,0,0,-1,-1,1},{4,-4,0,-1,1,0,0,0}};
AGClasses[48,10]={{{0,0,0}},{{4,0,0}},{{2,0,0},{5,1,1},{7,1,1},{6,0,0},{1,1,1},{3,1,1}},
{{4,1,0},{6,1,0},{5,0,1},{7,0,1},{4,2,0},{1,2,1},{3,2,1},{2,2,0}},
{{0,1,0},{2,1,0},{1,0,1},{3,0,1},{0,2,0},{5,2,1},{7,2,1},{6,2,0}},
{{1,0,0},{3,2,0},{6,0,1},{7,0,0},{2,2,1},{5,1,0}},
{{5,0,0},{7,2,0},{2,0,1},{3,0,0},{6,2,1},{1,1,0}},
{{3,1,0},{0,0,1},{1,2,0},{6,1,1},{4,2,1},{4,1,1},
{7,1,0},{4,0,1},{5,2,0},{2,1,1},{0,2,1},{0,1,1}}};
AGCharTab[48,11]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1},
{1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega],1,\[Omega],\[Omega]\[Conjugate],1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega],1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega],1,\[Omega],\[Omega]\[Conjugate],1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega]},
{1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega],1,\[Omega],\[Omega]\[Conjugate],-1,\[Omega]\[Conjugate],-\[Omega],1,-\[Omega]\[Conjugate],\[Omega],1,-\[Omega]\[Conjugate],\[Omega],-1,\[Omega]\[Conjugate],-\[Omega],1,\[Omega],\[Omega]\[Conjugate],-1,\[Omega]\[Conjugate],-\[Omega],1,-\[Omega]\[Conjugate],\[Omega]},
{1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate]},
{1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],-1,-\[Omega],-\[Omega]\[Conjugate],-1,-\[Omega],-\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],-1,-\[Omega],-\[Omega]\[Conjugate],-1,-\[Omega],-\[Omega]\[Conjugate]},
{1,-1,1,-1,1,-1,1,1,1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,1,1,1,-1,1,-1,1,-1},
{1,-1,1,-1,1,-1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,1,-1,1,-1,1,-1,1},
{1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega],\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega]},
{1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega],\[Omega]\[Conjugate],-1,-\[Omega]\[Conjugate],-\[Omega],-1,-\[Omega]\[Conjugate],-\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega]\[Conjugate],\[Omega],1,\[Omega],\[Omega]\[Conjugate],-1,-\[Omega]\[Conjugate],-\[Omega],-1,-\[Omega]\[Conjugate],-\[Omega]},
{1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate],1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate]},
{1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],-1,\[Omega],-\[Omega]\[Conjugate],1,-\[Omega],\[Omega]\[Conjugate],1,-\[Omega],\[Omega]\[Conjugate],-1,\[Omega],-\[Omega]\[Conjugate],1,\[Omega]\[Conjugate],\[Omega],-1,\[Omega],-\[Omega]\[Conjugate],1,-\[Omega],\[Omega]\[Conjugate]},
{1,-I,-1,I,1,-I,-1,1,-1,1,-I,-1,I,1,-I,-1,I,1,-I,-1,I,1,-1,1,-1,I,1,-I,-1,I},
{1,-I,-1,I,1,-I,-1,1,-1,-1,I,1,-I,-1,I,-1,I,1,-I,-1,I,1,-1,1,1,-I,-1,I,1,-I},
{1,I \[Omega]\[Conjugate],-\[Omega],-I,\[Omega]\[Conjugate],I \[Omega],-1,\[Omega],-\[Omega]\[Conjugate],1,I \[Omega]\[Conjugate],-\[Omega],-I,\[Omega]\[Conjugate],I \[Omega],-1,-I \[Omega]\[Conjugate],\[Omega],I,-\[Omega]\[Conjugate],-I \[Omega],1,-\[Omega],\[Omega]\[Conjugate],-1,-I \[Omega]\[Conjugate],\[Omega],I,-\[Omega]\[Conjugate],-I \[Omega]},
{1,I \[Omega]\[Conjugate],-\[Omega],-I,\[Omega]\[Conjugate],I \[Omega],-1,\[Omega],-\[Omega]\[Conjugate],-1,-I \[Omega]\[Conjugate],\[Omega],I,-\[Omega]\[Conjugate],-I \[Omega],-1,-I \[Omega]\[Conjugate],\[Omega],I,-\[Omega]\[Conjugate],-I \[Omega],1,-\[Omega],\[Omega]\[Conjugate],1,I \[Omega]\[Conjugate],-\[Omega],-I,\[Omega]\[Conjugate],I \[Omega]},
{1,-I \[Omega],-\[Omega]\[Conjugate],I,\[Omega],-I \[Omega]\[Conjugate],-1,\[Omega]\[Conjugate],-\[Omega],1,-I \[Omega],-\[Omega]\[Conjugate],I,\[Omega],-I \[Omega]\[Conjugate],-1,I \[Omega],\[Omega]\[Conjugate],-I,-\[Omega],I \[Omega]\[Conjugate],1,-\[Omega]\[Conjugate],\[Omega],-1,I \[Omega],\[Omega]\[Conjugate],-I,-\[Omega],I \[Omega]\[Conjugate]},
{1,-I \[Omega],-\[Omega]\[Conjugate],I,\[Omega],-I \[Omega]\[Conjugate],-1,\[Omega]\[Conjugate],-\[Omega],-1,I \[Omega],\[Omega]\[Conjugate],-I,-\[Omega],I \[Omega]\[Conjugate],-1,I \[Omega],\[Omega]\[Conjugate],-I,-\[Omega],I \[Omega]\[Conjugate],1,-\[Omega]\[Conjugate],\[Omega],1,-I \[Omega],-\[Omega]\[Conjugate],I,\[Omega],-I \[Omega]\[Conjugate]},
{1,I,-1,-I,1,I,-1,1,-1,1,I,-1,-I,1,I,-1,-I,1,I,-1,-I,1,-1,1,-1,-I,1,I,-1,-I},
{1,I,-1,-I,1,I,-1,1,-1,-1,-I,1,I,-1,-I,-1,-I,1,I,-1,-I,1,-1,1,1,I,-1,-I,1,I},
{1,-I \[Omega]\[Conjugate],-\[Omega],I,\[Omega]\[Conjugate],-I \[Omega],-1,\[Omega],-\[Omega]\[Conjugate],1,-I \[Omega]\[Conjugate],-\[Omega],I,\[Omega]\[Conjugate],-I \[Omega],-1,I \[Omega]\[Conjugate],\[Omega],-I,-\[Omega]\[Conjugate],I \[Omega],1,-\[Omega],\[Omega]\[Conjugate],-1,I \[Omega]\[Conjugate],\[Omega],-I,-\[Omega]\[Conjugate],I \[Omega]},
{1,-I \[Omega]\[Conjugate],-\[Omega],I,\[Omega]\[Conjugate],-I \[Omega],-1,\[Omega],-\[Omega]\[Conjugate],-1,I \[Omega]\[Conjugate],\[Omega],-I,-\[Omega]\[Conjugate],I \[Omega],-1,I \[Omega]\[Conjugate],\[Omega],-I,-\[Omega]\[Conjugate],I \[Omega],1,-\[Omega],\[Omega]\[Conjugate],1,-I \[Omega]\[Conjugate],-\[Omega],I,\[Omega]\[Conjugate],-I \[Omega]},
{1,I \[Omega],-\[Omega]\[Conjugate],-I,\[Omega],I \[Omega]\[Conjugate],-1,\[Omega]\[Conjugate],-\[Omega],1,I \[Omega],-\[Omega]\[Conjugate],-I,\[Omega],I \[Omega]\[Conjugate],-1,-I \[Omega],\[Omega]\[Conjugate],I,-\[Omega],-I \[Omega]\[Conjugate],1,-\[Omega]\[Conjugate],\[Omega],-1,-I \[Omega],\[Omega]\[Conjugate],I,-\[Omega],-I \[Omega]\[Conjugate]},
{1,I \[Omega],-\[Omega]\[Conjugate],-I,\[Omega],I \[Omega]\[Conjugate],-1,\[Omega]\[Conjugate],-\[Omega],-1,-I \[Omega],\[Omega]\[Conjugate],I,-\[Omega],-I \[Omega]\[Conjugate],-1,-I \[Omega],\[Omega]\[Conjugate],I,-\[Omega],-I \[Omega]\[Conjugate],1,-\[Omega]\[Conjugate],\[Omega],1,I \[Omega],-\[Omega]\[Conjugate],-I,\[Omega],I \[Omega]\[Conjugate]},
{2,0,-2 \[Omega]\[Conjugate],0,2 \[Omega],0,-2,2 \[Omega]\[Conjugate],-2 \[Omega],0,0,0,0,0,0,2,0,-2 \[Omega]\[Conjugate],0,2 \[Omega],0,-2,2 \[Omega]\[Conjugate],-2 \[Omega],0,0,0,0,0,0},
{2,0,-2,0,2,0,-2,2,-2,0,0,0,0,0,0,2,0,-2,0,2,0,-2,2,-2,0,0,0,0,0,0},
{2,0,-2 \[Omega],0,2 \[Omega]\[Conjugate],0,-2,2 \[Omega],-2 \[Omega]\[Conjugate],0,0,0,0,0,0,2,0,-2 \[Omega],0,2 \[Omega]\[Conjugate],0,-2,2 \[Omega],-2 \[Omega]\[Conjugate],0,0,0,0,0,0},
{2,0,2 \[Omega]\[Conjugate],0,2 \[Omega],0,2,2 \[Omega]\[Conjugate],2 \[Omega],0,0,0,0,0,0,-2,0,-2 \[Omega]\[Conjugate],0,-2 \[Omega],0,-2,-2 \[Omega]\[Conjugate],-2 \[Omega],0,0,0,0,0,0},
{2,0,2,0,2,0,2,2,2,0,0,0,0,0,0,-2,0,-2,0,-2,0,-2,-2,-2,0,0,0,0,0,0},
{2,0,2 \[Omega],0,2 \[Omega]\[Conjugate],0,2,2 \[Omega],2 \[Omega]\[Conjugate],0,0,0,0,0,0,-2,0,-2 \[Omega],0,-2 \[Omega]\[Conjugate],0,-2,-2 \[Omega],-2 \[Omega]\[Conjugate],0,0,0,0,0,0}};
AGClasses[48,11]={{{0,0,0}},{{1,0,0},{7,0,1}},{{2,0,0}},{{3,0,0},{9,0,1}},
{{4,0,0}},{{5,0,0},{11,0,1}},{{6,0,0}},{{8,0,0}},{{10,0,0}},
{{0,1,0},{6,1,1}},{{1,1,0},{7,1,1}},{{2,1,0},{8,1,1}},
{{3,1,0},{9,1,1}},{{4,1,0},{10,1,1}},{{5,1,0},{11,1,1}},
{{0,0,1}},{{1,0,1},{7,0,0}},{{2,0,1}},{{3,0,1},{9,0,0}},
{{4,0,1}},{{5,0,1},{11,0,0}},{{6,0,1}},{{8,0,1}},{{10,0,1}},
{{0,1,1},{6,1,0}},{{1,1,1},{7,1,0}},{{2,1,1},{8,1,0}},
{{3,1,1},{9,1,0}},{{4,1,1},{10,1,0}},{{5,1,1},{11,1,0}}};
AGCharTab[48,12]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,1,-1,-1},
{1,1,1,1,-1,-1,-1,1,-1,1,1,1,1,-1,-1,-1,1,-1},
{1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,1},
{2,2,-1,-1,-2,1,1,0,0,2,2,-1,-1,-2,1,1,0,0},
{2,2,-1,-1,2,-1,-1,0,0,2,2,-1,-1,2,-1,-1,0,0},
{2,-2,-1,1,0,Sqrt[3],-Sqrt[3],0,0,2,-2,-1,1,0,Sqrt[3],-Sqrt[3],0,0},
{2,-2,-1,1,0,-Sqrt[3],Sqrt[3],0,0,2,-2,-1,1,0,-Sqrt[3],Sqrt[3],0,0},
{2,-2,2,-2,0,0,0,0,0,2,-2,2,-2,0,0,0,0,0},
{1,1,1,1,1,1,1,I,I,-1,-1,-1,-1,-1,-1,-1,-I,-I},
{1,1,1,1,1,1,1,-I,-I,-1,-1,-1,-1,-1,-1,-1,I,I},
{1,1,1,1,-1,-1,-1,I,-I,-1,-1,-1,-1,1,1,1,-I,I},
{1,1,1,1,-1,-1,-1,-I,I,-1,-1,-1,-1,1,1,1,I,-I},
{2,2,-1,-1,-2,1,1,0,0,-2,-2,1,1,2,-1,-1,0,0},
{2,2,-1,-1,2,-1,-1,0,0,-2,-2,1,1,-2,1,1,0,0},
{2,-2,-1,1,0,Sqrt[3],-Sqrt[3],0,0,-2,2,1,-1,0,-Sqrt[3],Sqrt[3],0,0},
{2,-2,-1,1,0,-Sqrt[3],Sqrt[3],0,0,-2,2,1,-1,0,Sqrt[3],-Sqrt[3],0,0},
{2,-2,2,-2,0,0,0,0,0,-2,2,-2,2,0,0,0,0,0}};
AGClasses[48,12]={{{0,0}},{{6,0}},{{4,0},{8,0}},{{2,0},{10,0}},{{3,0},{9,0}},
{{1,0},{11,0}},{{5,0},{7,0}},{{0,1},{2,1},{4,1},{6,1},{8,1},{10,1}},
{{1,1},{3,1},{5,1},{7,1},{9,1},{11,1}},{{0,2}},{{6,2}},{{4,2},{8,2}},
{{2,2},{10,2}},{{3,2},{9,2}},{{1,2},{11,2}},{{5,2},{7,2}},
{{0,3},{2,3},{4,3},{6,3},{8,3},{10,3}},{{1,3},{3,3},{5,3},{7,3},{9,3},{11,3}}};
AGCharTab[48,13]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1},
{1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1},
{1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1},
{1,1,-1,-1,1,1,-1,-1,I,-I,I,I,-I,-I,1,-1,I,-I},
{1,1,-1,-1,1,1,-1,-1,I,-I,I,I,-I,-I,-1,1,-I,I},
{1,1,-1,-1,1,1,-1,-1,-I,I,-I,-I,I,I,1,-1,-I,I},
{1,1,-1,-1,1,1,-1,-1,-I,I,-I,-I,I,I,-1,1,I,-I},
{2,2,2,2,-1,-1,-1,-1,2,2,-1,-1,-1,-1,0,0,0,0},
{2,2,2,2,-1,-1,-1,-1,-2,-2,1,1,1,1,0,0,0,0},
{2,2,-2,-2,-1,-1,1,1,2 I,-2 I,-I,-I,I,I,0,0,0,0},
{2,2,-2,-2,-1,-1,1,1,-2 I,2 I,I,I,-I,-I,0,0,0,0},
{2,-2,2,-2,-2,2,-2,2,0,0,0,0,0,0,0,0,0,0},
{2,-2,2,-2,1,-1,1,-1,0,0,I Sqrt[3],-I Sqrt[3],I Sqrt[3],-I Sqrt[3],0,0,0,0},
{2,-2,2,-2,1,-1,1,-1,0,0,-I Sqrt[3],I Sqrt[3],-I Sqrt[3],I Sqrt[3],0,0,0,0},
{2,-2,-2,2,-2,2,2,-2,0,0,0,0,0,0,0,0,0,0},
{2,-2,-2,2,1,-1,-1,1,0,0,Sqrt[3],-Sqrt[3],-Sqrt[3],Sqrt[3],0,0,0,0},
{2,-2,-2,2,1,-1,-1,1,0,0,-Sqrt[3],Sqrt[3],Sqrt[3],-Sqrt[3],0,0,0,0}};
AGClasses[48,13]={{{0,0,0}},{{3,0,0}},{{0,0,2}},{{3,0,2}},{{1,0,0},{5,0,0}},{{2,0,0},{4,0,0}},
{{1,0,2},{5,0,2}},{{2,0,2},{4,0,2}},{{0,0,1},{3,0,1}},{{0,0,3},{3,0,3}},
{{1,0,1},{2,0,1}},{{4,0,1},{5,0,1}},{{1,0,3},{2,0,3}},{{4,0,3},{5,0,3}},
{{0,1,0},{1,1,0},{2,1,0},{3,1,0},{4,1,0},{5,1,0}},
{{0,1,2},{1,1,2},{2,1,2},{3,1,2},{4,1,2},{5,1,2}},
{{0,1,1},{1,1,1},{2,1,1},{3,1,1},{4,1,1},{5,1,1}},
{{0,1,3},{1,1,3},{2,1,3},{3,1,3},{4,1,3},{5,1,3}}};
AGCharTab[48,14]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,-1,-1,1,1,1,1,1,1,1,-1,-1},
{1,1,1,1,-1,-1,-1,1,-1,1,1,1,1,-1,-1,-1,1,-1},
{1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,1},
{1,1,-1,-1,I,I,-I,1,I,-1,-1,1,1,-I,-I,I,-1,-I},
{1,1,-1,-1,I,I,-I,-1,-I,-1,-1,1,1,-I,-I,I,1,I},
{1,1,-1,-1,-I,-I,I,1,-I,-1,-1,1,1,I,I,-I,-1,I},
{1,1,-1,-1,-I,-I,I,-1,I,-1,-1,1,1,I,I,-I,1,-I},
{2,2,-1,-1,2,-1,-1,0,0,2,2,-1,-1,2,-1,-1,0,0},
{2,2,-1,-1,-2,1,1,0,0,2,2,-1,-1,-2,1,1,0,0},
{2,2,1,1,2 I,-I,I,0,0,-2,-2,-1,-1,-2 I,I,-I,0,0},
{2,2,1,1,-2 I,I,-I,0,0,-2,-2,-1,-1,2 I,-I,I,0,0},
{2,-2,-1,1,0,I Sqrt[3],-I Sqrt[3],0,0,2,-2,-1,1,0,I Sqrt[3],-I Sqrt[3],0,0},
{2,-2,-1,1,0,-I Sqrt[3],I Sqrt[3],0,0,2,-2,-1,1,0,-I Sqrt[3],I Sqrt[3],0,0},
{2,-2,1,-1,0,Sqrt[3],Sqrt[3],0,0,-2,2,-1,1,0,-Sqrt[3],-Sqrt[3],0,0},
{2,-2,1,-1,0,-Sqrt[3],-Sqrt[3],0,0,-2,2,-1,1,0,Sqrt[3],Sqrt[3],0,0},
{2,-2,2,-2,0,0,0,0,0,2,-2,2,-2,0,0,0,0,0},
{2,-2,-2,2,0,0,0,0,0,-2,2,2,-2,0,0,0,0,0}};
AGClasses[48,14]={{{0,0,0}},{{2,0,0}},{{0,1,0},{0,5,0}},{{2,1,0},{2,5,0}},{{0,0,1},{2,0,1}},
{{0,2,1},{2,4,1}},{{0,1,1},{2,5,1}},
{{1,0,0},{1,4,0},{1,2,0},{3,0,0},{3,4,0},{3,2,0}},
{{1,0,1},{1,4,1},{1,2,1},{3,0,1},{3,4,1},{3,2,1}},
{{0,3,0}},{{2,3,0}},{{0,4,0},{0,2,0}},{{2,4,0},{2,2,0}},
{{0,3,1},{2,3,1}},{{0,5,1},{2,1,1}},{{0,4,1},{2,2,1}},
{{1,3,0},{1,1,0},{1,5,0},{3,3,0},{3,1,0},{3,5,0}},
{{1,3,1},{1,1,1},{1,5,1},{3,3,1},{3,1,1},{3,5,1}}};
AGCharTab[48,15]=otimesG21[AGCharTab[24,11]];
AGClasses[48,15]={{{0,0,0}},{{6,0,0}},{{1,0,0},{11,0,0}},{{5,0,0},{7,0,0}},{{2,0,0},{10,0,0}},
{{4,0,0},{8,0,0}},{{3,0,0},{9,0,0}},
{{0,1,0},{2,1,0},{4,1,0},{6,1,0},{8,1,0},{10,1,0}},
{{1,1,0},{3,1,0},{5,1,0},{7,1,0},{9,1,0},{11,1,0}},
{{0,0,1}},{{6,0,1}},{{1,0,1},{11,0,1}},{{5,0,1},{7,0,1}},{{2,0,1},{10,0,1}},
{{4,0,1},{8,0,1}},{{3,0,1},{9,0,1}},
{{0,1,1},{2,1,1},{4,1,1},{6,1,1},{8,1,1},{10,1,1}},
{{1,1,1},{3,1,1},{5,1,1},{7,1,1},{9,1,1},{11,1,1}}};
AGCharTab[64,1]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1},
{1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,1,-1},
{1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,1,-1,1},
{1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1},
{1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1},
{1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,1},
{1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,1,1,-1},
{2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,2,2,-2,-2,0,0,0,0},
{2,2,-2,-2,2,-2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0},
{2,2,-2,-2,2,-2,-2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0},
{2,2,-2,-2,-2,2,0,0,0,0,2 I,2 I,-2 I,-2 I,0,0,0,0,0,0,0,0},
{2,2,-2,-2,-2,2,0,0,0,0,-2 I,-2 I,2 I,2 I,0,0,0,0,0,0,0,0},
{2,2,2,2,-2,-2,0,0,0,0,0,0,0,0,-2,-2,2,2,0,0,0,0},
{2,-2,-2,2,0,0,Sqrt[2],-Sqrt[2],-Sqrt[2],Sqrt[2],Sqrt[2],-Sqrt[2],-Sqrt[2],Sqrt[2],2,-2,0,0,0,0,0,0},
{2,-2,-2,2,0,0,Sqrt[2],-Sqrt[2],-Sqrt[2],Sqrt[2],-Sqrt[2],Sqrt[2],Sqrt[2],-Sqrt[2],-2,2,0,0,0,0,0,0},
{2,-2,-2,2,0,0,-Sqrt[2],Sqrt[2],Sqrt[2],-Sqrt[2],-Sqrt[2],Sqrt[2],Sqrt[2],-Sqrt[2],2,-2,0,0,0,0,0,0},
{2,-2,-2,2,0,0,-Sqrt[2],Sqrt[2],Sqrt[2],-Sqrt[2],Sqrt[2],-Sqrt[2],-Sqrt[2],Sqrt[2],-2,2,0,0,0,0,0,0},
{2,-2,2,-2,0,0,Sqrt[2],-Sqrt[2],Sqrt[2],-Sqrt[2],I Sqrt[2],-I Sqrt[2],I Sqrt[2],-I Sqrt[2],0,0,2 I,-2 I,0,0,0,0},
{2,-2,2,-2,0,0,Sqrt[2],-Sqrt[2],Sqrt[2],-Sqrt[2],-I Sqrt[2],I Sqrt[2],-I Sqrt[2],I Sqrt[2],0,0,-2 I,2 I,0,0,0,0},
{2,-2,2,-2,0,0,-Sqrt[2],Sqrt[2],-Sqrt[2],Sqrt[2],-I Sqrt[2],I Sqrt[2],-I Sqrt[2],I Sqrt[2],0,0,2 I,-2 I,0,0,0,0},
{2,-2,2,-2,0,0,-Sqrt[2],Sqrt[2],-Sqrt[2],Sqrt[2],I Sqrt[2],-I Sqrt[2],I Sqrt[2],-I Sqrt[2],0,0,-2 I,2 I,0,0,0,0}};
AGClasses[64,1]={{{0,0,0}},{{0,0,4}},{{0,2,0}},{{0,2,4}},{{0,0,2},{0,0,6}},{{0,2,2},{0,2,6}},
{{0,0,1},{0,0,7}},{{0,0,5},{0,0,3}},{{0,2,1},{0,2,7}},{{0,2,5},{0,2,3}},
{{1,0,1},{1,2,3}},{{1,0,5},{1,2,7}},{{1,2,1},{1,0,3}},{{1,2,5},{1,0,7}},
{{1,0,0},{1,2,4}},{{1,0,4},{1,2,0}},{{1,0,2},{1,2,2}},{{1,0,6},{1,2,6}},
{{1,1,0},{1,1,2},{1,3,4},{1,3,6},{1,1,4},{1,1,6},{1,3,0},{1,3,2}},
{{1,1,1},{1,1,3},{1,3,5},{1,3,7},{1,1,5},{1,1,7},{1,3,1},{1,3,3}},
{{0,1,0},{0,1,2},{0,3,4},{0,3,6},{0,1,4},{0,1,6},{0,3,0},{0,3,2}},
{{0,1,3},{0,1,1},{0,3,7},{0,3,5},{0,1,7},{0,1,5},{0,3,3},{0,3,1}}};
AGCharTab[64,2]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1},
{1,1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,-1,-1},
{1,1,1,1,1,1,-1,-1,1,1,1,-1,-1,-1,1,1,-1,1,1},
{1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,-1,-1,-1},
{1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1},
{1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,-1,-1,-1,1,1},
{1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,-1},
{2,2,-2,-2,2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0},
{2,2,2,2,-2,-2,0,0,2,2,-2,0,0,0,0,0,0,0,0},
{2,2,-2,-2,-2,2,0,0,0,0,0,2,-2,0,0,0,0,0,0},
{2,2,-2,-2,2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0},
{2,2,2,2,-2,-2,0,0,-2,-2,2,0,0,0,0,0,0,0,0},
{2,2,-2,-2,-2,2,0,0,0,0,0,-2,2,0,0,0,0,0,0},
{2,-2,2,-2,0,0,0,0,-2,2,0,0,0,0,Sqrt[2],-Sqrt[2],0,-Sqrt[2],Sqrt[2]},
{2,-2,2,-2,0,0,0,0,2,-2,0,0,0,0,Sqrt[2],-Sqrt[2],0,Sqrt[2],-Sqrt[2]},
{2,-2,2,-2,0,0,0,0,-2,2,0,0,0,0,-Sqrt[2],Sqrt[2],0,Sqrt[2],-Sqrt[2]},
{2,-2,2,-2,0,0,0,0,2,-2,0,0,0,0,-Sqrt[2],Sqrt[2],0,-Sqrt[2],Sqrt[2]},
{4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}};
AGClasses[64,2]={{{0,0,0}},{{4,0,0}},{{4,2,0}},{{0,2,0}},{{2,0,0},{6,0,0}},{{2,2,0},{6,2,0}},
{{3,0,1},{1,0,1},{7,0,1},{5,0,1}},{{3,2,1},{1,2,1},{7,2,1},{5,2,1}},
{{0,1,1},{4,3,1}},{{4,1,1},{0,3,1}},{{2,3,1},{6,1,1},{6,3,1},{2,1,1}},
{{1,1,0},{7,3,0},{5,1,0},{3,3,0}},{{1,3,0},{7,1,0},{5,3,0},{3,1,0}},
{{0,0,1},{2,0,1},{4,2,1},{6,2,1},{4,0,1},{6,0,1},{0,2,1},{2,2,1}},
{{1,0,0},{7,0,0},{5,2,0},{3,2,0}},{{5,0,0},{3,0,0},{1,2,0},{7,2,0}},
{{0,1,0},{2,1,0},{4,3,0},{6,3,0},{4,1,0},{6,1,0},{0,3,0},{2,3,0}},
{{1,1,1},{7,1,1},{5,3,1},{3,3,1}},{{5,1,1},{3,1,1},{1,3,1},{7,3,1}}};
AGCharTab[64,3]={{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1},
{1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,-I,-I,I,I,-I,-I,I,I,I,I,-I,-I,-1,-1,1,1},
{1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,-I,-I,I,I,-I,-I,I,I,-I,-I,I,I,1,1,-1,-1},
{1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1},
{1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1},
{1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,I,I,-I,-I,I,I,-I,-I,-I,-I,I,I,-1,-1,1,1},
{1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,I,I,-I,-I,I,I,-I,-I,I,I,-I,-I,1,1,-1,-1},
{1,-1,I,-I,-1,1,-I,I,-I,I,1,-1,I \[Theta],-I \[Theta],-\[Theta],\[Theta],-I \[Theta],I \[Theta],\[Theta],-\[Theta],I \[Theta],-I \[Theta],-\[Theta],\[Theta],1,-1,I,-I},
{1,-1,I,-I,-1,1,-I,I,-I,I,1,-1,I \[Theta],-I \[Theta],-\[Theta],\[Theta],-I \[Theta],I \[Theta],\[Theta],-\[Theta],-I \[Theta],I \[Theta],\[Theta],-\[Theta],-1,1,-I,I},
{1,-1,I,-I,-1,1,-I,I,-I,I,1,-1,-I \[Theta],I \[Theta],\[Theta],-\[Theta],I \[Theta],-I \[Theta],-\[Theta],\[Theta],I \[Theta],-I \[Theta],-\[Theta],\[Theta],-1,1,-I,I},
{1,-1,I,-I,-1,1,-I,I,-I,I,1,-1,-I \[Theta],I \[Theta],\[Theta],-\[Theta],I \[Theta],-I \[Theta],-\[Theta],\[Theta],-I \[Theta],I \[Theta],\[Theta],-\[Theta],1,-1,I,-I},
{1,-1,-I,I,-1,1,I,-I,I,-I,1,-1,\[Theta],-\[Theta],-I \[Theta],I \[Theta],-\[Theta],\[Theta],I \[Theta],-I \[Theta],\[Theta],-\[Theta],-I \[Theta],I \[Theta],1,-1,-I,I},
{1,-1,-I,I,-1,1,I,-I,I,-I,1,-1,\[Theta],-\[Theta],-I \[Theta],I \[Theta],-\[Theta],\[Theta],I \[Theta],-I \[Theta],-\[Theta],\[Theta],I \[Theta],-I \[Theta],-1,1,I,-I},
{1,-1,-I,I,-1,1,I,-I,I,-I,1,-1,-\[Theta],\[Theta],I \[Theta],-I \[Theta],\[Theta],-\[Theta],-I \[Theta],I \[Theta],\[Theta],-\[Theta],-I \[Theta],I \[Theta],-1,1,I,-I},
{1,-1,-I,I,-1,1,I,-I,I,-I,1,-1,-\[Theta],\[Theta],I \[Theta],-I \[Theta],\[Theta],-\[Theta],-I \[Theta],I \[Theta],-\[Theta],\[Theta],I \[Theta],-I \[Theta],1,-1,-I,I},
{2,2,2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{2,2,-2,-2,2,2,-2,-2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{2,-2,2 I,-2 I,-2,2,-2 I,2 I,2 I,-2 I,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{2,-2,-2 I,2 I,-2,2,2 I,-2 I,-2 I,2 I,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{2,2,-2 I,-2 I,-2,-2,2 I,2 I,0,0,0,0,1+I,1+I,1-I,1-I,-1-I,-1-I,-1+I,-1+I,0,0,0,0,0,0,0,0},
{2,2,-2 I,-2 I,-2,-2,2 I,2 I,0,0,0,0,-1-I,-1-I,-1+I,-1+I,1+I,1+I,1-I,1-I,0,0,0,0,0,0,0,0},
{2,2,2 I,2 I,-2,-2,-2 I,-2 I,0,0,0,0,1-I,1-I,1+I,1+I,-1+I,-1+I,-1-I,-1-I,0,0,0,0,0,0,0,0},
{2,2,2 I,2 I,-2,-2,-2 I,-2 I,0,0,0,0,-1+I,-1+I,-1-I,-1-I,1-I,1-I,1+I,1+I,0,0,0,0,0,0,0,0},
{2,-2,2,-2,2,-2,2,-2,0,0,0,0,Sqrt[2],-Sqrt[2],Sqrt[2],-Sqrt[2],Sqrt[2],-Sqrt[2],Sqrt[2],-Sqrt[2],0,0,0,0,0,0,0,0},
{2,-2,2,-2,2,-2,2,-2,0,0,0,0,-Sqrt[2],Sqrt[2],-Sqrt[2],Sqrt[2],-Sqrt[2],Sqrt[2],-Sqrt[2],Sqrt[2],0,0,0,0,0,0,0,0},
{2,-2,-2,2,2,-2,-2,2,0,0,0,0,I Sqrt[2],-I Sqrt[2],-I Sqrt[2],I Sqrt[2],I Sqrt[2],-I Sqrt[2],-I Sqrt[2],I Sqrt[2],0,0,0,0,0,0,0,0},
{2,-2,-2,2,2,-2,-2,2,0,0,0,0,-I Sqrt[2],I Sqrt[2],I Sqrt[2],-I Sqrt[2],-I Sqrt[2],I Sqrt[2],I Sqrt[2],-I Sqrt[2],0,0,0,0,0,0,0,0}};
AGClasses[64,3]={{{0,0}},{{4,0}},{{4,2}},{{0,2}},{{0,4}},{{4,4}},{{4,6}},{{0,6}},
{{2,0},{6,4}},{{6,0},{2,4}},{{6,2},{2,6}},{{2,2},{6,6}},{{1,0},{3,6}},
{{5,0},{7,6}},{{5,2},{7,0}},{{1,2},{3,0}},{{1,4},{3,2}},{{5,4},{7,2}},
{{5,6},{7,4}},{{1,6},{3,4}},{{0,1},{4,5},{2,7},{6,3}},{{4,1},{0,5},{6,7},{2,3}},
{{4,3},{0,7},{6,1},{2,5}},{{0,3},{4,7},{2,1},{6,5}},{{5,3},{1,7},{7,1},{3,5}},
{{1,3},{5,7},{3,1},{7,5}},{{1,5},{5,1},{3,3},{7,7}},{{5,5},{1,1},{7,3},{3,7}}};
AGCharTab[64,4]=otimesG21[AGCharTab[32,11]];
AGClasses[64,4]={{{0,0,0}},{{4,0,0}},{{2,0,0},{6,0,0}},{{0,2,0}},{{4,2,0}},{{2,2,0},{6,2,0}},
{{1,0,0},{3,2,0}},{{1,2,0},{3,0,0}},{{5,0,0},{7,2,0}},{{5,2,0},{7,0,0}},
{{1,1,0},{3,3,0},{5,1,0},{7,3,0}},{{1,3,0},{3,1,0},{5,3,0},{7,1,0}},
{{0,1,0},{2,3,0},{4,1,0},{6,3,0}},{{0,3,0},{2,1,0},{4,3,0},{6,1,0}},