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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 perf11.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 524880-786240 ## All data is based on Holt/Plesken: Perfect Groups, OUP 1989 ## PERFGRP[250]:=[# 524880.1 [[1,"abcuvwxyz", function(a,b,c,u,v,w,x,y,z) return [[a^4,b^3,c^3,(b*c)^4*a^2,(b*c^-1)^5,a^2*b*a^2 *b^-1,a^2*c*a^2*c^-1, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,u^3, v^3,w^3,x^3,y^3,z^3,u^-1*v^-1*u*v, u^-1*w^-1*u*w,u^-1*x^-1*u*x, u^-1*y^-1*u*y,u^-1*z^-1*u*z, v^-1*w^-1*v*w,v^-1*x^-1*v*x, v^-1*y^-1*v*y,v^-1*z^-1*v*z, 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*u*a*(u^2*v*w^2*x^2*y)^-1, a^-1*v*a*(u*v*w^2*z)^-1, a^-1*w*a*(u^2*w*x*y^2*z^2)^-1, a^-1*x*a*(v^2*w*y^2)^-1, a^-1*y*a*(u*v^2*w^2*y^2*z)^-1, a^-1*z*a*(u^2*v^2*x^2*y*z)^-1, b^-1*u*b*(u*w^2*y)^-1, b^-1*v*b*(v*x^2*z)^-1, b^-1*w*b*(w*y)^-1,b^-1*x*b*(x*z)^-1, b^-1*y*b*y^-1,b^-1*z*b*z^-1, c^-1*u*c*u^-1,c^-1*v*c*v^-1, c^-1*w*c*(v*w)^-1, c^-1*x*c*(u*v^2*x)^-1, c^-1*y*c*(u*v^2*x^2*y)^-1, c^-1*z*c*(u^2*v^2*w^2*x*z)^-1], [[c*b*a^-1,b,u,v],[b,c*a*b*c,y,z,w,x]]]; end, [80,90]], "A6 2^1 x 3^6",[14,6,1],2, 3,[80,90]], # 524880.2 [[1,"abcuvwxyz", function(a,b,c,u,v,w,x,y,z) return [[a^4*v^-1*w*x*y^-1,b^3*z^-1,c^3*v,(b*c)^4 *a^2*(v^-1*w*x*y^-1)^-1 *(v*x^-1*y^-1)^-1, (b*c^-1)^5*(v*x^-1*y)^-1, a^2*(v^-1*w*x*y^-1)^-1*b*v^-1*w*x *y^-1*a^(-1*2)*b^-1, a^2*(v^-1*w*x*y^-1)^-1*c*v^-1*w*x *y^-1*a^(-1*2)*c^-1, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,u^3, v^3,w^3,x^3,y^3,z^3,u^-1*v^-1*u*v, u^-1*w^-1*u*w,u^-1*x^-1*u*x, u^-1*y^-1*u*y,u^-1*z^-1*u*z, v^-1*w^-1*v*w,v^-1*x^-1*v*x, v^-1*y^-1*v*y,v^-1*z^-1*v*z, 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*u*a*(u^-1*v*w^-1*x^-1*y)^-1 ,a^-1*v*a*(u*v*w^-1*z)^-1, a^-1*w*a*(u^-1*w*x*y^-1*z^-1)^-1 ,a^-1*x*a*(v^-1*w*y^-1)^-1, a^-1*y*a*(u*v^-1*w^-1*y^-1*z)^-1 ,a^-1*z*a*(u^-1*v^-1*x^-1*y*z) ^-1,b^-1*u*b*(u*w^-1*y)^-1, b^-1*v*b*(v*x^-1*z)^-1, b^-1*w*b*(w*y)^-1,b^-1*x*b*(x*z)^-1, b^-1*y*b*y^-1,b^-1*z*b*z^-1, c^-1*u*c*u^-1,c^-1*v*c*v^-1, c^-1*w*c*(v*w)^-1, c^-1*x*c*(u*v^-1*x)^-1, c^-1*y*c*(u*v^-1*x^-1*y)^-1, c^-1*z*c*(u^-1*v^-1*w^-1*x*z)^-1 ],[[c*b*a^-1,b,u,v],[b,c*a*b*c,y,z,w,x]]]; end, [80,90],[0,[2,-3]]], "A6 2^1 x N 3^6",[14,6,2],2, 3,[80,90]], # 524880.3 [[1,"abcdwxyze", function(a,b,c,d,w,x,y,z,e) return [[a^4*d,b^3,c^3*(w*x*y^-1)^-1,(b*c)^4*(a^2*d ^-1)^-1,(b*c^-1)^5, a^2*d^-1*b*(a^2*d^-1)^-1*b^-1, a^2*d^-1*c*(a^2*d^-1)^-1*c^-1, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,e^3, a^-1*e*a*e^-1,b^-1*e*b*e^-1, c^-1*e*c*e^-1,d^-1*e*d*e^-1, w^-1*e*w*e^-1,x^-1*e*x*e^-1, y^-1*e*y*e^-1,z^-1*e*z*e^-1, d^3*e^-1,w^3,x^3,y^3,z^3,d^-1*w^-1*d*w, d^-1*x^-1*d*x,d^-1*y^-1*d*y, d^-1*z^-1*d*z,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*d*a*d^-1, 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*d*b*(d*w*y^-1*z*e)^-1, b^-1*w*b*(x*e)^-1, b^-1*x*b*(y*e^-1)^-1, b^-1*y*b*w^-1, b^-1*z*b*(z*e^-1)^-1, c^-1*d*c*(d*x^-1*z^-1*e)^-1, c^-1*w*c*(w^-1*x*y^-1*z^-1*e^-1) ^-1,c^-1*x*c*(x^-1*z*e^-1)^-1, c^-1*y*c*(w*x^-1*e)^-1, c^-1*z*c*(x^-1*e)^-1], [[c*b*a^-1,b,w], [a*b,b*a*b*a*b^-1*a*b^-1,w*e]]]; end, [80,324],[0,[2,-3]]], "A6 2^1 x ( 3^1 E 3^4' E 3^1 ) A",[14,6,3],6, 3,[80,324]], # 524880.4 [[1,"abcwxyzef", function(a,b,c,w,x,y,z,e,f) return [[a^4,b^3,c^3,(b*c)^4*a^2,(b*c^-1)^5,a^2*b*a^2 *b^-1,a^2*c*a^2*c^-1, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,w^3, x^3,y^3,z^3,e^3,f^3,w^-1*e^-1*w*e, x^-1*e^-1*x*e,y^-1*e^-1*y*e, z^-1*e^-1*z*e,w^-1*f^-1*w*f, x^-1*f^-1*x*f,y^-1*f^-1*y*f, z^-1*f^-1*z*f,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, a^-1*e*a*e^-1,a^-1*f*a*f^-1, b^-1*w*b*x^-1, b^-1*x*b*(y*e^-1)^-1, b^-1*y*b*(w*e)^-1,b^-1*z*b*(z*e)^-1, b^-1*e*b*e^-1,b^-1*f*b*f^-1, c^-1*w*c*(w^-1*x*y^-1*z^-1*f)^-1 ,c^-1*x*c*(x^-1*z*f)^-1, c^-1*y*c*(w*x^-1*f)^-1, c^-1*z*c*(x^-1*f^-1)^-1, c^-1*e*c*e^-1,c^-1*f*c*f^-1], [[c*b*a^-1,b,w],[a,b,w],[a,c,w]]]; end, [80,18,18]], "A6 2^1 x 3^4' E ( 3^1 x 3^1 )",[14,6,4],18, 3,[80,18,18]], # 524880.5 [[1,"abcwxyzdf", function(a,b,c,w,x,y,z,d,f) return [[a^4*d,b^3,c^3,(b*c)^4*(a^2*d^-1)^-1,(b*c^(-1 *1))^5,a^2*d^-1*b*(a^2*d^-1)^-1 *b^-1,a^2*d^-1*c*(a^2*d^-1)^-1 *c^-1,a^-1*b^-1*c*b*c*b^-1*c*b *c^-1,b^-1*d^-1*b*d, c^-1*d^-1*c*d,w^3,x^3,y^3,z^3,d^3,f^3, w^-1*d^-1*w*d,x^-1*d^-1*x*d, y^-1*d^-1*y*d,z^-1*d^-1*z*d, d^-1*f^-1*d*f,w^-1*f^-1*w*f, x^-1*f^-1*x*f,y^-1*f^-1*y*f, z^-1*f^-1*z*f,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, a^-1*f*a*f^-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,b^-1*f*b*f^-1, c^-1*w*c*(w^-1*x*y^-1*z^-1*f)^-1 ,c^-1*x*c*(x^-1*z*f)^-1, c^-1*y*c*(w*x^-1*f)^-1, c^-1*z*c*(x^-1*f^-1)^-1, c^-1*f*c*f^-1], [[c*b*a^-1,b,w],[a,b,w],[a*d,c*d,w]]]; end, [80,18,18]], "A6 2^1 x 3^1 x ( 3^4' E 3^1 ) I",[14,6,5],18, 3,[80,18,18]], # 524880.6 [[1,"abcwxyzde", function(a,b,c,w,x,y,z,d,e) return [[a^4*d,b^3,c^3,(b*c)^4*(a^2*d^-1)^-1,(b*c^(-1 *1))^5,a^2*d^-1*b*(a^2*d^-1)^-1 *b^-1,a^2*d^-1*c*(a^2*d^-1)^-1 *c^-1,a^-1*b^-1*c*b*c*b^-1*c*b *c^-1,b^-1*d^-1*b*d, c^-1*d^-1*c*d,d^3,w^3,x^3,y^3,z^3,e^3, w^-1*d^-1*w*d,x^-1*d^-1*x*d, y^-1*d^-1*y*d,z^-1*d^-1*z*d, e^-1*d^-1*e*d,w^-1*e^-1*w*e, x^-1*e^-1*x*e,y^-1*e^-1*y*e, z^-1*e^-1*z*e,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, a^-1*e*a*e^-1,b^-1*w*b*x^-1, b^-1*x*b*(y*e^-1)^-1, b^-1*y*b*(w*e)^-1,b^-1*z*b*(z*e)^-1, b^-1*e*b*e^-1, c^-1*w*c*(w^-1*x*y^-1*z^-1*e^-1) ^-1,c^-1*x*c*(x^-1*z*e^-1)^-1, c^-1*y*c*(w*x^-1*e^-1)^-1, c^-1*z*c*(x^-1*e)^-1, c^-1*e*c*e^-1], [[c*b*a^-1,b,w],[a*b,b*a*b*a*b^-1*a*b^-1 ,w*e,d],[a*d,c*d,w]]]; end, [80,108,18]], "A6 2^1 x 3^1 x ( 3^4' E 3^1 ) II",[14,6,6],18, 3,[80,108,18]], # 524880.7 [[1,"abcstuvde", function(a,b,c,s,t,u,v,d,e) return [[a^4*d,b^3,c^3,(b*c)^4*a^(-1*2)*d,(b*c^-1)^5,a^(-1 *1)*b^-1*c*b*c*b^-1*c*b *c^-1,a^(-1*2)*b^-1*a^2*b, a^(-1*2)*c^-1*a^2*c,d^3,s^3,t^3,u^3,v^3,e^3, d^-1*e^-1*d*e,d^-1*s^-1*d*s, d^-1*t^-1*d*t,d^-1*u^-1*d*u, d^-1*v^-1*d*v,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^-1*t^-1*s*t, s^-1*u^-1*s*u*e^-1,s^-1*v^-1*s *v,t^-1*u^-1*t*u,t^-1*v^-1*t*v *e^-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*e)^-1, a^-1*v*a*(t^-1*e)^-1, a^-1*e*a*e^-1, b^-1*s*b*(s*v^-1*e^-1)^-1, b^-1*t*b*(t*u^-1*v*e)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1, b^-1*e*b*e^-1, c^-1*s*c*(s^-1*t*u^-1*v*e)^-1, c^-1*t*c*(s*t*u*v*e^-1)^-1, c^-1*u*c*(s^-1*v^-1)^-1, c^-1*v*c*(t^-1*u^-1*v)^-1, c^-1*e*c*e^-1],[[a,b,c],[a*d,c*d,s]]]; end, [243,18]], "A6 2^1 3^1 x ( 3^4 C 3^1 )",[14,6,7],9, 3,[243,18]], # 524880.8 [[1,"abcstuved", function(a,b,c,s,t,u,v,e,d) return [[a^4*d,b^3,c^3,(b*c)^4*a^(-1*2)*d,(b*c^-1)^5,a^(-1 *1)*b^-1*c*b*c*b^-1*c*b *c^-1,a^(-1*2)*b^-1*a^2*b, a^(-1*2)*c^-1*a^2*c,s^3,t^3,u^3,v^3,e^3,d^3, e^-1*s^-1*e*s,e^-1*t^-1*e*t, e^-1*u^-1*e*u,e^-1*v^-1*e*v, d^-1*s^-1*d*s,d^-1*t^-1*d*t, d^-1*u^-1*d*u,d^-1*v^-1*d*v, d^-1*e^-1*d*e,s^-1*t^-1*s*t, s^-1*u^-1*s*u*e^-1, s^-1*v^-1*s*v*d^-1, t^-1*u^-1*t*u*d^-1, t^-1*v^-1*t*v*(e*d^-1)^-1, u^-1*v^-1*u*v, a^-1*s*a*(u*d^-1)^-1, a^-1*t*a*(v*d)^-1, a^-1*u*a*(s^-1*e)^-1, a^-1*v*a*(t^-1*e)^-1, a^-1*e*a*e^-1, b^-1*s*b*(s*v^-1*e^-1)^-1, b^-1*t*b*(t*u^-1*v*e*d^-1)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1, b^-1*e*b*e^-1, c^-1*s*c*(s^-1*t*u^-1*v*e*d)^-1, c^-1*t*c*(s*t*u*v*e^-1)^-1, c^-1*u*c*(s^-1*v^-1*d^-1)^-1, c^-1*v*c*(t^-1*u^-1*v)^-1, c^-1*e*c*e^-1], [[a*d,b*d^-1,e],[a,b,c,d]]]; end, [1458,243]], "A6 2^1 3^4 C ( 3^1 x N 3^1 )",[14,6,8],9, 3,[1458,243]], # 524880.9 [[1,"abcstuvef", function(a,b,c,s,t,u,v,e,f) return [[a^4,b^3,c^3,(b*c)^4*a^(-1*2),(b*c^-1)^5,a^-1 *b^-1*c*b*c*b^-1*c*b*c^-1, a^(-1*2)*b^-1*a^2*b,a^(-1*2)*c^-1*a^2*c, s^3,t^3,u^3,v^3,e^3,f^3,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*u^-1*e*u, e^-1*v^-1*e*v,f^-1*s^-1*f*s, f^-1*t^-1*f*t,f^-1*u^-1*f*u, f^-1*v^-1*f*v,f^-1*e^-1*f*e, s^-1*t^-1*s*t,s^-1*u^-1*s*u *e^-1,s^-1*v^-1*s*v*f^-1, t^-1*u^-1*t*u*f^-1, t^-1*v^-1*t*v*(e*f^-1)^-1, u^-1*v^-1*u*v, a^-1*s*a*(u*f^-1)^-1, a^-1*t*a*(v*f)^-1, a^-1*u*a*(s^-1*e)^-1, a^-1*v*a*(t^-1*e)^-1, a^-1*e*a*e^-1,a^-1*f*a*f^-1, b^-1*s*b*(s*v^-1*e^-1)^-1, b^-1*t*b*(t*u^-1*v*e*f^-1)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1, b^-1*e*b*e^-1,b^-1*f*b*f^-1, c^-1*s*c*(s^-1*t*u^-1*v*e*f)^-1, c^-1*t*c*(s*t*u*v*e^-1)^-1, c^-1*u*c*(s^-1*v^-1*f^-1)^-1, c^-1*v*c*(t^-1*u^-1*v)^-1, c^-1*e*c*e^-1,c^-1*f*c*f^-1], [[a,b,c,e],[a,b,c,f]]]; end, [243,243]], "A6 2^1 3^4 C ( 3^1 x 3^1 )",[14,6,9],9, 3,[243,243]] ]; PERFGRP[251]:=[# 531360.1 [[1,"abc", function(a,b,c) return [[c^40*a^2,b^3,c^(-1*12)*b*c*b*c^11*b^-1,c^(-1*20) *b*c^20*b^(-1*2),a^4,a^2*b^-1*a^2*b, a^2*c^-1*a^2*c,c*a*c*a^-1,(b*a)^3, c^2*b^2*c^2*b*c*a*b*a*c^3*b*c*a*b^(-1*2) *c^(-1*2)*b^-1*a],[[b,c^16]]]; end, [1312],[0,0,2,2,2]], "L2(81) 2^1 = SL(2,81)",22,-2, 42,1312] ]; PERFGRP[252]:=[# 544320.1 [[2,1080,1,504,1], "A6 3^1 x L2(8)",40,3, [3,4],[18,9]] ]; PERFGRP[253]:=[# 546312.1 [[1,"abc", function(a,b,c) return [[c^51,c*b^25*c^-1*b^-1,b^103,a^2,c*a*c*a^(-1 *1),(b*a)^3],[[b,c]]]; end, [104],[0,4,3]], "L2(103)",22,-1, 49,104] ]; PERFGRP[254]:=[# 550368.1 [[2,504,1,1092,1], "L2(8) x L2(13)",40,1, [4,6],[9,14]] ]; PERFGRP[255]:=[# 552960.1 [[4,184320,1,1080,2,360,1,1], "A6 3^1 x ( 2^4 x 2^4 ) 2^1 I",[13,9,1],6, 3,[16,12,18]], # 552960.2 [[4,184320,2,1080,2,360,2,1], "A6 3^1 x ( 2^4 x 2^4 ) 2^1 II",[13,9,2],6, 3,[16,80,18]], # 552960.3 [[4,184320,3,1080,2,360,3,1], "A6 3^1 x ( 2^4 x 2^4 ) 2^1 III",[13,9,3],6, 3,[16,16,80,18]], # 552960.4 [[4,184320,4,1080,2,360,4,1], "A6 3^1 x ( 2^4 x 2^4 ) 2^1 IV",[13,9,4],6, 3,[32,18]], # 552960.5 [[4,184320,5,1080,2,360,5,1], "A6 3^1 x ( 2^4 x 2^4 ) 2^1 V",[13,9,5],6, 3,[1280,18]], # 552960.6 [[4,184320,6,1080,2,360,6,1], "A6 3^1 x ( 2^4 E 2^1 E 2^4 ) A",[13,9,6],3, 3,[480,18]], # 552960.7 [[4,184320,7,1080,2,360,7,1], "A6 3^1 x 2^4 E 2^1 E 2^4'",[13,9,7],3, 3,[240,18]], # 552960.8 [[4,184320,8,1080,2,360,8,1], "A6 3^1 x ( 2^4 E N 2^1 E 2^4 ) A",[13,9,8],3, 3,[480,18]], # 552960.9 [[4,184320,9,1080,2,360,9,1], "A6 3^1 x 2^4 E N 2^1 E 2^4'",[13,9,9],3, 3,[240,18]], # 552960.10 [[4,184320,10,1080,2,360,10,1], "A6 3^1 x ( 2^4 x 2^4' ) 2^1 I",[13,9,10],6, 3,[16,12,18]], # 552960.11 [[4,184320,11,1080,2,360,11,1], "A6 3^1 x ( 2^4 x 2^4' ) 2^1 II",[13,9,11],6, 3,[16,80,18]], # 552960.12 [[4,184320,12,1080,2,360,12,1], "A6 3^1 x ( 2^4 x 2^4' ) 2^1 III",[13,9,12],6, 3,[16,16,80,18]], # 552960.13 [[4,184320,13,1080,2,360,13,1], "A6 3^1 x ( 2^4 x 2^4' ) 2^1 IV",[13,9,13],6, 3,[20,18]], # 552960.14 [[4,184320,14,1080,2,360,14,1], "A6 3^1 x ( 2^4 x 2^4' ) 2^1 V",[13,9,14],6, 3,[80,18]], # 552960.15 [[4,184320,15,1080,2,360,15,1], "A6 3^1 x 2^1 ( 2^4 x 2^4 )",[13,9,15],3, 3,[256,18]], # 552960.16 [[4,184320,16,1080,2,360,16,1], "A6 3^1 x 2^4 x ( 2^1 E 2^4 )",[13,9,16],3, 3,[16,80,18]], # 552960.17 [[4,184320,17,1080,2,360,17,1], "A6 3^1 x 2^4 x ( 2^1 E 2^4' )",[13,9,17],3, 3,[16,80,18]], # 552960.18 [[4,184320,18,1080,2,360,18,1], "A6 3^1 x 2^1 E 2^4 A 2^4",[13,9,18],3, 3,[480,18]], # 552960.19 [[4,184320,19,1080,2,360,19,1], "A6 3^1 x 2^1 E ( 2^4 x 2^4' )",[13,9,19],3, 3,[80,80,18]] ]; PERFGRP[256]:=[# 571704.1 [[1,"abc", function(a,b,c) return [[c^41*a^2,c*b^4*c^-1*b^-1,b^83,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, [168]], "L2(83) 2^1 = SL(2,83)",22,-2, 43,168] ]; PERFGRP[257]:=[# 574560.1 [[2,168,1,3420,1], "L3(2) x L2(19)",40,1, [2,9],[7,20]] ]; PERFGRP[258]:=[# 583200.1 [[2,60,1,9720,1], "( A5 x A5 ) 2^1 # 3^4 [1]",[30,4,1],2, [1,1],[5,24,15]], # 583200.2 [[2,120,1,4860,1], "( A5 x A5 ) 2^1 # 3^4 [2]",[30,4,1],2, [1,1],[24,15]], # 583200.3 [[3,120,1,9720,1,"d1","a2","a2"], "( A5 x A5 ) 2^1 # 3^4 [3]",[30,4,1],2, [1,1],[288,180]], # 583200.4 [[2,60,1,9720,2], "( A5 x A5 ) 2^1 # 3^4 [4]",[30,4,2],2, [1,1],[5,24,60]], # 583200.5 [[2,120,1,4860,2], "( A5 x A5 ) 2^1 # 3^4 [5]",[30,4,2],2, [1,1],[24,60]], # 583200.6 [[3,120,1,9720,2,"d1","a2","a2"], "( A5 x A5 ) 2^1 # 3^4 [6]",[30,4,2],2, [1,1],[288,720]], # 583200.7 [[2,60,1,9720,3], "( A5 x A5 ) 2^1 # 3^4 [7]",[30,4,3],1, [1,1],[5,45]] ]; PERFGRP[259]:=[# 587520.1 [[2,120,1,4896,1], "( A5 x L2(17) ) 2^2",40,4, [1,7],[24,288]] ]; PERFGRP[260]:=[# 589680.1 [[2,60,1,9828,1], "A5 x L2(27)",40,1, [1,16],[5,28]] ]; PERFGRP[261]:=[# 600000.1 [[4,960,1,37500,1,60], "A5 # 2^4 5^4 [1]",6,5, 1,[16,25]], # 600000.2 [[4,960,2,37500,1,60], "A5 # 2^4 5^4 [2]",6,5, 1,[10,25]] ]; PERFGRP[262]:=[# 604800.1 [[1,"ab", function(a,b) return [[a^2,b^5,(a*b)^10,(a^-1*b^(-1*2)*a*b^2)^3,(a*b^2*a *b^-1)^7,a*b^2*a*b^2*a*b^(-1*2) *(a*b^-1*a*b^2*a*b*a*b^2)^2], [[a*b^2*a*b^(-1*2)*a,(b*a*b)^2]]]; end, [100]], "J2",28,-1, 50,100], # 604800.2 [[2,120,1,5040,1], "( A5 x A7 ) 2^2",40,4, [1,8],[24,240]], # 604800.3 [[2,3600,1,168,1], "A5 x A5 x L3(2)",40,1, [1,1,2],[5,5,7]] ]; PERFGRP[263]:=[# 604920.1 [[1,"abyz", function(a,b,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^71,z^71,y^-1 *z^-1*y*z,a^-1*y*a*z^-1, a^-1*z*a*y, b^-1*y*b*(y^-1*z^(-1*25))^-1, b^-1*z*b*y^17],[[a*b,a^2,y]]]; end, [852],[0,0,2,2,2,2,2,2]], "A5 2^1 71^2",[5,2,1],1, 1,852] ]; PERFGRP[264]:=[# 607500.1 [[4,4860,1,7500,1,60], "A5 # 3^4 5^3 [1]",6,1, 1,[15,30]], # 607500.2 [[4,4860,2,7500,1,60], "A5 # 3^4 5^3 [2]",6,1, 1,[60,30]], # 607500.3 [[4,4860,1,7500,2,60], "A5 # 3^4 5^3 [3]",6,1, 1,[15,30]], # 607500.4 [[4,4860,2,7500,2,60], "A5 # 3^4 5^3 [4]",6,1, 1,[60,30]] ]; PERFGRP[265]:=[# 612468.1 [[1,"abc", function(a,b,c) return [[c^53,c*b^4*c^-1*b^-1,b^107,a^2,c*a*c*a^-1 ,(b*a)^3],[[b,c]]]; end, [108]], "L2(107)",22,-1, 51,108] ]; PERFGRP[266]:=[# 622080.1 [[4,7680,1,4860,1,60], "A5 # 2^7 3^4 [1]",6,8, 1,[12,64,15]], # 622080.2 [[4,7680,2,4860,1,60], "A5 # 2^7 3^4 [2]",6,8, 1,[24,64,15]], # 622080.3 [[4,7680,3,4860,1,60], "A5 # 2^7 3^4 [3]",6,8, 1,[24,64,15]], # 622080.4 [[4,7680,4,4860,1,60], "A5 # 2^7 3^4 [4]",6,8, 1,[24,64,15]], # 622080.5 [[4,7680,5,4860,1,60], "A5 # 2^7 3^4 [5]",6,8, 1,[24,24,15]], # 622080.6 [[4,7680,1,4860,2,60], "A5 # 2^7 3^4 [6]",6,8, 1,[12,64,60]], # 622080.7 [[4,7680,2,4860,2,60], "A5 # 2^7 3^4 [7]",6,8, 1,[24,64,60]], # 622080.8 [[4,7680,3,4860,2,60], "A5 # 2^7 3^4 [8]",6,8, 1,[24,64,60]], # 622080.9 [[4,7680,4,4860,2,60], "A5 # 2^7 3^4 [9]",6,8, 1,[24,64,60]], # 622080.10 [[4,7680,5,4860,2,60], "A5 # 2^7 3^4 [10]",6,8, 1,[24,24,60]], # 622080.11 [[4,7680,4,9720,4,120,4,3], "A5 # 2^7 3^4 [11]",6,4, 1,[24,64,45]], # 622080.12 [[4,7680,5,9720,4,120,5,3], "A5 # 2^7 3^4 [12]",6,4, 1,[24,24,45]] ]; PERFGRP[267]:=[# 626688.1 [[1,"abcstuvwxyz", function(a,b,c,s,t,u,v,w,x,y,z) return [[a^2,b^17,c^8,(a*b)^3,(a*c)^2,c^-1*b*c*b^(-1*9), b^5*a*b^-1*a*b^2*a*b^6*a*c^-1,s^2,t^2, u^2,v^2,w^2,x^2,y^2,z^2,s^-1*t^-1*s*t, s^-1*u^-1*s*u,s^-1*v^-1*s*v, s^-1*w^-1*s*w,s^-1*x^-1*s*x, s^-1*y^-1*s*y,s^-1*z^-1*s*z, t^-1*u^-1*t*u,t^-1*v^-1*t*v, t^-1*w^-1*t*w,t^-1*x^-1*t*x, t^-1*y^-1*t*y,t^-1*z^-1*t*z, u^-1*v^-1*u*v,u^-1*w^-1*u*w, u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,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*s*a*t^-1, a^-1*t*a*s^-1, a^-1*u*a*(s*u*v*w*x)^-1, a^-1*v*a*(s*t*v*x*z)^-1, a^-1*w*a*(s*t*u*w*y*z)^-1, a^-1*x*a*(s*t*u*y)^-1, a^-1*y*a*(t*u*v*w)^-1, a^-1*z*a*(s*t*u*x*y*z)^-1, b^-1*s*b*t^-1,b^-1*t*b*(s*v)^-1, b^-1*u*b*(w*x)^-1,b^-1*v*b*(u*z)^-1, b^-1*w*b*x^-1,b^-1*x*b*(y*z)^-1, b^-1*y*b*(t*u*v*y*z)^-1, b^-1*z*b*(t*u*v*y)^-1, c^-1*s*c*(s*u)^-1, c^-1*t*c*(t*u*w)^-1, c^-1*u*c*(s*t*w*x*y)^-1, c^-1*v*c*(s*t*u*w*x)^-1, c^-1*w*c*(w*y*z)^-1, c^-1*x*c*(s*u*z)^-1, c^-1*y*c*(u*v*w*y*z)^-1, c^-1*z*c*(u*v*w*x*y)^-1],[[a,b,c]]]; end, [256]], "L2(17) 2^8",[21,8,1],1, 7,256] ]; PERFGRP[268]:=[# 633600.1 [[2,960,1,660,1], "( A5 x L2(11) ) # 2^4 [1]",[36,4,1],1, [1,5],[16,11]], # 633600.2 [[2,960,2,660,1], "( A5 x L2(11) ) # 2^4 [2]",[36,4,2],1, [1,5],[10,11]] ]; PERFGRP[269]:=[# 645120.1 [[1,"abduvwxyze", function(a,b,d,u,v,w,x,y,z,e) return [[a^2*d^-1,b^4*d^-1,(a*b)^7,(a*b)^2*a*b^2*( a*b*a*b^-1)^2*(a*b)^2 *(a*b^-1)^2*a*b*a*b^-1,d^2,e^2, e^-1*d^-1*e*d,a^-1*d*a*d^-1, b^-1*d*b*d^-1,u^-1*e*u*e^-1, u^-1*d*u*d^-1,v^-1*e*v*e^-1, v^-1*d*v*d^-1,w^-1*e*w*e^-1, w^-1*d*w*d^-1,x^-1*e*x*e^-1, x^-1*d*x*d^-1,y^-1*e*y*e^-1, y^-1*d*y*d^-1,z^-1*e*z*e^-1, z^-1*d*z*d^-1,u^2*e^-1,v^2*e^-1, w^2*e^-1,x^2*e^-1,y^2*e^-1, z^2*e^-1,u^-1*v^-1*u*v*e^-1, u^-1*w^-1*u*w*e^-1, u^-1*x^-1*u*x*e^-1, u^-1*y^-1*u*y*e^-1, u^-1*z^-1*u*z*e^-1, v^-1*w^-1*v*w*e^-1, v^-1*x^-1*v*x*e^-1, v^-1*y^-1*v*y*e^-1, v^-1*z^-1*v*z*e^-1, w^-1*x^-1*w*x*e^-1, w^-1*y^-1*w*y*e^-1, w^-1*z^-1*w*z*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^-1, a^-1*u*a*u^-1,a^-1*v*a*v^-1, a^-1*w*a*(y*e)^-1,a^-1*x*a*x^-1, a^-1*y*a*(w*e)^-1, a^-1*z*a*(u*v*w*x*y*z*e)^-1, a^-1*e*a*e^-1,b^-1*u*b*w^-1, b^-1*v*b*z^-1,b^-1*w*b*v^-1, b^-1*x*b*(y*e)^-1,b^-1*y*b*(x*e)^-1, b^-1*z*b*u^-1,b^-1*e*b*e^-1], [[a,b], [a*b,b*a*b*a*b^2*a*b^-1*a*b*a*b^-1*a*b *a*b^2*d,u]]]; end, [128,240]], "A7 2^1 x ( 2^6 C 2^1 )",[23,8,1],4, 8,[128,240]], # 645120.2 [[1,"abwxyzWXYZ", function(a,b,w,x,y,z,W,X,Y,Z) return [[a^2,b^4,(a*b)^7,(a*b)^2*a*b^2*(a*b*a*b^-1)^2 *(a*b)^2*(a*b^-1)^2*a*b*a*b^-1,w^2, x^2,y^2,z^2,W^2,X^2,Y^2,Z^2,w*x*w*x,w*y*w*y, w*z*w*z,x*y*x*y,x*z*x*z,y*z*y*z,w*W*w*W, w*X*w*X,w*Y*w*Y,w*Z*w*Z,W*X*W*X,W*Y*W*Y, W*Z*W*Z,X*Y*X*Y,X*Z*X*Z,Y*Z*Y*Z, a^-1*w*a*y^-1,a^-1*x*a*z^-1, a^-1*y*a*w^-1,a^-1*z*a*x^-1, b^-1*w*b*(w*x*y*z)^-1,b^-1*x*b*y^-1 ,b^-1*y*b*(w*x)^-1, b^-1*z*b*(w*z)^-1,a^-1*W*a*Y^-1, a^-1*X*a*Z^-1,a^-1*Y*a*W^-1, a^-1*Z*a*X^-1,b^-1*W*b*(W*X*Y*Z)^-1 ,b^-1*X*b*Y^-1,b^-1*Y*b*(W*X)^-1, b^-1*Z*b*(W*Z)^-1],[[a,b,w],[a,b,W]]]; end, [16,16]], "A7 2^4 x 2^4",[23,8,2],1, 8,[16,16]], # 645120.3 [[1,"abwxyzWXYZ", function(a,b,w,x,y,z,W,X,Y,Z) return [[a^2,b^4,(a*b)^7,(a*b)^2*a*b^2*(a*b*a*b^-1)^2 *(a*b)^2*(a*b^-1)^2*a*b*a*b^-1,w^2, x^2,y^2,z^2,W^2,X^2,Y^2,Z^2,w*x*w*x,w*y*w*y, w*z*w*z,x*y*x*y,x*z*x*z,y*z*y*z,w*W*w*W, w*X*w*X,w*Y*w*Y,w*Z*w*Z,W*X*W*X,W*Y*W*Y, W*Z*W*Z,X*Y*X*Y,X*Z*X*Z,Y*Z*Y*Z, a^-1*w*a*y^-1,a^-1*x*a*z^-1, a^-1*y*a*w^-1,a^-1*z*a*x^-1, b^-1*w*b*(w*x*y*z)^-1,b^-1*x*b*y^-1 ,b^-1*y*b*(w*x)^-1, b^-1*z*b*(w*z)^-1,a^-1*W*a*Y^-1, a^-1*X*a*Z^-1,a^-1*Y*a*W^-1, a^-1*Z*a*X^-1,b^-1*W*b*(W*X*Y*Z)^-1 ,b^-1*X*b*(W*X*Z)^-1,b^-1*Y*b*X^-1 ,b^-1*Z*b*(W*X*Y)^-1],[[a,b,w],[a,b,W]]]; end, [16,16]], "A7 2^4 x 2^4'",[23,8,3],1, 8,[16,16]], # 645120.4 [[1,"abdwxyz", function(a,b,d,w,x,y,z) return [[a^2*d,b^4,(a*b)^15,(a*b^2)^6,(a*b)^2*(a*b^-1*a *b^2)^2*a*b^-1*(a*b)^2*(a*b^-1)^7, a*b*a*b^-1*a*b*a*b^2*(a*b^-1)^5*a*b^2 *(a*b^-1)^5*a*b^2,d^2,d^-1*a^-1*d*a ,d^-1*b^-1*d*b,d^-1*w^-1*d*w, d^-1*x^-1*d*x,d^-1*y^-1*d*y, d^-1*z^-1*d*z,w^2,x^2,y^2,z^2, 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*y^-1,a^-1*x*a*z^-1, a^-1*y*a*w^-1,a^-1*z*a*x^-1, b^-1*w*b*(w*x)^-1,b^-1*x*b*(w*z)^-1, b^-1*y*b*(w*x*y*z)^-1, b^-1*z*b*w^-1],[[a,b],[b,a*b^2*a,w]]]; end, [16,240],[[1,2],[8,8,8]]], "A8 ( 2^1 x 2^4 )",[26,5,1],2, 19,[16,240]], # 645120.5 [[1,"abdwxyz", function(a,b,d,w,x,y,z) return [[a^2*(d*x*z)^-1,b^4*(w*x*z)^-1,(a*b)^15,(a*b^2) ^6, (a*b)^2*(a*b^-1*a*b^2)^2*a*b^-1*(a*b)^2 *(a*b^-1)^7*(y*z)^-1, a*b*a*b^-1*a*b*a*b^2*(a*b^-1)^5*a*b^2 *(a*b^-1)^5*a*b^2*y^-1,d^2, d^-1*a^-1*d*a,d^-1*b^-1*d*b, d^-1*w^-1*d*w,d^-1*x^-1*d*x, d^-1*y^-1*d*y,d^-1*z^-1*d*z,w^2, x^2,y^2,z^2,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*y^-1, a^-1*x*a*z^-1,a^-1*y*a*w^-1, a^-1*z*a*x^-1,b^-1*w*b*(w*x)^-1, b^-1*x*b*(w*z)^-1, b^-1*y*b*(w*x*y*z)^-1, b^-1*z*b*w^-1], [[b*z,(a*b)^2*(a*b^-1)^2*a*z,y*z],[b,a*b*b*a,w] ]]; end, [30,240],[[1,2],[8,8,8]]], "A8 ( 2^1 x N 2^4 )",[26,5,2],2, 19,[30,240]], # 645120.6 [[2,60,1,10752,1], "( A5 x L3(2) ) # 2^6 [1]",[31,6,1],1, [1,2],[5,8,8]], # 645120.7 [[2,60,1,10752,2], "( A5 x L3(2) ) # 2^6 [2]",[31,6,2],1, [1,2],[5,8,14]], # 645120.8 [[2,60,1,10752,3], "( A5 x L3(2) ) # 2^6 [3]",[31,6,3],1, [1,2],[5,28]], # 645120.9 [[2,60,1,10752,4], "( A5 x L3(2) ) # 2^6 [4]",[31,6,4],1, [1,2],[5,112]], # 645120.10 [[2,60,1,10752,5], "( A5 x L3(2) ) # 2^6 [5]",[31,6,5],1, [1,2],[5,8,8]], # 645120.11 [[2,60,1,10752,6], "( A5 x L3(2) ) # 2^6 [6]",[31,6,6],1, [1,2],[5,8,14]], # 645120.12 [[2,60,1,10752,7], "( A5 x L3(2) ) # 2^6 [7]",[31,6,7],1, [1,2],[5,14,14]], # 645120.13 [[2,60,1,10752,8], "( A5 x L3(2) ) # 2^6 [8]",[31,6,8],1, [1,2],[5,56]], # 645120.14 [[2,60,1,10752,9], "( A5 x L3(2) ) # 2^6 [9]",[31,6,9],1, [1,2],[5,64]], # 645120.15 [[2,120,1,5376,1], "( A5 x L3(2) ) # 2^6 [10]",[31,6,10],8, [1,2],[24,16,16]], # 645120.16 [[2,3840,1,168,1], "( A5 x L3(2) ) # 2^6 [11]",[31,6,11],4, [1,2],[64,7]], # 645120.17 [[2,3840,2,168,1], "( A5 x L3(2) ) # 2^6 [12]",[31,6,12],4, [1,2],[64,7]], # 645120.18 [[2,3840,3,168,1], "( A5 x L3(2) ) # 2^6 [13]",[31,6,13],4, [1,2],[24,7]], # 645120.19 [[2,3840,4,168,1], "( A5 x L3(2) ) # 2^6 [14]",[31,6,14],4, [1,2],[48,7]], # 645120.20 [[2,3840,5,168,1], "( A5 x L3(2) ) # 2^6 [15]",[31,6,15],4, [1,2],[24,12,7]], # 645120.21 [[2,3840,6,168,1], "( A5 x L3(2) ) # 2^6 [16]",[31,6,16],2, [1,2],[48,7]], # 645120.22 [[2,3840,7,168,1], "( A5 x L3(2) ) # 2^6 [17]",[31,6,17],4, [1,2],[32,24,7]], # 645120.23 [[2,1920,1,336,1], "( A5 x L3(2) ) # 2^6 [18]",[31,6,18],4, [1,2],[12,16]], # 645120.24 [[2,1920,2,336,1], "( A5 x L3(2) ) # 2^6 [19]",[31,6,19],4, [1,2],[24,16]], # 645120.25 [[2,1920,3,336,1], "( A5 x L3(2) ) # 2^6 [20]",[31,6,20],4, [1,2],[16,24,16]], # 645120.26 [[2,1920,4,336,1], "( A5 x L3(2) ) # 2^6 [21]",[31,6,21],2, [1,2],[80,16]], # 645120.27 [[2,1920,5,336,1], "( A5 x L3(2) ) # 2^6 [22]",[31,6,22],4, [1,2],[10,24,16]], # 645120.28 [[2,1920,6,336,1], "( A5 x L3(2) ) # 2^6 [23]",[31,6,23],4, [1,2],[80,16]], # 645120.29 [[2,1920,7,336,1], "( A5 x L3(2) ) # 2^6 [24]",[31,6,24],4, [1,2],[32,16]], # 645120.30 [[3,3840,1,336,1,"e1","e1","d2"], "( A5 x L3(2) ) # 2^6 [25]",[31,6,25],4, [1,2],512], # 645120.31 [[3,3840,2,336,1,"e1","e1","d2"], "( A5 x L3(2) ) # 2^6 [26]",[31,6,26],4, [1,2],512], # 645120.32 [[3,3840,3,336,1,"e1","d2"], "( A5 x L3(2) ) # 2^6 [27]",[31,6,27],4, [1,2],192], # 645120.33 [[3,3840,4,336,1,"e1","d2"], "( A5 x L3(2) ) # 2^6 [28]",[31,6,28],4, [1,2],384], # 645120.34 [[3,3840,4,336,1,"d1","d2"], "( A5 x L3(2) ) # 2^6 [29]",[31,6,29],4, [1,2],384], # 645120.35 [[3,3840,5,336,1,"d1","d2"], "( A5 x L3(2) ) # 2^6 [30]",[31,6,30],4, [1,2],[192,96]], # 645120.36 [[3,3840,5,336,1,"e1","d2"], "( A5 x L3(2) ) # 2^6 [31]",[31,6,31],4, [1,2],[192,96]], # 645120.37 [[3,3840,5,336,1,"d1","e1","d2"], "( A5 x L3(2) ) # 2^6 [32]",[31,6,32],4, [1,2],[192,96]], # 645120.38 [[3,3840,6,336,1,"e1","d2"], "( A5 x L3(2) ) # 2^6 [33]",[31,6,33],2, [1,2],384], # 645120.39 [[3,3840,7,336,1,"d1","d2"], "( A5 x L3(2) ) # 2^6 [34]",[31,6,34],4, [1,2],[256,192]], # 645120.40 [[3,3840,7,336,1,"e1","d2"], "( A5 x L3(2) ) # 2^6 [35]",[31,6,35],4, [1,2],[256,192]], # 645120.41 [[3,3840,7,336,1,"d1","e1","d2"], "( A5 x L3(2) ) # 2^6 [36]",[31,6,36],4, [1,2],[256,192]] ]; PERFGRP[270]:=[# 647460.1 [[1,"abc", function(a,b,c) return [[c^54,c*b^12*c^-1*b^-1,b^109,a^2,c*a*c*a^(-1 *1),(b*a)^3, c^(-1*14)*b*c*b^2*c^2*b*a*b^2*a*c^3*b*c*b*a], [[b,c]]]; end, [110],[0,2,2]], "L2(109)",22,-1, 52,110] ]; PERFGRP[271]:=[# 665280.1 [[2,504,1,1320,1], "L2(8) x L2(11) 2^1",40,2, [4,5],[9,24]] ]; PERFGRP[272]:=[# 673920.1 [[2,120,1,5616,1], "A5 2^1 x L3(3)",40,2, [1,11],[24,13]] ]; PERFGRP[273]:=[# 675840.1 [[1,"abqrstuvwxyz", function(a,b,q,r,s,t,u,v,w,x,y,z) return [[a^2,b^3,(a*b)^11,(a*b)^4*(a*b^-1)^5*(a*b)^4*(a *b^-1)^5,q^2,r^2,s^2,t^2,u^2,v^2,w^2,x^2, y^2,z^2,q^-1*r^-1*q*r,q^-1*s^-1*q*s ,q^-1*t^-1*q*t,q^-1*u^-1*q*u, q^-1*v^-1*q*v,q^-1*w^-1*q*w, q^-1*x^-1*q*x,q^-1*y^-1*q*y, q^-1*z^-1*q*z,r^-1*s^-1*r*s, r^-1*t^-1*r*t,r^-1*u^-1*r*u, r^-1*v^-1*r*v,r^-1*w^-1*r*w, r^-1*x^-1*r*x,r^-1*y^-1*r*y, r^-1*z^-1*r*z,s^-1*t^-1*s*t, s^-1*u^-1*s*u,s^-1*v^-1*s*v, s^-1*w^-1*s*w,s^-1*x^-1*s*x, s^-1*y^-1*s*y,s^-1*z^-1*s*z, t^-1*u^-1*t*u,t^-1*v^-1*t*v, t^-1*w^-1*t*w,t^-1*x^-1*t*x, t^-1*y^-1*t*y,t^-1*z^-1*t*z, u^-1*v^-1*u*v,u^-1*w^-1*u*w, u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,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*q*a*y^-1, a^-1*r*a*v^-1,a^-1*s*a*s^-1, a^-1*t*a*u^-1,a^-1*u*a*t^-1, a^-1*v*a*r^-1,a^-1*w*a*x^-1, a^-1*x*a*w^-1,a^-1*y*a*q^-1, a^-1*z*a*z^-1,b^-1*q*b*x^-1, b^-1*r*b*u^-1,b^-1*s*b*r^-1, b^-1*t*b*t^-1,b^-1*u*b*s^-1, b^-1*v*b*q^-1,b^-1*w*b*w^-1, b^-1*x*b*v^-1, b^-1*y*b*(q*r*s*t*u*v*w*x*y*z)^-1, b^-1*z*b*y^-1],[[b,a*b*a*b^-1*a,y*z]] ]; end, [22]], "L2(11) 2^10",[17,10,1],1, 5,22], # 675840.2 [[1,"abqrstuvwxyz", function(a,b,q,r,s,t,u,v,w,x,y,z) return [[a^2,b^3,(a*b)^11,(a*b)^4*(a*b^-1)^5*(a*b)^4*(a *b^-1)^5,q^2,r^2,s^2,t^2,u^2,v^2,w^2,x^2, y^2,z^2,q^-1*r^-1*q*r,q^-1*s^-1*q*s ,q^-1*t^-1*q*t,q^-1*u^-1*q*u, q^-1*v^-1*q*v,q^-1*w^-1*q*w, q^-1*x^-1*q*x,q^-1*y^-1*q*y, q^-1*z^-1*q*z,r^-1*s^-1*r*s, r^-1*t^-1*r*t,r^-1*u^-1*r*u, r^-1*v^-1*r*v,r^-1*w^-1*r*w, r^-1*x^-1*r*x,r^-1*y^-1*r*y, r^-1*z^-1*r*z,s^-1*t^-1*s*t, s^-1*u^-1*s*u,s^-1*v^-1*s*v, s^-1*w^-1*s*w,s^-1*x^-1*s*x, s^-1*y^-1*s*y,s^-1*z^-1*s*z, t^-1*u^-1*t*u,t^-1*v^-1*t*v, t^-1*w^-1*t*w,t^-1*x^-1*t*x, t^-1*y^-1*t*y,t^-1*z^-1*t*z, u^-1*v^-1*u*v,u^-1*w^-1*u*w, u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,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*q*a*q^-1, a^-1*r*a*r^-1,a^-1*s*a*(s*u*w*z)^-1 ,a^-1*t*a*(t*v*x*y*z)^-1, a^-1*u*a*(t*u*x*y)^-1, a^-1*v*a*(s*t*v*w*x*z)^-1, a^-1*w*a*(s*v*x)^-1, a^-1*x*a*(t*u*v*w*x)^-1, a^-1*y*a*(t*u*w*x*z)^-1, a^-1*z*a*(s*t*v*w*y*z)^-1, b^-1*q*b*(s*t*u*v*w*x*y)^-1, b^-1*r*b*(s*u*w*z)^-1, b^-1*s*b*(q*r*s*t*u*y*z)^-1, b^-1*t*b*(q*s*v*y)^-1, b^-1*u*b*(r*z)^-1, b^-1*v*b*(q*r*y*z)^-1, b^-1*w*b*(q*r*u*v*x*y*z)^-1, b^-1*x*b*(q*u*w*x*y)^-1, b^-1*y*b*(s*v*x)^-1, b^-1*z*b*(t*u*v*w*x)^-1], [[a,b^-1*a*b*a*b^-1*a*b,x]]]; end, [132],[[1,-2]]], "L2(11) 2^10'",[17,10,2],1, 5,132], # 675840.3 [[1,"abqrstuvwxyz", function(a,b,q,r,s,t,u,v,w,x,y,z) return [[a^2*q^-1,b^3,(a*b)^11,(a*b)^4*(a*b^-1)^5*(a*b) ^4*(a*b^-1)^5*(q*r*s*t*x*z)^-1,q^2, r^2,s^2,t^2,u^2,v^2,w^2,x^2,y^2,z^2, q^-1*r^-1*q*r,q^-1*s^-1*q*s, q^-1*t^-1*q*t,q^-1*u^-1*q*u, q^-1*v^-1*q*v,q^-1*w^-1*q*w, q^-1*x^-1*q*x,q^-1*y^-1*q*y, q^-1*z^-1*q*z,r^-1*s^-1*r*s, r^-1*t^-1*r*t,r^-1*u^-1*r*u, r^-1*v^-1*r*v,r^-1*w^-1*r*w, r^-1*x^-1*r*x,r^-1*y^-1*r*y, r^-1*z^-1*r*z,s^-1*t^-1*s*t, s^-1*u^-1*s*u,s^-1*v^-1*s*v, s^-1*w^-1*s*w,s^-1*x^-1*s*x, s^-1*y^-1*s*y,s^-1*z^-1*s*z, t^-1*u^-1*t*u,t^-1*v^-1*t*v, t^-1*w^-1*t*w,t^-1*x^-1*t*x, t^-1*y^-1*t*y,t^-1*z^-1*t*z, u^-1*v^-1*u*v,u^-1*w^-1*u*w, u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,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*q*a*q^-1, a^-1*r*a*r^-1,a^-1*s*a*(s*u*w*z)^-1 ,a^-1*t*a*(t*v*x*y*z)^-1, a^-1*u*a*(t*u*x*y)^-1, a^-1*v*a*(s*t*v*w*x*z)^-1, a^-1*w*a*(s*v*x)^-1, a^-1*x*a*(t*u*v*w*x)^-1, a^-1*y*a*(t*u*w*x*z)^-1, a^-1*z*a*(s*t*v*w*y*z)^-1, b^-1*q*b*(s*t*u*v*w*x*y)^-1, b^-1*r*b*(s*u*w*z)^-1, b^-1*s*b*(q*r*s*t*u*y*z)^-1, b^-1*t*b*(q*s*v*y)^-1, b^-1*u*b*(r*z)^-1, b^-1*v*b*(q*r*y*z)^-1, b^-1*w*b*(q*r*u*v*x*y*z)^-1, b^-1*x*b*(q*u*w*x*y)^-1, b^-1*y*b*(s*v*x)^-1, b^-1*z*b*(t*u*v*w*x)^-1], [[a,b^-1*a*b*a*b^-1*a*b]]]; end, [132],[[1,-2],[1,2]]], "L2(11) N 2^10'",[17,10,3],1, 5,132] ]; PERFGRP[274]:=[# 677376.1 [[2,1344,1,504,1], "( L3(2) x L2(8) ) # 2^3 [1]",[38,3,1],1, [2,4],[8,9]], # 677376.2 [[2,1344,2,504,1], "( L3(2) x L2(8) ) # 2^3 [2]",[38,3,2],1, [2,4],[14,9]] ]; PERFGRP[275]:=[# 685440.1 [[2,168,1,4080,1], "L3(2) x L2(16)",40,1, [2,10],[7,17]] ]; PERFGRP[276]:=fail; PERFGRP[277]:=[# 691200.1 [[2,60,1,11520,1], "( A5 x A6 ) # 2^5 [1]",[33,5,1],2, [1,3],[5,12]], # 691200.2 [[2,60,1,11520,2], "( A5 x A6 ) # 2^5 [2]",[33,5,2],2, [1,3],[5,80]], # 691200.3 [[2,60,1,11520,3], "( A5 x A6 ) # 2^5 [3]",[33,5,3],2, [1,3],[5,16,80]], # 691200.4 [[2,60,1,11520,4], "( A5 x A6 ) # 2^5 [4]",[33,5,4],1, [1,3],[5,80]], # 691200.5 [[2,120,1,5760,1], "( A5 x A6 ) # 2^5 [5]",[33,5,5],2, [1,3],[24,16]], # 691200.6 [[3,120,1,11520,1,"d1","e2"], "( A5 x A6 ) # 2^5 [6]",[33,5,6],2, [1,3],144], # 691200.7 [[3,120,1,11520,2,"d1","e2"], "( A5 x A6 ) # 2^5 [7]",[33,5,7],2, [1,3],960], # 691200.8 [[3,120,1,11520,3,"d1","d2"], "( A5 x A6 ) # 2^5 [8]",[33,5,8],2, [1,3],[192,960]], # 691200.9 [[2,1920,1,360,1], "( A5 x A6 ) # 2^5 [9]",[33,5,9],2, [1,3],[12,6]], # 691200.10 [[2,1920,2,360,1], "( A5 x A6 ) # 2^5 [10]",[33,5,10],2, [1,3],[24,6]], # 691200.11 [[2,1920,3,360,1], "( A5 x A6 ) # 2^5 [11]",[33,5,11],2, [1,3],[16,24,6]], # 691200.12 [[2,1920,4,360,1], "( A5 x A6 ) # 2^5 [12]",[33,5,12],1, [1,3],[80,6]], # 691200.13 [[2,1920,5,360,1], "( A5 x A6 ) # 2^5 [13]",[33,5,13],2, [1,3],[10,24,6]], # 691200.14 [[2,1920,6,360,1], "( A5 x A6 ) # 2^5 [14]",[33,5,14],2, [1,3],[80,6]], # 691200.15 [[2,1920,7,360,1], "( A5 x A6 ) # 2^5 [15]",[33,5,15],2, [1,3],[32,6]], # 691200.16 [[2,960,1,720,1], "( A5 x A6 ) # 2^5 [16]",[33,5,16],2, [1,3],[16,80]], # 691200.17 [[2,960,2,720,1], "( A5 x A6 ) # 2^5 [17]",[33,5,17],2, [1,3],[10,80]], # 691200.18 [[3,1920,1,720,1,"e1","d2"], "( A5 x A6 ) # 2^5 [18]",[33,5,18],2, [1,3],480], # 691200.19 [[3,1920,2,720,1,"d1","d2"], "( A5 x A6 ) # 2^5 [19]",[33,5,19],2, [1,3],960], # 691200.20 [[3,1920,3,720,1,"d1","d2"], "( A5 x A6 ) # 2^5 [20]",[33,5,20],2, [1,3],[640,960]], # 691200.21 [[3,1920,5,720,1,"d1","d2"], "( A5 x A6 ) # 2^5 [21]",[33,5,21],2, [1,3],[400,960]], # 691200.22 [[3,1920,6,720,1,"d1","d2"], "( A5 x A6 ) # 2^5 [22]",[33,5,22],2, [1,3],3200], # 691200.23 [[3,1920,7,720,1,"e1","d2"], "( A5 x A6 ) # 2^5 [23]",[33,5,23],2, [1,3],1280] ]; PERFGRP[278]:=[# 693120.1 [[4,1920,3,43320,2,120,3,1], "A5 # 2^5 19^2 [1]",6,1, 1,[16,24,361]], # 693120.2 [[4,1920,4,43320,2,120,4,1], "A5 # 2^5 19^2 [2]",6,1, 1,[80,361]], # 693120.3 [[4,1920,5,43320,2,120,5,1], "A5 # 2^5 19^2 [3]",6,1, 1,[10,24,361]] ]; PERFGRP[279]:=[# 699840.1 [[4,960,1,43740,1,60], "A5 # 2^4 3^6 [1]",6,1, 1,[16,18]], # 699840.2 [[4,960,2,43740,1,60], "A5 # 2^4 3^6 [2]",6,1, 1,[10,18]] ]; PERFGRP[280]:=[# 704880.1 [[1,"abc", function(a,b,c) return [[c^44*a^2,c*b^9*c^-1*b^-1,b^89,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*b^3*c*b^3*a*b^3*a*c*b^3*a],[[b,c^8]]] ; end, [720],[0,3,3]], "L2(89) 2^1 = SL(2,89)",22,-2, 44,720] ]; PERFGRP[281]:=[# 712800.1 [[2,1080,1,660,1], "A6 3^1 x L2(11)",40,3, [3,5],[18,11]] ]; PERFGRP[282]:=[# 720720.1 [[2,660,1,1092,1], "L2(11) x L2(13)",40,1, [5,6],[11,14]] ]; PERFGRP[283]:=[# 721392.1 [[1,"abc", function(a,b,c) return [[c^56,c*b^9*c^-1*b^-1,b^113,a^2,c*a*c*a^-1 ,(b*a)^3,c^(-1*3)*b^2*c*b^2*c^2*a*b^3*a*c*b^3 *a],[[b,c]]]; end, [114],[0,3,3]], "L2(113)",22,-1, 53,114] ]; PERFGRP[284]:=[# 725760.1 [[2,336,1,2160,1], "( L3(2) x A6 3^1 ) 2^2",[37,2,1],12, [2,3],[16,18,80]], # 725760.2 [[2,120,1,6048,1], "A5 2^1 x U3(3)",40,2, [1,12],[24,28]] ]; PERFGRP[285]:=[# 728640.1 [[2,60,1,12144,1], "( A5 x L2(23) ) 2^1 [1]",40,2, [1,13],[5,48]], # 728640.2 [[2,120,1,6072,1], "( A5 x L2(23) ) 2^1 [2]",40,2, [1,13],[24,24]], # 728640.3 [[3,120,1,12144,1,"d1","a2","a2"], "( A5 x L2(23) ) 2^1 [3]",40,2, [1,13],576] ]; PERFGRP[286]:=[# 729000.1 [[4,29160,5,3000,2,120,2,1], "A5 2^1 # 3^5 5^2 [1]",6,3, 1,[243,25]], # 729000.2 [[4,29160,6,3000,2,120,3,1], "A5 2^1 # 3^5 5^2 [2]",6,3, 1,[243,25]] ]; PERFGRP[287]:=[# 730800.1 [[2,60,1,12180,1], "A5 x L2(29)",40,1, [1,17],[5,30]] ]; PERFGRP[288]:=[# 733824.1 [[2,336,1,2184,1], "( L3(2) x L2(13) ) 2^2",40,4, [2,6],[16,56]] ]; PERFGRP[289]:=[# 734832.1 [[1,"abuvwxyzd", function(a,b,u,v,w,x,y,z,d) return [[a^4,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4*a^2,a^2*b *a^2*b^-1,d^3,a^-1*d*a*d^-1, b^-1*d*b*d^-1,u^-1*d*u*d^-1, v^-1*d*v*d^-1,w^-1*d*w*d^-1, x^-1*d*x*d^-1,y^-1*d*y*d^-1, z^-1*d*z*d^-1,u^3,v^3,w^3,x^3,y^3,z^3, u^-1*v^-1*u*v*d,u^-1*w^-1*u*w *d^-1,u^-1*x^-1*u*x*d^-1, u^-1*y^-1*u*y*d^-1,u^-1*z^-1*u *z,v^-1*w^-1*v*w*d^-1, v^-1*x^-1*v*x*d,v^-1*y^-1*v*y*d, v^-1*z^-1*v*z*d,w^-1*x^-1*w*x, w^-1*y^-1*w*y*d^-1, w^-1*z^-1*w*z*d^-1, x^-1*y^-1*x*y*d^-1, x^-1*z^-1*x*z*d,y^-1*z^-1*y*z*d, a^-1*u*a*(x*y^-1*z^-1*d)^-1, a^-1*v*a*(w*x^-1*y^-1*d)^-1, a^-1*w*a*(u*w^-1*x*y^-1*z^-1)^-1 ,a^-1*x*a*(v*w*x*y^-1)^-1, a^-1*y*a*(u*v*w*z^-1*d)^-1, a^-1*z*a*(u*x*y^-1*z*d^-1)^-1, b^-1*u*b*(v*w^-1*x^-1)^-1, b^-1*v*b*(u*v^-1*w^-1*d^-1)^-1, b^-1*w*b*(u^-1*v*w^-1*x^-1*z^-1) ^-1,b^-1*x*b*(u*v*w^-1*y^-1*z*d) ^-1,b^-1*y*b*(u*x^-1*y*d)^-1, b^-1*z*b*(v*w^-1*x*z)^-1], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,u], [a,b]]]; end, [16,2187]], "L3(2) 2^1 x 3^6 C 3^1",[9,7,1],6, 2,[16,2187]], # 734832.2 [[1,"abtuvwxyz", function(a,b,t,u,v,w,x,y,z) return [[a^4,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4*a^2,a^2*b *a^2*b^-1,t^3,u^3,v^3,w^3,x^3,y^3,z^3, t^-1*u^-1*t*u,t^-1*v^-1*t*v, t^-1*w^-1*t*w,t^-1*x^-1*t*x, t^-1*y^-1*t*y,t^-1*z^-1*t*z, u^-1*v^-1*u*v,u^-1*w^-1*u*w, u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,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*t*a*t^-1, a^-1*u*a*w^-1,a^-1*v*a*v, a^-1*w*a*u^-1,a^-1*x*a*z^-1, a^-1*y*a*y,a^-1*z*a*x^-1, b^-1*t*b*u^-1,b^-1*u*b*v^-1, b^-1*v*b*t^-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], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,t], [a*b,a^2,t*u^-1]]]; end, [16,72]], "L3(2) 2^1 x 3^7",[9,7,2],2, 2,[16,72]], # 734832.3 [[1,"abtuvwxyz", function(a,b,t,u,v,w,x,y,z) return [[a^4,b^3/(t*u*v*z^-1),(a*b)^7,(a^-1*b^-1*a*b)^4*a^2,a^2*b *a^2*b^-1,t^3,u^3,v^3,w^3,x^3,y^3,z^3, t^-1*u^-1*t*u,t^-1*v^-1*t*v, t^-1*w^-1*t*w,t^-1*x^-1*t*x, t^-1*y^-1*t*y,t^-1*z^-1*t*z, u^-1*v^-1*u*v,u^-1*w^-1*u*w, u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,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*t*a*t^-1, a^-1*u*a*w^-1,a^-1*v*a*v, a^-1*w*a*u^-1,a^-1*x*a*z^-1, a^-1*y*a*y,a^-1*z*a*x^-1, b^-1*t*b*u^-1,b^-1*u*b*v^-1, b^-1*v*b*t^-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], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,t], [a*b,a^2,t*u^-1]]]; end, [16,72]], "L3(2) 2^1 x N 3^7",[9,7,3],2, 2,[16,72]] ]; PERFGRP[290]:=[fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail]; PERFGRP[291]:=[# 748920.1 [[1,"abyz", function(a,b,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^79,z^79,y^-1 *z^-1*y*z,a^-1*y*a*z^-1, a^-1*z*a*y,b^-1*y*b*(y^(-1*21)*z^4)^-1, b^-1*z*b*(y^33*z^20)^-1], [[b,a^2,y*z^(-1*36)]]]; end, [1580],[0,0,3,3,3,3]], "A5 2^1 79^2",[5,2,1],1, 1,1580] ]; PERFGRP[292]:=[# 768000.1 [[4,30720,1,3000,2,120,1,1], "A5 # 2^9 5^2 [1]",6,16, 1,[24,64,64,25]], # 768000.2 [[4,30720,4,3000,2,120,4,1], "A5 # 2^9 5^2 [2]",6,1, 1,[240,25]], # 768000.3 [[4,30720,9,3000,2,120,9,1], "A5 # 2^9 5^2 [3]",6,1, 1,[16,16,24,25]], # 768000.4 [[4,30720,10,3000,2,120,10,1], "A5 # 2^9 5^2 [4]",6,1, 1,[16,80,25]], # 768000.5 [[4,30720,11,3000,2,120,11,1], "A5 # 2^9 5^2 [5]",6,1, 1,[240,25]], # 768000.6 [[4,30720,14,3000,2,120,14,1], "A5 # 2^9 5^2 [6]",6,1, 1,[40,24,25]], # 768000.7 [[4,30720,18,3000,2,120,18,1], "A5 # 2^9 5^2 [7]",6,1, 1,[10,16,24,25]], # 768000.8 [[4,30720,22,3000,2,120,22,1], "A5 # 2^9 5^2 [8]",6,1, 1,[160,25]], # 768000.9 [[4,30720,23,3000,2,120,23,1], "A5 # 2^9 5^2 [9]",6,1, 1,[10,80,25]], # 768000.10 [[4,30720,26,3000,2,120,26,1], "A5 # 2^9 5^2 [10]",6,1, 1,[10,10,24,25]], # 768000.11 [[4,30720,33,3000,2,120,33,1], "A5 # 2^9 5^2 [11]",6,1, 1,[24,20,25]], # 768000.12 [[4,30720,36,3000,2,120,36,1], "A5 # 2^9 5^2 [12]",6,1, 1,[80,25]], # 768000.13 [[4,30720,37,3000,2,120,37,1], "A5 # 2^9 5^2 [13]",6,1, 1,[80,25]] ]; PERFGRP[293]:=[# 774144.1 [[1,"abuvwxyzd", function(a,b,u,v,w,x,y,z,d) return [[a^2,b^6,(a*b)^7,(a*b^2)^3*(a*b^(-1*2))^3,(a*b*a*b ^(-1*2))^3*a*b*(a*b^-1)^2,u^2,v^2,w^2, x^2,y^2,z^2,d^2,u^-1*d*u*d^-1, v^-1*d*v*d^-1,w^-1*d*w*d^-1, x^-1*d*x*d^-1,y^-1*d*y*d^-1, z^-1*d*z*d^-1,u^-1*v^-1*u*v, u^-1*w^-1*u*w,u^-1*x^-1*u*x, u^-1*y^-1*u*y,u^-1*z^-1*u*z, v^-1*w^-1*v*w,v^-1*x^-1*v*x, v^-1*y^-1*v*y,v^-1*z^-1*v*z, 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*u*a*(u*z)^-1, a^-1*v*a*(u*v*x*z*d)^-1, a^-1*w*a*(u*w*x*z*d)^-1, a^-1*x*a*(x*z)^-1, a^-1*y*a*(u*x*y*d)^-1,a^-1*z*a*z^-1 ,a^-1*d*a*d^-1, b^-1*u*b*(u*w*x*y*z*d)^-1, b^-1*v*b*(u*x*z*d)^-1, b^-1*w*b*(u*w*z)^-1, b^-1*x*b*(u*v*w*x*z)^-1, b^-1*y*b*(v*y*z*d)^-1, b^-1*z*b*(u*v*w*x*y*z)^-1, b^-1*d*b*d^-1],[[a,b]]]; end, [128]], "U3(3) ( 2^6 E 2^1 )",[25,7,1],2, 12,128], # 774144.2 [[1,"abuvwxyzd", function(a,b,u,v,w,x,y,z,d) return [[a^2*(u*x*z)^-1,b^6*d^-1,(a*b)^7*d^-1,(a *b^2)^3*(a*b^(-1*2))^3*(w*y*z)^-1, (a*b*a*b^(-1*2))^3*a*b*(a*b^-1)^2 *(w*x*y)^-1*d^-1,u^2,v^2,w^2,x^2,y^2, z^2,d^2,u^-1*d*u*d^-1,v^-1*d*v*d^-1 ,w^-1*d*w*d^-1,x^-1*d*x*d^-1, y^-1*d*y*d^-1,z^-1*d*z*d^-1, u^-1*v^-1*u*v,u^-1*w^-1*u*w, u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,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*u*a*(u*z*d)^-1, a^-1*v*a*(u*v*x*z*d)^-1, a^-1*w*a*(u*w*x*z*d)^-1, a^-1*x*a*(x*z*d)^-1, a^-1*y*a*(u*x*y)^-1,a^-1*z*a*z^-1, a^-1*d*a*d^-1, b^-1*u*b*(u*w*x*y*z)^-1, b^-1*v*b*(u*x*z*d)^-1, b^-1*w*b*(u*w*z)^-1, b^-1*x*b*(u*v*w*x*z*d)^-1, b^-1*y*b*(v*y*z)^-1, b^-1*z*b*(u*v*w*x*y*z*d)^-1, b^-1*d*b*d^-1], [[(b^-1*a*b)^-1*(a*b*a*b*a*b^(-1*2))^-1 *b^-1*a*b*a*b*a*b*a*b^(-1*2), a*b*a*b*a*b^(-1*2)*(b^-1*a*b)^-1 *(a*b*a*b*a*b^(-1*2))^-1*b^-1*a*b,u ]]]; end, [448],[[1,2],[10,10,10],[2,2],[1,-12]]], "U3(3) ( N 2^6 E 2^1 )",[25,7,2],2, 12,448] ]; PERFGRP[294]:=[# 777600.1 [[2,360,1,2160,1], "( A6 x A6 ) 3^1 2^1 [1]",40,6, [3,3],[6,18,80]], # 777600.2 [[2,720,1,1080,1], "( A6 x A6 ) 3^1 2^1 [2]",40,6, [3,3],[80,18]], # 777600.3 [[3,720,1,2160,1,"d1","d2"], "( A6 x A6 ) 3^1 2^1 [3]",40,6, [3,3],[720,3200]], # 777600.4 [[3,1080,1,2160,1,"a1","a1","a2","a2","a2","a2"], "( A6 x A6 ) 3^1 2^1 [4]",40,6, [3,3],[108,480]], # 777600.5 [[3,2160,1,2160,1,"a1","a1","a2","a2"], "( A6 x A6 ) 3^1 2^1 [5]",40,6, [3,3],[108,240,240,3200]] ]; PERFGRP[295]:=[# 786240.1 [[2,360,1,2184,1], "( A6 x L2(13) ) 2^1 [1]",40,2, [3,6],[6,56]], # 786240.2 [[2,720,1,1092,1], "( A6 x L2(13) ) 2^1 [2]",40,2, [3,6],[80,14]], # 786240.3 [[3,720,1,2184,1,"d1","a2","a2"], "( A6 x L2(13) ) 2^1 [3]",40,2, [3,6],2240] ]; ############################################################################# ## #E perf11.grp . . . . . . . . . . . . . . . . . . . . . . . . . ends here ##