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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346############################################################################# ## #W perf3.grp GAP Groups Library Volkmar Felsch ## Alexander Hulpke ## ## #Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany ## ## This file contains the perfect groups of sizes 21504-30240 ## All data is based on Holt/Plesken: Perfect Groups, OUP 1989 ## PERFGRP[60]:=[# 21504.1 [[1,"abdxyzXYZ", function(a,b,d,x,y,z,X,Y,Z) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *d^-1,d^2,d^-1*b^-1*d*b,x^2,y^2,z^2, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,X^2,Y^2,Z^2, X^-1*Y^-1*X*Y,X^-1*Z^-1*X*Z, Y^-1*Z^-1*Y*Z,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,a^-1*X*a*Z^-1, a^-1*Y*a*(X*Y*Z)^-1,a^-1*Z*a*X^-1, b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1, b^-1*Z*b*Z^-1,x^-1*X*x*X^-1, x^-1*Y*x*Y^-1,x^-1*Z*x*Z^-1, y^-1*X*y*X^-1,y^-1*Y*y*Y^-1, y^-1*Z*y*Z^-1,z^-1*X*z*X^-1, z^-1*Y*z*Y^-1,z^-1*Z*z*Z^-1], [[a,b,X],[a,b,x], [a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,X]] ]; end, [8,8,16]], "L3(2) 2^7",[8,7,1],2, 2,[8,8,16]], # 21504.2 [[1,"abxyzXYZf", function(a,b,x,y,z,X,Y,Z,f) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,x^2,y^2, z^2,x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,X^2,Y^2,Z^2, X^-1*Y^-1*X*Y,X^-1*Z^-1*X*Z, Y^-1*Z^-1*Y*Z,f^2,f^-1*x^-1*f*x, f^-1*y^-1*f*y,f^-1*z^-1*f*z, f^-1*X^-1*f*X,f^-1*Y^-1*f*Y, f^-1*Z^-1*f*Z,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,a^-1*X*a*(Z*f)^-1, a^-1*Y*a*(X*Y*Z)^-1, a^-1*Z*a*(X*f)^-1,a^-1*f^-1*a*f, b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1, b^-1*Z*b*Z^-1,b^-1*f^-1*b*f, x^-1*X*x*X^-1,x^-1*Y*x*Y^-1, x^-1*Z*x*Z^-1,y^-1*X*y*X^-1, y^-1*Y*y*Y^-1,y^-1*Z*y*Z^-1, z^-1*X*z*X^-1,z^-1*Y*z*Y^-1, z^-1*Z*z*Z^-1],[[a,b,x],[a,b,X]]]; end, [16,8]], "L3(2) 2^7",[8,7,2],2, 2,[16,8]], # 21504.3 [[1,"abdxyzXYZ", function(a,b,d,x,y,z,X,Y,Z) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *(d*Y*Z)^-1,d^2,d^-1*b^-1*d*b,x^2,y^2, z^2,x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,X^2,Y^2,Z^2, X^-1*Y^-1*X*Y,X^-1*Z^-1*X*Z, Y^-1*Z^-1*Y*Z,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,a^-1*X*a*Z^-1, a^-1*Y*a*(X*Y*Z)^-1,a^-1*Z*a*X^-1, b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1, b^-1*Z*b*Z^-1,x^-1*X*x*X^-1, x^-1*Y*x*Y^-1,x^-1*Z*x*Z^-1, y^-1*X*y*X^-1,y^-1*Y*y*Y^-1, y^-1*Z*y*Z^-1,z^-1*X*z*X^-1, z^-1*Y*z*Y^-1,z^-1*Z*z*Z^-1], [[a,b,X],[b,a*b*a*b^-1*a,x,z,X], [a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,X]] ]; end, [8,14,16]], "L3(2) 2^7",[8,7,3],2, 2,[8,14,16]], # 21504.4 [[1,"abxyzXYZe", function(a,b,x,y,z,X,Y,Z,e) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4*(Y*Z)^-1 ,x^2,y^2,z^2,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z,X^2, Y^2,Z^2,X^-1*Y^-1*X*Y,X^-1*Z^-1*X*Z ,Y^-1*Z^-1*Y*Z,e^2,e^-1*x^-1*e*x, e^-1*y^-1*e*y,e^-1*z^-1*e*z, e^-1*X^-1*e*X,e^-1*Y^-1*e*Y, e^-1*Z^-1*e*Z,a^-1*x*a*(z*e)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*e)^-1,b^-1*x*b*y^-1, b^-1*y*b*(x*y)^-1,b^-1*z*b*z^-1, a^-1*X*a*Z^-1,a^-1*Y*a*(X*Y*Z)^-1, a^-1*Z*a*X^-1,a^-1*e^-1*a*e, b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1, b^-1*Z*b*Z^-1,b^-1*e^-1*b*e, x^-1*X*x*X^-1,x^-1*Y*x*Y^-1, x^-1*Z*x*Z^-1,y^-1*X*y*X^-1, y^-1*Y*y*Y^-1,y^-1*Z*y*Z^-1, z^-1*X*z*X^-1,z^-1*Y*z*Y^-1, z^-1*Z*z*Z^-1], [[b,a*b*a*b^-1*a,x,z,X],[a,b,X]]]; end, [14,16]], "L3(2) 2^7",[8,7,4],2, 2,[14,16]], # 21504.5 [[1,"abdxyzXYZ", function(a,b,d,x,y,z,X,Y,Z) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *d^-1,d^2,b^-1*d^-1*b*d,x^2*X^-1, y^2*Y^-1,z^2*Z^-1,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, a^-1*x*a*(z*Y)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*X*Y*Z)^-1, b^-1*x*b*(y*X)^-1, b^-1*y*b*(x*y*Z)^-1, b^-1*z*b*(z*X*Y)^-1,a^-1*X*a*Z^-1, a^-1*Y*a*(X*Y*Z)^-1,a^-1*Z*a*X^-1, b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1, b^-1*Z*b*Z^-1], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x], [b,a*b*a*b^-1*a,x*Z]]]; end, [16,28]], "L3(2) 2^7",[8,7,5],2, 2,[16,28]], # 21504.6 [[1,"abxyzeXYZ", function(a,b,x,y,z,e,X,Y,Z) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,e^2,x^2*X ^-1,y^2*Y^-1,z^2*Z^-1, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,e^2,e^-1*x^-1*e*x, e^-1*y^-1*e*y,e^-1*z^-1*e*z, a^-1*x*a*(z*e*Y)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*e*X*Y*Z)^-1, a^-1*e^-1*a*e,b^-1*x*b*(y*X)^-1, b^-1*y*b*(x*y*Z)^-1, b^-1*z*b*(z*X*Y)^-1,b^-1*e^-1*b*e, a^-1*X*a*Z^-1,a^-1*Y*a*(X*Y*Z)^-1, a^-1*Z*a*X^-1,b^-1*X*b*Y^-1, b^-1*Y*b*(X*Y)^-1,b^-1*Z*b*Z^-1], [[a,b,X],[b,a*b*a*b^-1*a,x*Z]]]; end, [16,28]], "L3(2) 2^7",[8,7,6],2, 2,[16,28]], # 21504.7 [[1,"abdxyzXYZ", function(a,b,d,x,y,z,X,Y,Z) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *d^-1,d^2,x^2*X^-1,y^2*Y^-1, z^2*Z^-1,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z,d^2, d^-1*x^-1*d*x,d^-1*y^-1*d*y, d^-1*z^-1*d*z,a^-1*x*a*(z*d*Y)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*d*X*Y*Z)^-1, a^-1*d^-1*a*d,b^-1*x*b*(y*X)^-1, b^-1*y*b*(x*y*Z)^-1, b^-1*z*b*(z*X*Y)^-1,b^-1*d^-1*b*d, a^-1*X*a*Z^-1,a^-1*Y*a*(X*Y*Z)^-1, a^-1*Z*a*X^-1,b^-1*X*b*Y^-1, b^-1*Y*b*(X*Y)^-1,b^-1*Z*b*Z^-1], [[a*y*z,b,X],[b,a*b*a*b^-1*a,x*Z]]]; end, [16,28]], "L3(2) 2^7",[8,7,7],2, 2,[16,28]], # 21504.8 [[1,"abdxyzXYZ", function(a,b,d,x,y,z,X,Y,Z) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *(d*y*z*X*Z)^-1,d^2,d^-1*b^-1*d*b, x^2*X^-1,y^2*Y^-1,z^2*Z^-1, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*x*a*(z*Y)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*X*Y*Z)^-1, b^-1*x*b*(y*X)^-1, b^-1*y*b*(x*y*Z)^-1, b^-1*z*b*(z*X*Y)^-1,a^-1*X*a*Z^-1, a^-1*Y*a*(X*Y*Z)^-1,a^-1*Z*a*X^-1, b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1, b^-1*Z*b*Z^-1], [[b,a*b*a*b*a*b^-1*a*b*a*b*a,x*Z], [a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x, a^2*d^-1]]]; end, [112,16]], "L3(2) 2^7",[8,7,8],2, 2,[112,16]], # 21504.9 [[1,"abxyzuvwg", function(a,b,x,y,z,u,v,w,g) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,u^2,v^2, w^2,u^-1*v^-1*u*v,u^-1*w^-1*u*w, v^-1*w^-1*v*w,x^2,y^2,z^2, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,g^2,g^-1*x^-1*g*x, g^-1*y^-1*g*y,g^-1*z^-1*g*z, g^-1*u^-1*g*u,g^-1*v^-1*g*v, g^-1*w^-1*g*w,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, a^-1*g*a*g^-1,b^-1*x*b*y^-1, b^-1*y*b*(x*y)^-1,b^-1*z*b*z^-1, b^-1*g*b*g^-1,u^-1*x*u*x^-1 *g^-1,u^-1*y*u*y^-1, u^-1*z*u*z^-1,v^-1*x*v*x^-1, v^-1*y*v*y^-1*g^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1 *g^-1],[[a,b,x]]]; end, [16]], "L3(2) ( 2^3 x 2^3' ) C 2^1",[8,7,9],2, 2,16], # 21504.10 [[1,"abxyzuvwf", function(a,b,x,y,z,u,v,w,f) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,u^2,v^2, w^2,u^-1*v^-1*u*v,u^-1*w^-1*u*w, v^-1*w^-1*v*w,x^2,y^2,z^2, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,f^2,f^-1*x^-1*f*x, f^-1*y^-1*f*y,f^-1*z^-1*f*z, f^-1*u^-1*f*u,f^-1*v^-1*f*v, f^-1*w^-1*f*w,a^-1*u*a*(v*w)^-1, a^-1*v*a*(v*f)^-1, a^-1*w*a*(u*v*f)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, a^-1*f*a*f^-1,b^-1*x*b*y^-1, b^-1*y*b*(x*y)^-1,b^-1*z*b*z^-1, b^-1*f*b*f^-1,u^-1*x*u*x^-1, u^-1*y*u*y^-1,u^-1*z*u*z^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1], [[a,b,x],[a,b,u]]]; end, [16,8]], "L3(2) 2^3 x ( 2^3' E 2^1 )",[8,7,10],2, 2,[16,8]], # 21504.11 [[1,"abdxyzuvw", function(a,b,d,x,y,z,u,v,w) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *d^-1,d^2,d^-1*b^-1*d*b,u^2,v^2,w^2, u^-1*v^-1*u*v,u^-1*w^-1*u*w, v^-1*w^-1*v*w,x^2,y^2,z^2, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,u^-1*x*u*x^-1, u^-1*y*u*y^-1,u^-1*z*u*z^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1], [[a,b,u],[a,b,x], [a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,u,x]] ]; end, [8,8,16]], "L3(2) 2^7",[8,7,11],2, 2,[8,8,16]], # 21504.12 [[1,"abxyzeuvw", function(a,b,x,y,z,e,u,v,w) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,u^2,v^2, w^2,u^-1*v^-1*u*v,u^-1*w^-1*u*w, v^-1*w^-1*v*w,x^2,y^2,z^2, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,e^2,e^-1*x^-1*e*x, e^-1*y^-1*e*y,e^-1*z^-1*e*z, e^-1*u^-1*e*u,e^-1*v^-1*e*v, e^-1*w^-1*e*w,a^-1*u*a*(v*w)^-1, a^-1*v*a*(v*e)^-1, a^-1*w*a*(u*v*e)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,a^-1*x*a*(z*e)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*e)^-1,a^-1*e*a*e^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,b^-1*e*b*e^-1, u^-1*x*u*x^-1,u^-1*y*u*y^-1, u^-1*z*u*z^-1,v^-1*x*v*x^-1, v^-1*y*v*y^-1,v^-1*z*v*z^-1, w^-1*x*w*x^-1,w^-1*y*w*y^-1, w^-1*z*w*z^-1], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,z,w]]]; end, [16]], "L3(2) 2^7",[8,7,12],2, 2,16], # 21504.13 [[1,"abdxyzuvw", function(a,b,d,x,y,z,u,v,w) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *d^-1,d^2,d^-1*b^-1*d*b,u^2,v^2,w^2, u^-1*v^-1*u*v,u^-1*w^-1*u*w, v^-1*w^-1*v*w,x^2,y^2,z^2, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,u^-1*x*u*x^-1 *d^-1,u^-1*y*u*y^-1, u^-1*z*u*z^-1,v^-1*x*v*x^-1, v^-1*y*v*y^-1*d^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1 *d^-1], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,u]]]; end, [128]], "L3(2) 2^7",[8,7,13],2, 2,128], # 21504.14 [[1,"abdxyzuvw", function(a,b,d,x,y,z,u,v,w) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *(d*u*v*w)^-1,d^2,d^-1*b^-1*d*b,u^2, v^2,w^2,u^-1*v^-1*u*v,u^-1*w^-1*u*w ,v^-1*w^-1*v*w,x^2,y^2,z^2, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,u^-1*x*u*x^-1, u^-1*y*u*y^-1,u^-1*z*u*z^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1], [[a,b,u],[b,a*b^-1*a*b*a,x,z,u], [a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,u,x]] ]; end, [8,14,16]], "L3(2) 2^7",[8,7,14],2, 2,[8,14,16]], # 21504.15 [[1,"abxyzeuvw", function(a,b,x,y,z,e,u,v,w) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4*(u*v*w)^(-1 *1),u^2,v^2,w^2,u^-1*v^-1*u*v, u^-1*w^-1*u*w,v^-1*w^-1*v*w,x^2, y^2,z^2,x^-1*y^-1*x*y,x^-1*z^-1*x*z ,y^-1*z^-1*y*z,e^2,e^-1*u^-1*e*u, e^-1*v^-1*e*v,e^-1*w^-1*e*w, e^-1*x^-1*e*x,e^-1*y^-1*e*y, e^-1*z^-1*e*z,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,a^-1*x*a*(z*e)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*e)^-1,a^-1*e*a*e^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,b^-1*e*b*e^-1, u^-1*x*u*x^-1,u^-1*y*u*y^-1, u^-1*z*u*z^-1,v^-1*x*v*x^-1, v^-1*y*v*y^-1,v^-1*z*v*z^-1, w^-1*x*w*x^-1,w^-1*y*w*y^-1, w^-1*z*w*z^-1], [[a,b,u],[b,a*b^-1*a*b*a,x,z,u]]]; end, [16,14]], "L3(2) 2^7",[8,7,15],2, 2,[16,14]], # 21504.16 [[1,"abdxyzuvw", function(a,b,d,x,y,z,u,v,w) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *(d*y*z*u*v*w)^-1,d^2,d^-1*b^-1*d*b, u^2,v^2,w^2,u^-1*v^-1*u*v, u^-1*w^-1*u*w,v^-1*w^-1*v*w,x^2, y^2,z^2,x^-1*y^-1*x*y,x^-1*z^-1*x*z ,y^-1*z^-1*y*z,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,u^-1*x*u*x^-1, u^-1*y*u*y^-1,u^-1*z*u*z^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1], [[b,a*b*a*b^-1*a,x,u,w], [b,a*b^-1*a*b*a,x,z,u], [a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,u]] ]; end, [14,14,16]], "L3(2) 2^7",[8,7,16],2, 2,[14,14,16]], # 21504.17 [[1,"abdxyzuvw", function(a,b,d,x,y,z,u,v,w) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *d^-1,d^2,d^-1*b^-1*d*b,u^2,v^2,w^2, u^-1*v^-1*u*v,u^-1*w^-1*u*w, v^-1*w^-1*v*w,x^2,y^2,z^2, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*(z*u)^-1,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,u^-1*x*u*x^-1, u^-1*y*u*y^-1,u^-1*z*u*z^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1], [[b,a*b*a*b^-1*a,x,w], [a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,u]] ]; end, [56,16]], "L3(2) 2^7",[8,7,17],2, 2,[56,16]], # 21504.18 [[1,"abxyzeuvw", function(a,b,x,y,z,e,u,v,w) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,u^2,v^2, w^2,u^-1*v^-1*u*v,u^-1*w^-1*u*w, v^-1*w^-1*v*w,x^2,y^2,z^2, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,e^2,e^-1*x^-1*e*x, e^-1*y^-1*e*y,e^-1*z^-1*e*z, e^-1*u^-1*e*u,e^-1*v^-1*e*v, e^-1*w^-1*e*w,a^-1*x*a*(z*e)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*e)^-1,a^-1*e*a*e^-1, b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*(z*u)^-1,b^-1*e*b*e^-1, a^-1*u*a*(v*w)^-1,a^-1*v*a*v^-1, a^-1*w*a*(u*v)^-1,b^-1*u*b*(u*v)^-1, b^-1*v*b*u^-1,b^-1*w*b*w^-1, u^-1*x*u*x^-1,u^-1*y*u*y^-1, u^-1*z*u*z^-1,v^-1*x*v*x^-1, v^-1*y*v*y^-1,v^-1*z*v*z^-1, w^-1*x*w*x^-1,w^-1*y*w*y^-1, w^-1*z*w*z^-1], [[b,a*b*a*b^-1*a,x,w],[a,b,u]]]; end, [56,16]], "L3(2) 2^7",[8,7,18],2, 2,[56,16]], # 21504.19 [[1,"abdxyzuvw", function(a,b,d,x,y,z,u,v,w) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *d^-1,u^2,v^2,w^2,u^-1*v^-1*u*v, u^-1*w^-1*u*w,v^-1*w^-1*v*w,x^2, y^2,z^2,x^-1*y^-1*x*y,x^-1*z^-1*x*z ,y^-1*z^-1*y*z,d^2,d^-1*x^-1*d*x, d^-1*y^-1*d*y,d^-1*z^-1*d*z, d^-1*u^-1*d*u,d^-1*v^-1*d*v, d^-1*w^-1*d*w,a^-1*x*a*(z*d)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*d)^-1,a^-1*d*a*d^-1, b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*(z*u)^-1,b^-1*d*b*d^-1, a^-1*u*a*(v*w)^-1,a^-1*v*a*v^-1, a^-1*w*a*(u*v)^-1,b^-1*u*b*(u*v)^-1, b^-1*v*b*u^-1,b^-1*w*b*w^-1, u^-1*x*u*x^-1,u^-1*y*u*y^-1, u^-1*z*u*z^-1,v^-1*x*v*x^-1, v^-1*y*v*y^-1,v^-1*z*v*z^-1, w^-1*x*w*x^-1,w^-1*y*w*y^-1, w^-1*z*w*z^-1], [[b,a*b*a*b^-1*a,x,w],[a*y*z,b,u]]]; end, [56,16]], "L3(2) 2^7",[8,7,19],2, 2,[56,16]], # 21504.20 [[1,"abxyzuvwf", function(a,b,x,y,z,u,v,w,f) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,u^2,v^2, w^2,u^-1*v^-1*u*v,u^-1*w^-1*u*w, v^-1*w^-1*v*w,x^2*f^-1,y^2*f^-1, z^2*f^-1,x^-1*y^-1*x*y*f^-1, x^-1*z^-1*x*z*f^-1,y^-1*z^-1*y *z,f^2,f^-1*x^-1*f*x,f^-1*y^-1*f*y ,f^-1*z^-1*f*z,f^-1*u^-1*f*u, f^-1*v^-1*f*v,f^-1*w^-1*f*w, a^-1*x*a*z^-1,a^-1*y*a*(x*y*z)^-1, a^-1*z*a*x^-1,a^-1*f*a*f^-1, b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*(z*u)^-1,b^-1*f*b*f^-1, a^-1*u*a*(v*w)^-1,a^-1*v*a*(v*f)^-1, a^-1*w*a*(u*v*f)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,u^-1*x*u*x^-1 *f^-1,u^-1*y*u*y^-1, u^-1*z*u*z^-1,v^-1*x*v*x^-1, v^-1*y*v*y^-1*f^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1 *f^-1], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,u]]]; end, [128]], "L3(2) 2^7",[8,7,20],2, 2,128], # 21504.21 [[1,"abxyzuvwe", function(a,b,x,y,z,u,v,w,e) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,u^2,v^2, w^2,u^-1*v^-1*u*v,u^-1*w^-1*u*w, v^-1*w^-1*v*w,x^2*e^-1,y^2*e^-1, z^2*e^-1,x^-1*y^-1*x*y*e^-1, x^-1*z^-1*x*z*e^-1,y^-1*z^-1*y *z,e^2,e^-1*x^-1*e*x,e^-1*y^-1*e*y ,e^-1*z^-1*e*z,e^-1*u^-1*e*u, e^-1*v^-1*e*v,e^-1*w^-1*e*w, a^-1*x*a*(z*e)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*e)^-1,a^-1*e*a*e^-1, b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*(z*u)^-1,b^-1*e*b*e^-1, a^-1*u*a*(v*w)^-1,a^-1*v*a*(v*e)^-1, a^-1*w*a*(u*v*e)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,u^-1*x*u*x^-1 *e^-1,u^-1*y*u*y^-1, u^-1*z*u*z^-1,v^-1*x*v*x^-1, v^-1*y*v*y^-1*e^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1 *e^-1],[[a*y*z,b,u]]]; end, [16]], "L3(2) 2^7",[8,7,21],2, 2,16], # 21504.22 [[1,"abdxyzuvw", function(a,b,d,x,y,z,u,v,w) return [[a^2*(d*u*w)^-1,b^3,(a*b)^7,d^2,d^-1*b^-1 *d*b,(a^-1*b^-1*a*b)^4*(d*y*z*v)^-1, u^2,v^2,w^2,u^-1*v^-1*u*v, u^-1*w^-1*u*w,v^-1*w^-1*v*w,x^2, y^2,z^2,x^-1*y^-1*x*y,x^-1*z^-1*x*z ,y^-1*z^-1*y*z,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*(z*u)^-1,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,u^-1*x*u*x^-1, u^-1*y*u*y^-1,u^-1*z*u*z^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1*x*y*u, x*u*w,d], [a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,u]] ]; end, [64,16]], "L3(2) 2^1 x ( N 2^3 E 2^3' )",[8,7,22],2, 2,[64,16]] ]; PERFGRP[61]:=[# 21600.1 [[1,"abcde", function(a,b,c,d,e) return [[a^2,b^3,(a*b)^5,c^2,d^3,e^3,(d*e)^4,(d*e^-1)^5, c^-1*d^-1*e*d*e*d^-1*e*d*e^-1, a^-1*d^-1*a*d,a^-1*e^-1*a*e, b^-1*d^-1*b*d,b^-1*e^-1*b*e], [[b,a*b*a*b^-1*a,d,e],[a,b,c,d]]]; end, [5,6]], "A5 x A6",[33,0,1],1, [1,3],[5,6]] ]; PERFGRP[62]:=[# 23040.1 [[1,"abcstuve", function(a,b,c,s,t,u,v,e) return [[a^2,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1*b^-1*c *b*c*b^-1*c*b*c^-1,e^4, e^-1*s^-1*e*s,e^-1*t^-1*e*t, e^-1*u^-1*e*u,e^-1*v^-1*e*v,s^2, t^2,u^2,v^2,s^-1*t^-1*s*t, s^-1*u^-1*s*u*e^2,s^-1*v^-1*s*v, t^-1*u^-1*t*u,t^-1*v^-1*t*v*e^2, u^-1*v^-1*u*v,a^-1*s*a*u^-1, a^-1*t*a*v^-1,a^-1*u*a*s^-1, a^-1*v*a*t^-1,b^-1*s*b*(t*v*e)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, c^-1*s*c*(t*u)^-1,c^-1*t*c*t^-1, c^-1*u*c*(s*u*e)^-1, c^-1*v*c*(s*t*u*v*e^2)^-1],[[b,c]]]; end, [64]], "A6 ( 2^4 E 2^1 A ) C 2^1",[13,6,1],4, 3,64], # 23040.2 [[1,"abcstuve", function(a,b,c,s,t,u,v,e) return [[a^2*e^2,b^3,c^3,(b*c)^4*e^2,(b*c^-1)^5,a^-1 *b^-1*c*b*c*b^-1*c*b*c^-1, e^4,e^-1*s^-1*e*s,e^-1*t^-1*e*t, e^-1*u^-1*e*u,e^-1*v^-1*e*v,s^2, t^2,u^2,v^2,s^-1*t^-1*s*t, s^-1*u^-1*s*u*e^2,s^-1*v^-1*s*v, t^-1*u^-1*t*u,t^-1*v^-1*t*v*e^2, u^-1*v^-1*u*v,a^-1*s*a*u^-1, a^-1*t*a*v^-1,a^-1*u*a*s^-1, a^-1*v*a*t^-1,b^-1*s*b*(t*v*e)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, c^-1*s*c*(t*u)^-1,c^-1*t*c*t^-1, c^-1*u*c*(s*u*e)^-1, c^-1*v*c*(s*t*u*v*e^2)^-1], [[a*e^-1,b*u]]]; end, [384]], "A6 ( 2^4 E 2^1 A ) C N 2^1",[13,6,2],4, 3,384], # 23040.3 [[1,"abcdstuve", function(a,b,c,d,s,t,u,v,e) return [[a^2*d^-1,b^3,c^3,(b*c)^4*d^-1,(b*c^-1)^5, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,d^2, d^-1*b^-1*d*b,d^-1*c^-1*d*c,e^2, e^-1*s^-1*e*s,e^-1*t^-1*e*t, e^-1*u^-1*e*u,e^-1*v^-1*e*v,s^2, t^2,u^2,v^2,s^-1*t^-1*s*t, s^-1*u^-1*s*u,s^-1*v^-1*s*v, t^-1*u^-1*t*u,t^-1*v^-1*t*v, u^-1*v^-1*u*v,a^-1*s*a*u^-1, a^-1*t*a*v^-1,a^-1*u*a*s^-1, a^-1*v*a*t^-1,b^-1*s*b*(t*v*e)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, c^-1*s*c*(t*u)^-1,c^-1*t*c*t^-1, c^-1*u*c*(s*u*e)^-1, c^-1*v*c*(s*t*u*v)^-1], [[a,c,v],[c*b*a*d,b,s,e]]]; end, [12,80]], "A6 2^1 x ( 2^4 E 2^1 )",[13,6,3],4, 3,[12,80]] ]; PERFGRP[63]:=[# 24360.1 [[1,"abc", function(a,b,c) return [[c^14*a^2,c*b^4*c^-1*b^-1,b^29,a^4,a^2*b^(-1 *1)*a^2*b,a^2*c^-1*a^2*c, c*a*c*a^-1,(b*a)^3, c^(-1*5)*b*c^2*b*c^3*a*b^2*a*c*b^2*a], [[b,c^4]]]; end, [120]], "L2(29) 2^1 = SL(2,29)",22,-2, 17,120] ]; PERFGRP[64]:=[# 25308.1 [[1,"abc", function(a,b,c) return [[c^18,c*b^4*c^-1*b^-1,b^37,a^2,c*a*c*a^-1, (b*a)^3,c^(-1*2)*b*c^2*b^3*a*b^2*a*c*b^2*a], [[b,c]]]; end, [38]], "L2(37)",22,-1, 21,38] ]; PERFGRP[65]:=[# 25920.1 [[1,"ab", function(a,b) return [[a^2,b^5,(a*b)^9,(a^-1*b^-1*a*b)^3,(b*a*b*a *b^-1*a*b^-1*a)^2], [[a*b*a*b^-1*a*b^-1*a,b]]]; end, [27]], "U4(2)",28,-1, 22,27] ]; PERFGRP[66]:=[# 28224.1 [[1,"abcd", function(a,b,c,d) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,c^2,d^3, (c*d)^7,(c^-1*d^-1*c*d)^4, a^-1*c^-1*a*c,a^-1*d^-1*a*d, b^-1*c^-1*b*c,b^-1*d^-1*b*d], [[b,a*b*a*b^-1*a,c,d],[a,b,c*d*c*d^-1*c,d]]] ; end, [7,7]], "L3(2) x L3(2)",[34,0,1],1, [2,2],[7,7]] ]; PERFGRP[67]:=[# 29120.1 [[1,"ab", function(a,b) return [[a^2,b^4,(a*b)^5,(a^-1*b^-1*a*b)^7,(a*b^2)^13, a*b^-1*a*b^2*a*b^2*(a*b^-1*a*b*a*b^2)^2 *a*b^2*a*b*(a*b^2)^4], [[b^-1*a*b*a*b,b*a*b*a*b^2*a*b^2*a]]]; end, [65]], "Sz(8)",28,-1, 23,65] ]; PERFGRP[68]:=[# 29160.1 [[1,"abwxyzd", function(a,b,w,x,y,z,d) return [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,w^3,x^3,y^3,z^3, d^3,a^-1*d*a*d^-1,b^-1*d*b*d^-1, w^-1*d^-1*w*d,x^-1*d^-1*x*d, y^-1*d^-1*y*d,z^-1*d^-1*z*d, w^-1*x^-1*w*x,w^-1*y^-1*w*y, w^-1*z^-1*w*z,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w^-1*x^-1*y^-1*z^-1) ^-1,a^-1*z*a*w^-1, b^-1*w*b*x^-1,b^-1*x*b*y^-1*d, b^-1*y*b*w^-1*d^-1, b^-1*z*b*z^-1*d^-1], [[a*b,w],[a*b,b*a*b*a*b^-1*a*b^-1,w*d]]]; end, [24,18]], "A5 2^1 x 3^4' E 3^1",[2,5,1],6, 1,[24,18]], # 29160.2 [[1,"abstuvd", function(a,b,s,t,u,v,d) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,d^3,d^-1*a ^-1*d*a,d^-1*b^-1*d*b, d^-1*s^-1*d*s,s^3,t^3,u^3,v^3, s^-1*t^-1*s*t,s^-1*u^-1*s*u *d^-1,s^-1*v^-1*s*v, t^-1*u^-1*t*u,t^-1*v^-1*t*v *d^-1,u^-1*v^-1*u*v, a^-1*s*a*u^-1,a^-1*t*a*v^-1, a^-1*u*a*(s^-1*d)^-1, a^-1*v*a*(t^-1*d)^-1, b^-1*s*b*(s*v^-1*d^-1)^-1, b^-1*t*b*(t*u^-1*v*d)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1], [[a,b]]]; end, [243]], "A5 2^1 3^4 C 3^1 I",[2,5,2],3, 1,243], # 29160.3 [[1,"abstuve", function(a,b,s,t,u,v,e) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,e^3,e^-1*a ^-1*e*a,e^-1*b^-1*e*b, e^-1*s^-1*e*s,s^3,t^3,u^3,v^3, s^-1*t^-1*s*t,s^-1*u^-1*s*u, s^-1*v^-1*s*v*e^-1, t^-1*u^-1*t*u*e^-1, t^-1*v^-1*t*v*e,u^-1*v^-1*u*v, a^-1*s*a*(u*e^-1)^-1, a^-1*t*a*(v*e)^-1,a^-1*u*a*s, a^-1*v*a*t,b^-1*s*b*(s*v^-1)^-1, b^-1*t*b*(t*u^-1*v*e^-1)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1], [[a,b]]]; end, [243]], "A5 2^1 3^4 C 3^1 II",[2,5,3],3, 1,243], # 29160.4 [[1,"abcwxyz", function(a,b,c,w,x,y,z) return [[a^2,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1*b^-1*c *b*c*b^-1*c*b*c^-1,w^3,x^3,y^3, z^3,w^-1*x^-1*w*x,w^-1*y^-1*w*y, w^-1*z^-1*w*z,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w^-1*x^-1*y^-1*z^-1) ^-1,a^-1*z*a*w^-1, b^-1*w*b*x^-1,b^-1*x*b*y^-1, b^-1*y*b*w^-1,b^-1*z*b*z^-1, c^-1*w*c*(w^-1*x*y^-1*z^-1)^-1, c^-1*x*c*(x^-1*z)^-1, c^-1*y*c*(w*x^-1)^-1, c^-1*z*c*x],[[b,c*a*b*c,z]]]; end, [30]], "A6 3^4'",[14,4,1],1, 3,30], # 29160.5 (otherpres.) [[1,"abDstuvd", function(a,b,D,s,t,u,v,d) return [[a^2*D^-1,b^3,(a*b)^5,D^2,D^-1*b^-1*D*b, d^3,d^-1*a^-1*d*a,d^-1*b^-1*d*b, d^-1*s^-1*d*s,s^3,t^3,u^3,v^3, s^-1*t^-1*s*t,s^-1*u^-1*s*u *d^-1,s^-1*v^-1*s*v, t^-1*u^-1*t*u,t^-1*v^-1*t*v *d^-1,u^-1*v^-1*u*v, a^-1*s*a*u^-1,a^-1*t*a*v^-1, a^-1*u*a*(s^-1*d)^-1, a^-1*v*a*(t^-1*d)^-1, b^-1*s*b*(s*v^-1*d^-1)^-1, b^-1*t*b*(t*u^-1*v*d)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1], [[a,b]]]; end, [243]]], # 29160.6 (otherpres.) [[1,"abdstuve", function(a,b,d,s,t,u,v,e) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b, e^3,e^-1*a^-1*e*a,e^-1*b^-1*e*b, e^-1*s^-1*e*s,s^3,t^3,u^3,v^3, s^-1*t^-1*s*t,s^-1*u^-1*s*u, s^-1*v^-1*s*v*e^-1, t^-1*u^-1*t*u*e^-1, t^-1*v^-1*t*v*e,u^-1*v^-1*u*v, a^-1*s*a*(u*e^-1)^-1, a^-1*t*a*(v*e)^-1,a^-1*u*a*s, a^-1*v*a*t,b^-1*s*b*(s*v^-1)^-1, b^-1*t*b*(t*u^-1*v*e^-1)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1], [[a,b]]]; end, [243]]] ]; PERFGRP[69]:=[# 29760.1 [[1,"abc", function(a,b,c) return [[c^15*a^2,c*b^9*c^-1*b^-1,b^31,a^4,a^2*b^(-1 *1)*a^2*b,a^2*c^-1*a^2*c, c*a*c*a^-1,(b*a)^3],[[b,c^2]]]; end, [64]], "L2(31) 2^1 = SL(2,31)",22,-2, 18,64] ]; PERFGRP[70]:=[# 30240.1 [[1,"abcde", function(a,b,c,d,e) return [[a^2,b^3,(a*b)^5,c^2,d^3,(c*d)^7,e^-1*d^-1* (c*d)^3, (e*d^-1*e*d)^-1*c^-1*e*d^-1*e*d*c, a^-1*c^-1*a*c,a^-1*d^-1*a*d, b^-1*c^-1*b*c,b^-1*d^-1*b*d], [[b,a*b*a*b^-1*a,c,d],[a,b,c,e]]]; end, [5,9]], "A5 x L2(8)",[35,0,1],1, [1,4],[5,9]] ]; ############################################################################# ## #E perf3.grp . . . . . . . . . . . . . . . . . . . . . . . . . ends here ##