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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 perf7.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 92160-174960 ## All data is based on Holt/Plesken: Perfect Groups, OUP 1989 ## PERFGRP[114]:=[# 92160.1 [[1,"abcstuvSTUV", function(a,b,c,s,t,u,v,S,T,U,V) 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,s^2,t^2,u^2, v^2,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,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,s^-1*S^-1*s*S, s^-1*T^-1*s*T,s^-1*U^-1*s*U, s^-1*V^-1*s*V,t^-1*S^-1*t*S, t^-1*T^-1*t*T,t^-1*U^-1*t*U, t^-1*V^-1*t*V,u^-1*S^-1*u*S, u^-1*T^-1*u*T,u^-1*U^-1*u*U, u^-1*V^-1*u*V,v^-1*S^-1*v*S, v^-1*T^-1*v*T,v^-1*U^-1*v*U, v^-1*V^-1*v*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,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)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*S*b*(T*V)^-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)^-1, c^-1*v*c*(s*t*u*v)^-1, c^-1*S*c*(T*U)^-1,c^-1*T*c*T^-1, c^-1*U*c*(S*U)^-1, c^-1*V*c*(S*T*U*V)^-1],[[b,c,S],[b,c,s]]]; end, [16,16]], "A6 2^4 x 2^4",[13,8,1],1, 3,[16,16]], # 92160.2 [[1,"abcstuvwxyz", function(a,b,c,s,t,u,v,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,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, t^-1*u^-1*t*u,t^-1*v^-1*t*v, u^-1*v^-1*u*v,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,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*w^-1*t*w, t^-1*x^-1*t*x,t^-1*y^-1*t*y, t^-1*z^-1*t*z,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,a^-1*s*a*u^-1, a^-1*t*a*v^-1,a^-1*u*a*s^-1, a^-1*v*a*t^-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*s*b*(t*v)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*(x*y)^-1,b^-1*x*b*x^-1, b^-1*y*b*(w*y)^-1, b^-1*z*b*(w*x*y*z)^-1, c^-1*s*c*(t*u)^-1,c^-1*t*c*t^-1, c^-1*u*c*(s*u)^-1, c^-1*v*c*(s*t*u*v)^-1, c^-1*w*c*(x*z)^-1, c^-1*x*c*(w*x*y*z)^-1, c^-1*y*c*(y*z)^-1,c^-1*z*c*y^-1], [[b,c,s],[b,c,w]]]; end, [16,16]], "A6 2^4 x 2^4'",[13,8,2],1, 3,[16,16]] ]; PERFGRP[115]:=[# 95040.1 [[1,"ab", function(a,b) return [[a^2,b^3,(a*b)^11,(a^-1*b^-1*a*b)^6,(a*b*a*b*a *b^-1)^6,(a*b*a*b*a*b^-1*a*b^-1)^5], [[a,b*a*b^-1*a*(b^-1*a*b*a)^2]]]; end, [12]], "M12",28,-1, 31,12] ]; PERFGRP[116]:=[# 96000.1 [[4,3840,5,3000,2,120,5,1], "A5 # 2^6 5^2 [1]",6,2, 1,[24,12,25]], # 96000.2 [[4,3840,6,3000,2,120,6,1], "A5 # 2^6 5^2 [2]",6,2, 1,[48,25]], # 96000.3 [[4,3840,7,3000,2,120,7,1], "A5 # 2^6 5^2 [3]",6,2, 1,[32,24,25]] ]; PERFGRP[117]:=[# 100920.1 [[1,"abyz", function(a,b,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^29,z^29,y^-1 *z^-1*y*z,a^-1*y*a*z^-1, a^-1*z*a*y,b^-1*y*b*(y^14*z^4)^-1, b^-1*z*b*(y^(-1*2)*z^14)^-1],[[a,b]]]; end, [841],[0,0,2,2,2,2]], "A5 2^1 29^2",[5,2,1],1, 1,841] ]; PERFGRP[118]:=[# 102660.1 [[1,"abc", function(a,b,c) return [[c^29,c*b^4*c^-1*b^-1,b^59,a^2,c*a*c*a^-1, (b*a)^3],[[b,c]]]; end, [60]], "L2(59)",22,-1, 32,60] ]; PERFGRP[119]:=[# 103776.1 [[1,"abc", function(a,b,c) return [[c^23*a^2,c*b^(-1*22)*c^-1*b^-1,b^47,a^4,a^2 *b^-1*a^2*b,a^2*c^-1*a^2*c, c*a*c*a^-1,(b*a)^3],[[b,c^2]]]; end, [96],[0,2,2,2]], "L2(47) 2^1 = SL(2,47)",22,-2, 27,96] ]; PERFGRP[120]:=[# 110880.1 [[2,168,1,660,1], "L3(2) x L2(11)",[39,0,1],1, [2,5],[7,11]] ]; PERFGRP[121]:=[# 112896.1 [[2,336,1,336,1], "( L3(2) x L3(2) ) 2^2",[34,2,1],4, [2,2],[16,16]] ]; PERFGRP[122]:=[# 113460.1 [[1,"abc", function(a,b,c) return [[c^30,c*b^4*c^-1*b^-1,b^61,a^2,c*a*c*a^-1, (b*a)^3,c^(-1*4)*(b*c)^3*c*a*b^2*a*c*b^2*a], [[b,c]]]; end, [62]], "L2(61)",22,-1, 33,62] ]; PERFGRP[123]:=[# 115200.1 [[2,960,1,120,1], "( A5 x A5 ) # 2^5 [1]",[29,5,1],2, [1,1],[16,24]], # 115200.2 [[2,960,2,120,1], "( A5 x A5 ) # 2^5 [2]",[29,5,2],2, [1,1],[10,24]], # 115200.3 [[2,1920,1,60,1], "( A5 x A5 ) # 2^5 [3]",[29,5,3],2, [1,1],[12,5]], # 115200.4 [[2,1920,2,60,1], "( A5 x A5 ) # 2^5 [4]",[29,5,4],2, [1,1],[24,5]], # 115200.5 [[2,1920,3,60,1], "( A5 x A5 ) # 2^5 [5]",[29,5,5],2, [1,1],[16,24,5]], # 115200.6 [[2,1920,4,60,1], "( A5 x A5 ) # 2^5 [6]",[29,5,6],1, [1,1],[80,5]], # 115200.7 [[2,1920,5,60,1], "( A5 x A5 ) # 2^5 [7]",[29,5,7],2, [1,1],[10,24,5]], # 115200.8 [[2,1920,6,60,1], "( A5 x A5 ) # 2^5 [8]",[29,5,8],2, [1,1],[80,5]], # 115200.9 [[2,1920,7,60,1], "( A5 x A5 ) # 2^5 [9]",[29,5,9],2, [1,1],[32,5]], # 115200.10 [[3,1920,1,120,1,"e1","d2"], "( A5 x A5 ) # 2^5 [10]",[29,5,10],2, [1,1],144], # 115200.11 [[3,1920,2,120,1,"d1","d2"], "( A5 x A5 ) # 2^5 [11]",[29,5,11],2, [1,1],288], # 115200.12 [[3,1920,3,120,1,"d1","d2"], "( A5 x A5 ) # 2^5 [12]",[29,5,12],2, [1,1],[192,288]], # 115200.13 [[3,1920,5,120,1,"d1","d2"], "( A5 x A5 ) # 2^5 [13]",[29,5,13],2, [1,1],[120,288]], # 115200.14 [[3,1920,6,120,1,"d1","d2"], "( A5 x A5 ) # 2^5 [14]",[29,5,14],2, [1,1],960], # 115200.15 [[3,1920,7,120,1,"e1","d2"], "( A5 x A5 ) # 2^5 [15]",[29,5,15],2, [1,1],384] ]; PERFGRP[124]:=[# 115248.1 [[1,"abxyz", function(a,b,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,x^7,y^7,z^7,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*y, a^-1*z*a*x^-1,b^-1*x*b*z^-1, b^-1*y*b*(y^-1*z^-1)^-1, b^-1*z*b*(x*y^2*z)^-1], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x], [a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,a^2,y ]]]; end, [16,56]], "L3(2) 2^1 x 7^3",[10,3,1],2, 2,[16,56]], # 115248.2 [[1,"abxyz", function(a,b,x,y,z) return [[a^4,b^3,(a*b)^7*z^-1,(a^-1*b^-1*a*b)^4 *a^2,a^2*b*a^2*b^-1,x^7,y^7,z^7, 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*y,a^-1*z*a*x^-1, b^-1*x*b*z^-1, b^-1*y*b*(y^-1*z^-1)^-1, b^-1*z*b*(x*y^2*z)^-1], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x], [a*b*x^2,b*a*b^-1*a*b^-1*a*b*a*b^-1, a^2,y]]]; end, [16,56]], "L3(2) 2^1 x N 7^3",[10,3,2],2, 2,[16,56]], # 115248.3 [[1,"abyzd", function(a,b,y,z,d) return [[a^4,b^3,(a*b)^7,a^2*b^-1*a^2*b,(a^-1*b^-1 *a*b)^4*a^2,d^7,a^-1*d*a*d^-1, b^-1*d*b*d^-1,y^-1*d*y*d^-1, z^-1*d*z*d^-1,y^7,z^7, y^-1*z^-1*y*z*d^-1, a^-1*y*a*(z^-1*d^(-1*2))^-1, a^-1*z*a*(y*d^2)^-1, b^-1*y*b*(z*d^(-1*2))^-1, b^-1*z*b*(y^-1*z^-1*d)^-1],[[a,b]]]; end, [343]], "L3(2) 2^1 7^2 C 7^1",[10,3,3],7, 2,343], # 115248.4 (otherpres.) [[1,"abDyzd", function(a,b,D,y,z,d) 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,d^7, a^-1*d*a*d^-1,b^-1*d*b*d^-1, y^-1*d*y*d^-1,z^-1*d*z*d^-1,y^7, z^7,y^-1*z^-1*y*z*d^-1, a^-1*y*a*(z^-1*d^(-1*2))^-1, a^-1*z*a*(y*d^2)^-1, b^-1*y*b*(z*d^(-1*2))^-1, b^-1*z*b*(y^-1*z^-1*d)^-1],[[a,b]]]; end, [343]]] ]; PERFGRP[125]:=[# 115320.1 [[1,"abyz", function(a,b,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^31,z^31,y^-1 *z^-1*y*z,a^-1*y*a*z^-1, a^-1*z*a*y,b^-1*y*b*(y^-1*z^15)^-1, b^-1*z*b*y^(-1*2)],[[a*b,a^2,y]]]; end, [372]], "A5 2^1 31^2",[5,2,1],1, 1,372] ]; PERFGRP[126]:=[# 116480.1 [[1,"abde", function(a,b,d,e) return [[a^2,b^4,(a*b)^5,(a^-1*b^-1*a*b)^7*(d*e)^-1 ,(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*e^-1,d^2,e^2, d^-1*e^-1*d*e,a^-1*d*a*d^-1, a^-1*e*a*e^-1,b^-1*d*b*d^-1, b^-1*e*b*e^-1], [[a*b^2,(a*b*a*b^2)^2*a*b^2*a*b^-1 *(a*b^2*a*b*a*b^2)^2]]]; end, [2240],[[1,2]]], "Sz(8) 2^1 x 2^1",28,-4, 23,2240] ]; PERFGRP[127]:=[# 117600.1 [[1,"abc", function(a,b,c) return [[c^24*a^2,b^7,c^(-1*8)*b^2*c^8*b^-1,c*b^3*c*b^2 *c^(-1*2)*b^(-1*3),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*c*b^2*a*b*a*c*a*b^2*a*b^-1*c^(-1*3) *b^-1*a],[[b,c^-1*b*c,c^16]]]; end, [800],[0,2,2,0,2,2]], "L2(49) 2^1 = SL(2,49)",22,-2, 28,800] ]; PERFGRP[128]:=[# 120000.1 [[4,960,1,7500,1,60], "A5 # 2^4 5^3 [1]",6,1, 1,[16,30]], # 120000.2 [[4,960,2,7500,1,60], "A5 # 2^4 5^3 [2]",6,1, 1,[10,30]], # 120000.3 [[4,960,1,7500,2,60], "A5 # 2^4 5^3 [3]",6,1, 1,[16,30]], # 120000.4 [[4,960,2,7500,2,60], "A5 # 2^4 5^3 [4]",6,1, 1,[10,30]] ]; PERFGRP[129]:=[# 120960.1 [[1,"abwxyz", function(a,b,w,x,y,z) return [[a^6,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 *a^2,a^2*b*a^(-1*2)*b^-1,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,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^3,(b^-1*a)^2*(b*a)^2*b^2*a*b*a,w],[a,b]]]; end, [45,16]], "A7 3^1 x 2^4",[23,4,1],3, 8,[45,16]], # 120960.2 [[1,"abde", function(a,b,d,e) return [[a^2,b^4,(a*b)^7*e*d^-1,(a^-1*b^-1*a*b)^5, (a*b^2)^5*e^-1,(a*b*a*b*a*b^3)^5, (a*b*a*b*a*b^2*a*b^-1)^5*d^(-1*2),d^3, a^-1*d*a*d^-1,b^-1*d*b*d^-1,e^2, a^-1*e*a*e^-1,b^-1*e*b*e^-1], [[a*b*a,b^2*a*b^-1*a*b*a*b^2*a*b*d], [a*e,b*a*b*a*b^-1*a*b^2]]]; end, [63,112]], "L3(4) 3^1 x 2^1",[27,1,1],-6, 20,[63,112]], # 120960.3 [[2,168,1,720,1], "( L3(2) x A6 ) 2^1 [1]",[37,1,1],2, [2,3],[7,80]], # 120960.4 [[2,336,1,360,1], "( L3(2) x A6 ) 2^1 [2]",[37,1,2],2, [2,3],[16,6]], # 120960.5 [[3,336,1,720,1,"d1","d2"], "( L3(2) x A6 ) 2^1 [3]",[37,1,3],2, [2,3],640] ]; PERFGRP[130]:=[# 122472.1 [[1,"abuvwxyz", function(a,b,u,v,w,x,y,z) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,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*(x*y^-1*z^-1)^-1, a^-1*v*a*(w*x^-1*y^-1)^-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)^-1, a^-1*z*a*(u*x*y^-1*z)^-1, b^-1*u*b*(v*w^-1*x^-1)^-1, b^-1*v*b*(u*v^-1*w^-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) ^-1,b^-1*y*b*(u*x^-1*y)^-1, b^-1*z*b*(v*w^-1*x*z)^-1], [[a,b^-1*a*b,z]]]; end, [63]], "L3(2) 3^6",[9,6,1],1, 2,63], # 122472.2 [[1,"abuvwxyz", function(a,b,u,v,w,x,y,z) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,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*w^-1,a^-1*v*a*v^-1, a^-1*w*a*u^-1,a^-1*x*a*z^-1, a^-1*y*a*y^-1,a^-1*z*a*x^-1, b^-1*u*b*v^-1, b^-1*v*b*(u^-1*v^-1*w^-1*x^-1 *y^-1*z^-1)^-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,a*b^-1*a*b*a,x*y^-1*z]]]; end, [21]], "L3(2) 3^6'",[9,6,2],1, 2,21] ]; PERFGRP[131]:=fail; PERFGRP[132]:=[# 126000.1 [[1,"ab", function(a,b) return [[a^2,b^4,(a*b)^10,(a*b*a*b^2)^7,a*b^-1*a*b^-1 *a*b*a*b^(-1*2)*a*b *a*b^-1*a*b^-1*a*b *a*b*a*b^-1*a*b*b*a*b^-1 *a*b*a*b, (a*b^-1*a*b^-1*a*b*a*b*a*b)^2*b*a *b^-1*a*b^-1*a*b*a*b*a *b^-1],[[b,a*b*a*b^-1*a]]]; end, [50],[[1,2],0,2]], "U3(5)",28,-1, 34,50] ]; PERFGRP[133]:=[# 129024.1 [[1,"abcuvwxyzde", function(a,b,c,u,v,w,x,y,z,d,e) return [[a^2,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,c*b^-1 *c*b*a^-1*b^-1*c^-1*b *c^-1*a,u^2,v^2,w^2,x^2,y^2,z^2,d^2,e^2, 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,u^-1*d^-1*u*d, u^-1*e^-1*u*e,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,v^-1*d^-1*v*d, v^-1*e^-1*v*e,w^-1*x^-1*w*x, w^-1*y^-1*w*y,w^-1*z^-1*w*z, w^-1*d^-1*w*d,w^-1*e^-1*w*e, x^-1*y^-1*x*y,x^-1*z^-1*x*z, x^-1*d^-1*x*d,x^-1*e^-1*x*e, y^-1*z^-1*y*z,y^-1*d^-1*y*d, y^-1*e^-1*y*e,z^-1*d^-1*z*d, z^-1*e^-1*z*e,d^-1*e^-1*d*e, a^-1*u*a*(u*x)^-1,a^-1*v*a*(v*y)^-1, a^-1*w*a*(w*z)^-1,a^-1*x*a*x^-1, a^-1*y*a*y^-1,a^-1*z*a*z^-1, a^-1*d*a*d^-1,a^-1*e*a*e^-1, b^-1*u*b*(x*y*d)^-1, b^-1*v*b*(y*z*e)^-1, b^-1*w*b*(x*y*z)^-1, b^-1*x*b*(v*w*x)^-1, b^-1*y*b*(u*v*w*y)^-1, b^-1*z*b*(u*w*z)^-1,b^-1*d*b*d^-1, b^-1*e*b*e^-1,c^-1*u*c*(v*d)^-1, c^-1*v*c*(w*d)^-1, c^-1*w*c*(u*v*e)^-1, c^-1*x*c*(x*z*d)^-1, c^-1*y*c*(x*e)^-1,c^-1*z*c*y^-1, c^-1*d*c*d^-1,c^-1*e*c*e^-1], [[b^-1*c,u*d,e],[b^-1*c,u*e,d]]]; end, [112,112]], "L2(8) 2^6 E ( 2^1 x 2^1 )",[16,8,1],4, 4,[112,112]], # 129024.2 [[1,"abcuvwxyzf", function(a,b,c,u,v,w,x,y,z,f) return [[a^2*f,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,b^-1 *c^-1*b*c^-1*a^-1*c *b^-1*c*b*a*(y*z*f^2)^-1,f^4,u^2, v^2*f^2,w^2,x^2*f^2,y^2,z^2*f^2, u^-1*v^-1*u*v,u^-1*w^-1*u*w, u^-1*x^-1*u*x*f^2,u^-1*y^-1*u*y *f^2,u^-1*z^-1*u*z,u^-1*f^-1*u*f, v^-1*w^-1*v*w,v^-1*x^-1*v*x*f^2, v^-1*y^-1*v*y,v^-1*z^-1*v*z, v^-1*f^-1*v*f,w^-1*x^-1*w*x, w^-1*y^-1*w*y,w^-1*z^-1*w*z*f^2, w^-1*f^-1*w*f,x^-1*y^-1*x*y, x^-1*z^-1*x*z,x^-1*f^-1*x*f, y^-1*z^-1*y*z,y^-1*f^-1*y*f, z^-1*f^-1*z*f,a^-1*u*a*(u*x)^-1, a^-1*v*a*(v*y*f^2)^-1, a^-1*w*a*(w*z)^-1, a^-1*x*a*(x*f^2)^-1,a^-1*y*a*y^-1, a^-1*z*a*(z*f^2)^-1,a^-1*f*a*f^-1, b^-1*u*b*(x*y*f^-1)^-1, b^-1*v*b*(y*z*f^2)^-1, b^-1*w*b*(x*y*z*f^2)^-1, b^-1*x*b*(v*w*x)^-1, b^-1*y*b*(u*v*w*y*f^2)^-1, b^-1*z*b*(u*w*z*f^-1)^-1, b^-1*f*b*f^-1, c^-1*u*c*(v*f^-1)^-1, c^-1*v*c*(w*f^-1)^-1, c^-1*w*c*(u*v*f)^-1, c^-1*x*c*(x*z*f)^-1, c^-1*y*c*(x*f)^-1, c^-1*z*c*(y*f^-1)^-1, c^-1*f*c*f^-1],[[c^-1*v^-1*a, w*c]]]; end, [288],[[1,2],[11,11,11]]], "L2(8) N ( 2^6 E 2^1 A ) C 2^1",[16,8,2],4, 4,288], # 129024.3 [[1,"abcuvwxyzdf", function(a,b,c,u,v,w,x,y,z,d,f) return [[a^2*f,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,b^-1 *c^-1*b*c^-1*a^-1*c *b^-1*c*b*a*(y*z*d)^-1,d^2,f^2,u^2, v^2,w^2,x^2,y^2,z^2,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, u^-1*d^-1*u*d,u^-1*f^-1*u*f, v^-1*w^-1*v*w,v^-1*x^-1*v*x, v^-1*y^-1*v*y,v^-1*z^-1*v*z, v^-1*d^-1*v*d,v^-1*f^-1*v*f, w^-1*x^-1*w*x,w^-1*y^-1*w*y, w^-1*z^-1*w*z,w^-1*d^-1*w*d, w^-1*f^-1*w*f,x^-1*y^-1*x*y, x^-1*z^-1*x*z,x^-1*d^-1*x*d, x^-1*f^-1*x*f,y^-1*z^-1*y*z, y^-1*d^-1*y*d,y^-1*f^-1*y*f, z^-1*d^-1*z*d,z^-1*f^-1*z*f, a^-1*u*a*(u*x)^-1,a^-1*v*a*(v*y)^-1, a^-1*w*a*(w*z)^-1,a^-1*x*a*x^-1, a^-1*y*a*y^-1,a^-1*z*a*z^-1, a^-1*d*a*d^-1,a^-1*f*a*f^-1, b^-1*u*b*(x*y*f^-1)^-1, b^-1*v*b*(y*z)^-1, b^-1*w*b*(x*y*z*d)^-1, b^-1*x*b*(v*w*x)^-1, b^-1*y*b*(u*v*w*y*d)^-1, b^-1*z*b*(u*w*z*f^-1)^-1, b^-1*d*b*d^-1,b^-1*f*b*f^-1, c^-1*u*c*(v*d*f^-1)^-1, c^-1*v*c*(w*d*f^-1)^-1, c^-1*w*c*(u*v*f)^-1, c^-1*x*c*(x*z*d*f)^-1, c^-1*y*c*(x*d*f)^-1, c^-1*z*c*(y*f^-1)^-1, c^-1*d*c*d^-1,c^-1*f*c*f^-1], [[b^-1*c,u*f,d],[b^-1*c*d,u*d,f]]]; end, [112,112],[[1,2]]], "L2(8) N 2^6 E ( 2^1 x 2^1 ) I",[16,8,3],4, 4,[112,112]], # 129024.4 [[1,"abcuvwxyzde", function(a,b,c,u,v,w,x,y,z,d,e) return [[a^2,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,b^-1*c ^-1*b*c^-1*a^-1*c*b^-1 *c*b*a*(y*z*d)^-1,d^2,e^2,u^2,v^2,w^2, x^2,y^2,z^2,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, u^-1*d^-1*u*d,u^-1*e^-1*u*e, v^-1*w^-1*v*w,v^-1*x^-1*v*x, v^-1*y^-1*v*y,v^-1*z^-1*v*z, v^-1*d^-1*v*d,v^-1*e^-1*v*e, w^-1*x^-1*w*x,w^-1*y^-1*w*y, w^-1*z^-1*w*z,w^-1*d^-1*w*d, w^-1*e^-1*w*e,x^-1*y^-1*x*y, x^-1*z^-1*x*z,x^-1*d^-1*x*d, x^-1*e^-1*x*e,y^-1*z^-1*y*z, y^-1*d^-1*y*d,y^-1*e^-1*y*e, z^-1*d^-1*z*d,z^-1*e^-1*z*e, a^-1*u*a*(u*x)^-1,a^-1*v*a*(v*y)^-1, a^-1*w*a*(w*z)^-1,a^-1*x*a*x^-1, a^-1*y*a*y^-1,a^-1*z*a*z^-1, a^-1*d*a*d^-1,a^-1*e*a*e^-1, b^-1*u*b*(x*y)^-1, b^-1*v*b*(y*z*e)^-1, b^-1*w*b*(x*y*z*d*e)^-1, b^-1*x*b*(v*w*x*e)^-1, b^-1*y*b*(u*v*w*y*d*e)^-1, b^-1*z*b*(u*w*z*e)^-1,b^-1*d*b*d^-1 ,b^-1*e*b*e^-1,c^-1*u*c*(v*d)^-1, c^-1*v*c*(w*d*e)^-1, c^-1*w*c*(u*v)^-1, c^-1*x*c*(x*z*d)^-1, c^-1*y*c*(x*d*e)^-1,c^-1*z*c*y^-1, c^-1*d*c*d^-1,c^-1*e*c*e^-1], [[b^-1*c*d,u*d,e],[b^-1*c*e,u*e,d]]]; end, [112,112]], "L2(8) N 2^6 E ( 2^1 x 2^1 ) II",[16,8,4],4, 4,[112,112]], # 129024.5 [[1,"abcuvwxyzde", function(a,b,c,u,v,w,x,y,z,d,e) return [[a^2*e^-1,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1, b^-1*c^-1*b*c^-1*a^-1*c*b^-1*c *b*a*(y*z*d)^-1,d^2,e^2,u^2,v^2,w^2,x^2, y^2,z^2,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,u^-1*d^-1*u*d, u^-1*e^-1*u*e,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,v^-1*d^-1*v*d, v^-1*e^-1*v*e,w^-1*x^-1*w*x, w^-1*y^-1*w*y,w^-1*z^-1*w*z, w^-1*d^-1*w*d,w^-1*e^-1*w*e, x^-1*y^-1*x*y,x^-1*z^-1*x*z, x^-1*d^-1*x*d,x^-1*e^-1*x*e, y^-1*z^-1*y*z,y^-1*d^-1*y*d, y^-1*e^-1*y*e,z^-1*d^-1*z*d, z^-1*e^-1*z*e,a^-1*u*a*(u*x)^-1, a^-1*v*a*(v*y)^-1,a^-1*w*a*(w*z)^-1, a^-1*x*a*x^-1,a^-1*y*a*y^-1, a^-1*z*a*z^-1,a^-1*d*a*d^-1, a^-1*e*a*e^-1,b^-1*u*b*(x*y*e)^-1, b^-1*v*b*(y*z*e)^-1, b^-1*w*b*(x*y*z*d*e)^-1, b^-1*x*b*(v*w*x*e)^-1, b^-1*y*b*(u*v*w*y*d*e)^-1, b^-1*z*b*(u*w*z)^-1,b^-1*d*b*d^-1, b^-1*e*b*e^-1,c^-1*u*c*(v*d*e)^-1, c^-1*v*c*(w*d)^-1, c^-1*w*c*(u*v*e)^-1, c^-1*x*c*(x*z*d*e)^-1, c^-1*y*c*(x*d)^-1,c^-1*z*c*(y*e)^-1, c^-1*d*c*d^-1,c^-1*e*c*e^-1], [[b^-1*c*d,u*d,e],[b^-1*c*e,u,d]]]; end, [112,112],[[1,2]]], "L2(8) N 2^6 E ( 2^1 x 2^1 ) III",[16,8,5],4, 4,[112,112]], # 129024.6 [[1,"abcstuvwxyz", function(a,b,c,s,t,u,v,w,x,y,z) return [[a^2,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,b^-1*c ^-1*b*c^-1*a^-1*c*b^-1 *c*b*a,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*s^-1,a^-1*t*a*v^-1, a^-1*u*a*y^-1,a^-1*v*a*t^-1, a^-1*w*a*x^-1,a^-1*x*a*w^-1, a^-1*y*a*u^-1, a^-1*z*a*(s*t*u*v*w*x*y*z)^-1, b^-1*s*b*u^-1,b^-1*t*b*s^-1, b^-1*u*b*t^-1,b^-1*v*b*x^-1, b^-1*w*b*v^-1,b^-1*x*b*w^-1, b^-1*y*b*z^-1, b^-1*z*b*(s*t*u*v*w*x*y*z)^-1, c^-1*s*c*s^-1,c^-1*t*c*t^-1, c^-1*u*c*y^-1,c^-1*v*c*w^-1, c^-1*w*c*u^-1,c^-1*x*c*z^-1, c^-1*y*c*(s*t*u*v*w*x*y*z)^-1, c^-1*z*c*v^-1],[[a,c,t*z]]]; end, [18]], "L2(8) 2^8",[16,8,6],1, 4,18] ]; PERFGRP[134]:=[# 129600.1 [[2,60,1,2160,1], "( A5 x A6 3^1 ) 2^1 [1]",[33,1,1],6, [1,3],[5,18,80]], # 129600.2 [[2,120,1,1080,1], "( A5 x A6 3^1 ) 2^1 [2]",[33,1,2],6, [1,3],[24,18]], # 129600.3 [[3,120,1,2160,1,"d1","d2"], "( A5 x A6 3^1 ) 2^1 [3]",[33,1,3],6, [1,3],[216,960]], # 129600.4 [[2,360,1,360,1], "A6 x A6",40,1, [3,3],[6,6]] ]; PERFGRP[135]:=[# 131040.1 [[2,60,1,2184,1], "( A5 x L2(13) ) 2^1 [1]",40,2, [1,6],[5,56]], # 131040.2 [[2,120,1,1092,1], "( A5 x L2(13) ) 2^1 [2]",40,2, [1,6],[24,14]], # 131040.3 [[3,120,1,2184,1,"d1","a2","a2"], "( A5 x L2(13) ) 2^1 [3]",40,2, [1,6],672] ]; PERFGRP[136]:=[# 131712.1 [[4,2688,1,16464,2,336,1,1], "L3(2) # 2^4 7^2 [1]",12,1, 2,[8,16,49]], # 131712.2 [[4,2688,3,16464,2,336,3,1], "L3(2) # 2^4 7^2 [2]",12,1, 2,[16,14,49]] ]; PERFGRP[137]:=[# 138240.1 [[4,46080,1,1080,2,360,1,1], "A6 3^1 x 2^1 x ( 2^4 E 2^1 A ) C 2^1",[13,7,1],24, 3,[64,80,18]], # 138240.2 [[1,"abcduvwxyz", function(a,b,c,d,u,v,w,x,y,z) return [[a^6*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,u^2, v^2,w^2,x^2,y^2,z^2,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*(v*x)^-1, a^-1*v*a*(u*v*w*x)^-1,a^-1*w*a*x^-1 ,a^-1*x*a*(w*x)^-1, a^-1*y*a*(x*z)^-1, a^-1*z*a*(w*x*y*z)^-1,b^-1*u*b*u^-1 ,b^-1*v*b*v^-1,b^-1*w*b*(u*x)^-1, b^-1*x*b*(v*w*x)^-1, b^-1*y*b*(u*y*z)^-1, b^-1*z*b*(v*y)^-1,c^-1*u*c*w^-1, c^-1*v*c*x^-1,c^-1*w*c*(y*z)^-1, c^-1*x*c*y^-1,c^-1*y*c*v^-1, c^-1*z*c*(u*v)^-1],[[b,c],[c*b*a*d,b,u]]]; end, [64,80]], "A6 ( ( 3^1 2^6 ) x 2^1 )",[13,7,2],2, 3,[64,80]] ]; PERFGRP[138]:=[# 144060.1 [[1,"abwxyz", function(a,b,w,x,y,z) return [[a^2,b^3,(a*b)^5,w^7,x^7,y^7,z^7,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*x*y*z, 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], [[b,a*b*a*b^-1*a,w*x^-1]]]; end, [35]], "A5 7^4",[4,4,1],1, 1,35] ]; PERFGRP[139]:=[# 146880.1 [[2,60,1,2448,1], "A5 x L2(17)",40,1, [1,7],[5,18]] ]; PERFGRP[140]:=[# 148824.1 [[1,"abc", function(a,b,c) return [[c^26*a^2,c*b^4*c^-1*b^-1,b^53,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*3)*b*c*b*c^2*a*b^2*a*c*b^2*a],[[b,c^4]]] ; end, [216]], "L2(53) 2^1 = SL(2,53)",22,-2, 30,216] ]; PERFGRP[141]:=[# 150348.1 [[1,"abc", function(a,b,c) return [[c^33,c*b^4*c^-1*b^-1,b^67,a^2,c*a*c*a^-1, (b*a)^3],[[b,c]]]; end, [68]], "L2(67)",22,-1, 35,68] ]; PERFGRP[142]:=[# 151200.1 [[2,60,1,2520,1], "A5 x A7",40,1, [1,8],[5,7]] ]; PERFGRP[143]:=[# 151632.1 [[1,"abxyz", function(a,b,x,y,z) return [[a^2,b^3,(a*b)^13,(a^-1*b^-1*a*b)^4,(a*b)^4*a *b^-1*(a*b)^4*a*b^-1*(a*b)^2 *(a*b^-1)^2*a*b*(a*b^-1)^2*(a*b)^2 *a*b^-1,x^3,y^3,z^3,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, a^-1*x*a*(x*z)^-1,a^-1*y*a*y, a^-1*z*a*z,b^-1*x*b*x*y, b^-1*y*b*x^-1,b^-1*z*b*(x*y*z)^-1], [[a,b]]]; end, [27]], "L3(3) 3^3",[24,3,1],1, 11,27] ]; PERFGRP[144]:=[# 155520.1 [[1,"abdwxyzstuv", function(a,b,d,w,x,y,z,s,t,u,v) return [[a^2*d^-1,b^3,(a*b)^5,d^2,a^-1*d^-1*a*d, b^-1*d^-1*b*d,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*x)^2*d, (w*y)^2*d,(w*z)^2*d,(x*y)^2*d,(x*z)^2*d,(y*z)^2*d, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w*x*y*z)^-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,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, t^-1*u^-1*t*u,t^-1*v^-1*t*v, u^-1*v^-1*u*v,a^-1*s*a*(s*t*u*v)^-1 ,a^-1*t*a*(s^-1*t*u*v^-1)^-1, a^-1*u*a*(s^-1*u^-1*v)^-1, a^-1*v*a*(t*u^-1*v^-1)^-1, b^-1*s*b*(s^-1*t^-1*u*v^-1)^-1, b^-1*t*b*(s^-1*v^-1)^-1, b^-1*u*b*(s*t^-1*u^-1*v^-1)^-1, b^-1*v*b*(t^-1*u^-1)^-1, d^-1*s*d*s,d^-1*t*d*t,d^-1*u*d*u, d^-1*v*d*v,w^-1*s*w*s^-1, w^-1*t*w*(s^-1*t*v)^-1, w^-1*u*w*(s*t*u^-1*v^-1)^-1, w^-1*v*w*(s^-1*v^-1)^-1, x^-1*s*x*(s*t*u*v^-1)^-1, x^-1*t*x*t^-1, x^-1*u*x*(s^-1*v^-1)^-1, x^-1*v*x*(s^-1*t^-1*u*v)^-1, y^-1*s*y*(s*v^-1)^-1, y^-1*t*y*(t*u*v^-1)^-1,y^-1*u*y*u, y^-1*v*y*v, z^-1*s*z*(s*t^-1*u^-1*v^-1)^-1, z^-1*t*z*(s*u*v)^-1, z^-1*u*z*(t*u^-1*v)^-1, z^-1*v*z*(s^-1*t*u^-1)^-1], [[a,b,w]]]; end, [81]], "A5 2^4' C N 2^1 3^4",[7,4,1],1, 1,81], # 155520.2 [[4,1920,1,4860,1,60], "A5 # 2^5 3^4 [1]",6,2, 1,[12,15]], # 155520.3 [[4,1920,2,4860,1,60], "A5 # 2^5 3^4 [2]",6,2, 1,[24,15]], # 155520.4 [[4,1920,3,4860,1,60], "A5 # 2^5 3^4 [3]",6,2, 1,[16,24,15]], # 155520.5 [[4,1920,4,4860,1,60], "A5 # 2^5 3^4 [4]",6,1, 1,[80,15]], # 155520.6 [[4,1920,5,4860,1,60], "A5 # 2^5 3^4 [5]",6,2, 1,[10,24,15]], # 155520.7 [[4,1920,6,4860,1,60], "A5 # 2^5 3^4 [6]",6,2, 1,[80,15]], # 155520.8 [[4,1920,7,4860,1,60], "A5 # 2^5 3^4 [7]",6,2, 1,[32,15]], # 155520.9 [[4,1920,1,4860,2,60], "A5 # 2^5 3^4 [8]",6,2, 1,[12,60]], # 155520.10 [[4,1920,2,4860,2,60], "A5 # 2^5 3^4 [9]",6,2, 1,[24,60]], # 155520.11 [[4,1920,3,4860,2,60], "A5 # 2^5 3^4 [10]",6,2, 1,[16,24,60]], # 155520.12 [[4,1920,4,4860,2,60], "A5 # 2^5 3^4 [11]",6,1, 1,[80,60]], # 155520.13 [[4,1920,5,4860,2,60], "A5 # 2^5 3^4 [12]",6,2, 1,[10,24,60]], # 155520.14 [[4,1920,6,4860,2,60], "A5 # 2^5 3^4 [13]",6,2, 1,[80,60]], # 155520.15 [[4,1920,7,4860,2,60], "A5 # 2^5 3^4 [14]",6,2, 1,[32,60]], # 155520.16 [[4,1920,3,9720,4,120,3,3], "A5 # 2^5 3^4 [15]",6,1, 1,[16,24,45]], # 155520.17 [[4,1920,4,9720,4,120,4,3], "A5 # 2^5 3^4 [16]",6,1, 1,[80,45]], # 155520.18 [[4,1920,5,9720,4,120,5,3], "A5 # 2^5 3^4 [17]",6,1, 1,[10,24,45]] ]; PERFGRP[145]:=[# 158400.1 [[2,120,1,1320,1], "( A5 x L2(11) ) 2^2",[36,2,1],4, [1,5],[24,24]] ]; PERFGRP[146]:=[# 159720.1 [[1,"abxyz", function(a,b,x,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,x^11,y^11,z^11, 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*y,a^-1*z*a*x^-1, b^-1*x*b*(x*y^(-1*5)*z^(-1*2))^-1, b^-1*y*b*(x^(-1*4)*y^-1)^-1, b^-1*z*b*x^(-1*5)], [[a*b,z],[a*b,b*a*b*a*b^-1*a*b^-1,y*z^5]]]; end, [24,66]], "A5 2^1 11^3",[5,3,1],2, 1,[24,66]], # 159720.2 [[1,"abyzd", function(a,b,y,z,d) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,d^11,d^-1*y ^-1*d*y,d^-1*z^-1*d*z,y^11,z^11, y^-1*z^-1*y*z*d^-1, a^-1*y*a*z^-1,a^-1*z*a*y, a^-1*d*a*d^-1, b^-1*y*b*(y^-1*z^(-1*3)*d^4)^-1, b^-1*z*b*y^(-1*4)],[[a,b]]]; end, [1331]], "A5 2^1 11^2 C 11^1",[5,3,2],11, 1,1331], # 159720.3 [[1,"abyz", function(a,b,y,z) return [[a^4,b^3,(a*b)^11,a^2*b^-1*a^2*b,(a*b*a*b*a*b*a *b*a*b^-1*a*b^-1*a*b^-1 *a*b^-1*a*b^-1)^2*a^2,y^11,z^11, y^-1*z^-1*y*z,a^-1*y*a*z, a^-1*z*a*y^-1,b^-1*y*b*z^-1, b^-1*z*b*(y^-1*z^-1)^-1],[[a,b]]]; end, [121]], "L2(11) 2^1 11^2",[19,2,1],1, 5,121] ]; PERFGRP[147]:=[# 160380.1 [[1,"abvwxyz", function(a,b,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,v^3,w^3,x^3,y^3,z^3, 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*v*a*v^-1,a^-1*w*a*w^-1, a^-1*x*a*(v^2*x^2*y)^-1, a^-1*y*a*y^-1,a^-1*z*a*(w*y*z^2)^-1 ,b^-1*v*b*w^-1,b^-1*w*b*x^-1, b^-1*x*b*v^-1,b^-1*y*b*(y^2*z)^-1, b^-1*z*b*y^(-1*2)],[[b,a*b*a*b^-1*a,y*z]] ]; end, [33]], "L2(11) 3^5",[18,5,1],1, 5,33] ]; PERFGRP[148]:=[# 161280.1 [[1,"abuvwxyz", function(a,b,u,v,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,u^2, v^2,w^2,x^2,y^2,z^2,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,a^-1*v*a*v^-1, a^-1*w*a*y^-1,a^-1*x*a*x^-1, a^-1*y*a*w^-1, a^-1*z*a*(u*v*w*x*y*z)^-1, b^-1*u*b*w^-1,b^-1*v*b*z^-1, b^-1*w*b*v^-1,b^-1*x*b*y^-1, b^-1*y*b*x^-1,b^-1*z*b*u^-1], [[a,b^2*a*b^-1*(a*b*a*b*b)^2*(a*b)^2, b*(a*b^-1)^2*a*b^2*(a*b)^2,y*z]]]; end, [14]], "A7 2^6",[23,6,1],1, 8,14], # 161280.2 [[1,"abef", function(a,b,e,f) return [[a^2,b^4*f^(-1*2),(a*b)^7*e,(a*b^2)^5*(e*f)^-1, (a^-1*b^-1*a*b)^5*f^(-1*2), (a*b*a*b*a*b^3)^5*f,(a*b*a*b*a*b^2*a*b^-1) ^5,e^2,f^4,e^-1*f^-1*e*f, a^-1*e*a*e^-1,a^-1*f*a*f^-1, b^-1*e*b*e^-1,b^-1*f*b*f^-1], [[a,b*a*b*a*b^-1*a*b^2*f^-1], [a*e^2,b^-1*a*b^-1*a*b*a*b^2]]]; end, [224,112]], "L3(4) 2^1 x ( 2^1 A 2^1 )",[27,3,1],-8, 20,[224,112]], # 161280.3 [[2,60,1,2688,1], "( A5 x L3(2) ) # 2^4 [1]",[31,4,1],2, [1,2],[5,8,16]], # 161280.4 [[2,60,1,2688,2], "( A5 x L3(2) ) # 2^4 [2]",[31,4,2],2, [1,2],[5,16]], # 161280.5 [[2,60,1,2688,3], "( A5 x L3(2) ) # 2^4 [3]",[31,4,3],2, [1,2],[5,16,14]], # 161280.6 [[2,120,1,1344,1], "( A5 x L3(2) ) # 2^4 [4]",[31,4,4],2, [1,2],[24,8]], # 161280.7 [[2,120,1,1344,2], "( A5 x L3(2) ) # 2^4 [5]",[31,4,5],2, [1,2],[24,14]], # 161280.8 [[3,120,1,2688,1,"d1","d2"], "( A5 x L3(2) ) # 2^4 [6]",[31,4,6],2, [1,2],[96,192]], # 161280.9 [[3,120,1,2688,2,"d1","e2"], "( A5 x L3(2) ) # 2^4 [7]",[31,4,7],2, [1,2],192], # 161280.10 [[3,120,1,2688,3,"d1","d2"], "( A5 x L3(2) ) # 2^4 [8]",[31,4,8],2, [1,2],[192,168]], # 161280.11 [[2,960,1,168,1], "( A5 x L3(2) ) # 2^4 [9]",[31,4,9],1, [1,2],[16,7]], # 161280.12 [[2,960,2,168,1], "( A5 x L3(2) ) # 2^4 [10]",[31,4,10],1, [1,2],[10,7]] ]; PERFGRP[149]:=[# 169344.1 [[2,336,1,504,1], "L3(2) 2^1 x L2(8)",[38,1,1],2, [2,4],[16,9]] ]; PERFGRP[150]:=fail; PERFGRP[151]:=[# 174960.1 [[1,"abcdwxyz", function(a,b,c,d,w,x,y,z) 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,d^3, 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)^-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*d*c*(d*x^-1*z^-1)^-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], [[c*b*a^-1,b,w],[b,c*a*b*c,d*y^-1*z]]]; end, [80,30]], "A6 2^1 x 3^1 E 3^4' I",[14,5,1],2, 3,[80,30]], # 174960.2 [[1,"abcdwxyz", function(a,b,c,d,w,x,y,z) return [[a^4*d,b^3*(w*x*y*z^-1)^-1,c^3*(w*y^-1 *z^-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,d^3,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*x^-1*z)^-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*d*c*(d*x)^-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], [[c*b*a^-1,b,w],[b*w^-1,c*a*b*c]]]; end, [80,30]], "A6 2^1 x 3^1 E 3^4' II",[14,5,2],2, 3,[80,30]], # 174960.3 [[1,"abcwxyzf", function(a,b,c,w,x,y,z,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,f^3,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]]]; end, [80,18]], "A6 2^1 x 3^4' E 3^1 I",[14,5,3],6, 3,[80,18]], # 174960.4 [[1,"abcwxyze", function(a,b,c,w,x,y,z,e) 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,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]]]; end, [80,108]], "A6 2^1 x 3^4' E 3^1 II",[14,5,4],6, 3,[80,108]], # 174960.5 [[1,"abcwxyzd", function(a,b,c,w,x,y,z,d) 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,d^3,b^-1*d*b*d^-1, c^-1*d*c*d^-1,w^3,x^3,y^3,z^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, 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], [[c*b*a^-1,b,w],[a*d,c*d,w],[b,c*a*b*c,z]]]; end, [80,18,30]], "A6 2^1 x 3^1 x 3^4'",[14,5,5],6, 3,[80,18,30]], # 174960.6 [[1,"abcdstuv", function(a,b,c,d,s,t,u,v) 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,b^-1*d^-1*b*d, c^-1*d^-1*c*d,s^3,t^3,u^3,v^3, s^-1*d^-1*s*d,t^-1*d^-1*t*d, u^-1*d^-1*u*d,v^-1*d^-1*v*d, 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,a^-1*v*a*t, b^-1*s*b*(s*v^-1)^-1, b^-1*t*b*(t*u^-1*v)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1, c^-1*s*c*(s^-1*t*u^-1*v)^-1, c^-1*t*c*(s*t*u*v)^-1, c^-1*u*c*(s^-1*v^-1)^-1, c^-1*v*c*(t^-1*u^-1*v)^-1], [[a*d,c*d,s],[a,b,c]]]; end, [18,81]], "A6 2^1 x 3^1 x 3^4",[14,5,6],3, 3,[18,81]], # 174960.7 [[1,"abcstuvd", function(a,b,c,s,t,u,v,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,d^3, d^-1*s^-1*d*s,d^-1*t^-1*d*t, d^-1*u^-1*d*u,d^-1*v^-1*d*v, s^-1*t^-1*s*t,s^-1*u^-1*s*u, s^-1*v^-1*s*v*d,t^-1*u^-1*t*u*d, t^-1*v^-1*t*v*d^-1,u^-1*v^-1*u *v,a^-1*s*a*(u*d)^-1, a^-1*t*a*(v*d^-1)^-1,a^-1*u*a*s, a^-1*v*a*t,a^-1*d*a*d^-1, b^-1*s*b*(s*v^-1)^-1, b^-1*t*b*(t*u^-1*v*d)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1, b^-1*d*b*d^-1, c^-1*s*c*(s^-1*t*u^-1*v*d^-1)^-1 ,c^-1*t*c*(s*t*u*v)^-1, c^-1*u*c*(s^-1*v^-1*d)^-1, c^-1*v*c*(t^-1*u^-1*v)^-1, c^-1*d*c*d^-1],[[a*d,b*d^-1]]]; end, [1458]], "A6 2^1 3^4 C N 3^1",[14,5,7],3, 3,1458], # 174960.8 [[1,"abcstuve", function(a,b,c,s,t,u,v,e) 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,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]]]; end, [243]], "A6 2^1 3^4 C 3^1",[14,5,8],3, 3,243] ]; ############################################################################# ## #E perf7.grp . . . . . . . . . . . . . . . . . . . . . . . . . ends here ##