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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 perf1.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 2-7680 ## All data is based on Holt/Plesken: Perfect Groups, OUP 1989 ## PERFGRP[1]:=[]; PERFGRP[2]:=[# 60.1 [[1,"ab", function(a,b) return [[a^2,b^3,(a*b)^5],[[b,a*b*a*b^-1*a]]]; end, [5]], "A5",[1,0,1,2,3,4,5],-1, 1,5] ]; PERFGRP[3]:=[# 120.1 [[1,"abd", function(a,b,d) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b], [[a*b]]]; end, [24]], "A5 2^1",[1,1,1,2,3,4,5],-2, 1,24] ]; PERFGRP[4]:=[# 168.1 [[1,"ab", function(a,b) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4], [[b,a*b*a*b^-1*a]]]; end, [7]], "L3(2)",[8,0,1,9,10,11],-1, 2,7] ]; PERFGRP[5]:=[# 336.1 [[1,"abd", function(a,b,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], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1]]]; end, [16]], "L3(2) 2^1 = SL(2,7)",[8,1,1,9,10,11],-2, 2,16] ]; PERFGRP[6]:=[# 360.1 [[1,"abc", function(a,b,c) 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],[[a,b]]]; end, [6]], "A6",[13,0,1,14],-1, 3,6] ]; PERFGRP[7]:=[# 504.1 [[1,"abc", function(a,b,c) 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],[[a,c]]]; end, [9]], "L2(8)",[16,0,1],-1, 4,9] ]; PERFGRP[8]:=[# 660.1 [[1,"ab", function(a,b) return [[a^2,b^3,(a*b)^11,(a*b)^4*(a*b^-1)^5*(a*b)^4*(a *b^-1)^5],[[b,a*b*a*b^-1*a]]]; end, [11]], "L2(11)",[17,0,1,18,19],-1, 5,11] ]; PERFGRP[9]:=[# 720.1 [[1,"abcd", function(a,b,c,d) 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], [[c*b*a*d,b]]]; end, [80]], "A6 2^1",[13,1,1,14],-2, 3,80] ]; PERFGRP[10]:=[# 960.1 [[1,"abstuv", function(a,b,s,t,u,v) return [[a^2,b^3,(a*b)^5,s^2,t^2,u^2,v^2,s^-1*t^-1*s *t,u^-1*v^-1*u*v,s^-1*u^-1*s*u, s^-1*v^-1*s*v,t^-1*u^-1*t*u, t^-1*v^-1*t*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)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1], [[a,b]]]; end, [16]], "A5 2^4",[1,4,1],1, 1,16], # 960.2 [[1,"abwxyz", function(a,b,w,x,y,z) return [[a^2,b^3,(a*b)^5,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*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],[[b,a*b*a*b^-1*a,w*x]] ]; end, [10]], "A5 2^4'",[1,4,2,7],1, 1,10] ]; PERFGRP[11]:=[# 1080.1 [[1,"abc", function(a,b,c) return [[a^6,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1*b^-1*c *b*c*b^-1*c*b*c^-1],[[a^3,c*a^2]] ]; end, [18]], "A6 3^1",[13,0,1,14],-3, 3,18], # 1080.2 (otherpres.) [[1,"abcd", function(a,b,c,d) return [[a^2*d^-1,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1 *b^-1*c*b*c*b^-1*c*b*c^-1, d^3,d^-1*b^-1*d*b,d^-1*c^-1*d*c], [[a^3,c*a^2]]]; end, [18]]] ]; PERFGRP[12]:=[# 1092.1 [[1,"abc", function(a,b,c) return [[a^2,b^13,(a*b)^3,c^6,(a*c)^2,c^-1*b*c*b^(-1*4), b^6*a*b^-1*a*b*a*b^7*a*c^-1],[[b,c]]]; end, [14]], "L2(13)",[20,0,1],-1, 6,14] ]; PERFGRP[13]:=[# 1320.1 [[1,"abd", function(a,b,d) return [[a^2*d^-1,b^3,(a*b)^11,(a*b)^4*(a*b^-1)^5*(a*b) ^4*(a*b^-1)^5*d^-1,d^2, b^-1*d*b*d^-1], [[a*b,(b*a)^2*(b^-1*a)^4*b^-1*d]]]; end, [24]], "L2(11) 2^1 = SL(2,11)",[17,1,1,18,19],-2, 5,24] ]; PERFGRP[14]:=[# 1344.1 [[1,"abxyz", function(a,b,x,y,z) 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,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]]]; end, [8]], "L3(2) 2^3",[8,3,1],1, 2,8], # 1344.2 [[1,"abxyz", function(a,b,x,y,z) 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, 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^-1*a,x]]]; end, [14]], "L3(2) N 2^3",[8,3,2],1, 2,14], # 1344.3 (otherpres.) [[1,"abuvw", function(a,b,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,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,b]]]; end, [8]]], # 1344.4 (otherpres.) [[1,"abuvw", function(a,b,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, 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], [[b,a*b^-1*a*b*a,u]]]; end, [14]]] ]; PERFGRP[15]:=[# 1920.1 [[1,"abstuve", function(a,b,s,t,u,v,e) return [[a^2,b^3,(a*b)^5,s^2,t^2,u^2,v^2,e^2,s^-1*t^-1 *s*t,u^-1*v^-1*u*v,s^-1*u^-1*s*u, s^-1*v^-1*s*v,t^-1*u^-1*t*u, t^-1*v^-1*t*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, e^-1*a^-1*e*a,e^-1*b^-1*e*b, e^-1*s^-1*e*s,e^-1*t^-1*e*t, e^-1*u^-1*e*u,e^-1*v^-1*e*v], [[a*b,b*a*b*a*b^-1*a*b^-1,s]]]; end, [12]], "A5 2^4 E 2^1",[1,5,1],2, 1,12], # 1920.2 [[1,"abstuvd", function(a,b,s,t,u,v,d) return [[a^2*d^-1,b^3,(a*b)^5,s^2,t^2,u^2,v^2,d^2,s^-1 *t^-1*s*t,u^-1*v^-1*u*v, s^-1*u^-1*s*u,s^-1*v^-1*s*v, t^-1*u^-1*t*u,t^-1*v^-1*t*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*d)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, d^-1*a^-1*d*a,d^-1*b^-1*d*b, d^-1*s^-1*d*s,d^-1*t^-1*d*t, d^-1*u^-1*d*u,d^-1*v^-1*d*v], [[a*b,s]]]; end, [24]], "A5 2^4 E N 2^1",[1,5,2],2, 1,24], # 1920.3 [[1,"abdstuv", function(a,b,d,s,t,u,v) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b, s^2,t^2,u^2,v^2,s^-1*t^-1*s*t, u^-1*v^-1*u*v,s^-1*u^-1*s*u, s^-1*v^-1*s*v,t^-1*u^-1*t*u, t^-1*v^-1*t*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)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, d^-1*a^-1*d*a,d^-1*s^-1*d*s, d^-1*t^-1*d*t,d^-1*u^-1*d*u, d^-1*v^-1*d*v],[[a,b],[a*b,s]]]; end, [16,24]], "A5 2^1 x 2^4",[1,5,3],2, 1,[16,24]], # 1920.4 [[1,"abdstuv", function(a,b,d,s,t,u,v) return [[a^2*d^-1,b^3,(a*b)^5,d^2,b^-1*d*b*(d*u*v) ^-1,s^2,t^2,u^2,v^2,s^-1*t^-1*s*t, u^-1*v^-1*u*v,s^-1*u^-1*s*u, s^-1*v^-1*s*v,t^-1*u^-1*t*u, t^-1*v^-1*t*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)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, d^-1*a^-1*d*a,d^-1*s^-1*d*s, d^-1*t^-1*d*t,d^-1*u^-1*d*u, d^-1*v^-1*d*v],[[b,d]]]; end, [80]], "A5 2^1 E 2^4",[1,5,4],1, 1,80], # 1920.5 [[1,"abdwxyz", function(a,b,d,w,x,y,z) return [[a^2*d^-1,b^3,(a*b)^5,d^2,b^-1*d^-1*b*d, a^-1*d^-1*a*d,w^2,x^2,y^2,z^2,(w*x)^2, (w*y)^2,(w*z)^2,(x*y)^2,(x*z)^2,(y*z)^2, 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, d^-1*w^-1*d*w,d^-1*x^-1*d*x, d^-1*y^-1*d*y,d^-1*z^-1*d*z], [[b,a*b*a*b^-1*a,w*x],[a*b,w]]]; end, [10,24]], "A5 2^1 x 2^4'",[1,5,5,7],2, 1,[10,24]], # 1920.6 [[1,"abdwxyz", function(a,b,d,w,x,y,z) return [[a^2*d^-1,b^3,(a*b)^5,d^2,a^-1*d^-1*a*d, b^-1*d^-1*b*d,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, d^-1*w^-1*d*w,d^-1*x^-1*d*x, d^-1*y^-1*d*y,d^-1*z^-1*d*z], [[b,a*b*a*b^-1*a^-1*w*x]]]; end, [80]], "A5 2^4' C N 2^1",[1,5,6,7],2, 1,80], # 1920.7 [[1,"abwxyze", function(a,b,w,x,y,z,e) return [[a^2,b^3,(a*b)^5,e^2,a^-1*e^-1*a*e,b^-1 *e^-1*b*e,w^2,x^2,y^2,z^2,(w*x)^2*e, (w*y)^2*e,(w*z)^2*e,(x*y)^2*e,(x*z)^2*e,(y*z)^2*e, 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, 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,b]]]; end, [32]], "A5 2^4' C 2^1",[1,5,7,7],2, 1,32], # 1920.8 (otherpres.) [[1,"abstuvf", function(a,b,s,t,u,v,f) return [[f^2,f^-1*a^-1*f*a,f^-1*b^-1*f*b,f^(-1 *1)*s^-1*f*s,f^-1*t^-1*f*t, f^-1*u^-1*f*u,f^-1*v^-1*f*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^2,b^3,(a*b)^5, 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*f)^-1, b^-1*t*b*(s*t*u*v*f)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1], [[a*b,b*a*b*a*b^-1*a*b^-1,s*f]]]; end, [12]]] ]; PERFGRP[16]:=[# 2160.1 [[1,"abcd", function(a,b,c,d) return [[b^3,c^3,(b*c)^4*d^-1,(b*c^-1)^5,a^-1*b^(-1 *1)*c*b*c*b^-1*c*b*c^-1,d^2, d^-1*b^-1*d*b,d^-1*c^-1*d*c], [[a^3,c*a^2],[c*b*a*d,b]]]; end, [18,80]], "A6 3^1 x 2^1",[13,1,1,14],-6, 3,[18,80]] ]; PERFGRP[17]:=[# 2184.1 [[1,"abc", function(a,b,c) return [[a^4,b^13,(a*b)^3,c^6*a^2,(a*c)^2*a^2,a^2*b^-1 *a^2*b,c^-1*b*c*b^(-1*4), b^6*a*b^-1*a*b*a*b^7*a*c^-1],[[b,c^4]]]; end, [56]], "L2(13) 2^1 = SL(2,13)",[20,0,1],-2, 6,56] ]; PERFGRP[18]:=[# 2448.1 [[1,"abc", function(a,b,c) return [[a^2,(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,c^8,b^17] ,[[b,c]]]; end, [18]], "L2(17)",[21,0,1],-1, 7,18] ]; PERFGRP[19]:=[# 2520.1 [[1,"ab", function(a,b) 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], [[a,b^2*a*b^-1*(a*b*a*b^2)^2*(a*b)^2, b*(a*b^-1)^2*a*b^2*(a*b)^2]]]; end, [7]], "A7",[23,0,1],-1, 8,7] ]; PERFGRP[20]:=[# 2688.1 [[1,"abdxyz", function(a,b,d,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,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,b],[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1, x]]]; end, [8,16]], "L3(2) 2^1 x 2^3",[8,4,1],2, 2,[8,16]], # 2688.2 [[1,"abxyze", function(a,b,x,y,z,e) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,x^2,y^2, z^2,e^2,e^-1*x^-1*e*x,e^-1*y^-1*e*y ,e^-1*z^-1*e*z,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, 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^-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], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,z]]]; end, [16]], "L3(2) 2^3 E 2^1",[8,4,2],2, 2,16], # 2688.3 [[1,"abdxyz", function(a,b,d,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,b^-1*d^-1*b*d,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*b,b*a*b^-1*a*b^-1*a*b*a*b^-1], [b,a*b*a*b^-1*a,x]]]; end, [16,14]], "L3(2) 2^1 x N 2^3",[8,4,3],2, 2,[16,14]] ]; PERFGRP[21]:=[# 3000.1 [[1,"abyz", function(a,b,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^5,z^5,y^-1 *z^-1*y*z,a^-1*y*a*z^-1, a^-1*z*a*y,b^-1*y*b*z, b^-1*z*b*(y*z^-1)^-1],[[a,b]]]; end, [25]], "A5 2^1 5^2",[3,2,1],1, 1,25], # 3000.2 (otherpres.) [[1,"abdyz", function(a,b,d,y,z) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b, y^5,z^5,y^-1*z^-1*y*z,a^-1*y*a*z^-1 ,a^-1*z*a*y,b^-1*y*b*z, b^-1*z*b*(y*z^-1)^-1],[[a,b]]]; end, [25]]] ]; PERFGRP[22]:=[# 3420.1 [[1,"abc", function(a,b,c) return [[c^9,c*b^4*c^-1*b^-1,b^19,a^2,c*a*c*a^-1, (b*a)^3],[[b,c]]]; end, [20]], "L2(19)",22,-1, 9,20] ]; PERFGRP[23]:=[# 3600.1 [[1,"abcd", function(a,b,c,d) return [[a^2,b^3,(a*b)^5,c^2,d^3,(c*d)^5,a^-1*c^-1*a*c ,a^-1*d^-1*a*d,b^-1*c^-1*b*c, b^-1*d^-1*b*d], [[a,b,c*d*c*d^-1*c,d],[a*b*a*b^-1*a,b,c,d]]] ; end, [5,5]], "A5 x A5",[29,0,1,30],1, [1,1],[5,5]] ]; PERFGRP[24]:=[# 3840.1 [[1,"abstuve", function(a,b,s,t,u,v,e) return [[a^2,b^3,(a*b)^5,e^4,e^-1*a^-1*e*a,e^-1 *b^-1*e*b,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], [[a,b]]]; end, [64]], "A5 ( 2^4 E 2^1 A ) C 2^1 I",[1,6,1],4, 1,64], # 3840.2 [[1,"abstuve", function(a,b,s,t,u,v,e) return [[a^2*e^2,b^3,(a*b)^5,e^4,e^-1*a^-1*e*a,e^(-1 *1)*b^-1*e*b,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], [[a*e^-1,b*u]]]; end, [64]], "A5 ( 2^4 E 2^1 A ) C 2^1 II",[1,6,2],4, 1,64], # 3840.3 [[1,"abstuvef", function(a,b,s,t,u,v,e,f) return [[a^2,b^3,(a*b)^5,e^2,f^2,e^-1*a^-1*e*a,e^(-1 *1)*b^-1*e*b,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*u^-1*e*u, e^-1*v^-1*e*v,e^-1*f^-1*e*f, f^-1*a^-1*f*a,f^-1*b^-1*f*b, f^-1*s^-1*f*s,f^-1*t^-1*f*t, f^-1*u^-1*f*u,f^-1*v^-1*f*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*f)^-1 ,b^-1*t*b*(s*t*u*v*f)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1], [[a*b,b*a*b*a*b^-1*a*b^-1,s*f]]]; end, [24]], "A5 2^4 E ( 2^1 x 2^1 )",[1,6,3],4, 1,24], # 3840.4 [[1,"abstuvde", function(a,b,s,t,u,v,d,e) return [[a^2*d,b^3,(a*b)^5,d^2,e^2,d^-1*a^-1*d*a,d ^-1*b^-1*d*b,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, e^-1*a^-1*e*a,e^-1*b^-1*e*b, 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*d)^-1 ,b^-1*t*b*(s*t*u*v*d)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1], [[a*b,s*d]]]; end, [48]], "A5 2^4 E ( 2^1 x N 2^1 )",[1,6,4],4, 1,48], # 3840.5 [[1,"abdstuve", function(a,b,d,s,t,u,v,e) return [[a^2*d,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b,e^2,d ^-1*a^-1*d*a,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, e^-1*a^-1*e*a,e^-1*b^-1*e*b, 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], [[a*b,s,e],[a*b,b*a*b*a*b^-1*a*b^-1,s]]]; end, [24,12]], "A5 2^1 x ( 2^4 E 2^1 )",[1,6,5],4, 1,[24,12]], # 3840.6 [[1,"abdstuve", function(a,b,d,s,t,u,v,e) return [[a^2*d^-1,b^3,(a*b)^5,d^2*e,b^-1*d*b*(d*u*v) ^-1,s^2,t^2,u^2,v^2,e^2,s^-1*t^-1*s*t ,u^-1*v^-1*u*v,s^-1*u^-1*s*u, s^-1*v^-1*s*v,t^-1*u^-1*t*u, t^-1*v^-1*t*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, d^-1*a^-1*d*a,d^-1*s^-1*d*s, d^-1*t^-1*d*t,d^-1*u^-1*d*u, d^-1*v^-1*d*v],[[a*b,s]]]; end, [48]], "A5 2^1 E 2^4 E 2^1",[1,6,6],2, 1,48], # 3840.7 [[1,"abdwxyze", function(a,b,d,w,x,y,z,e) return [[a^2*d^-1,b^3,(a*b)^5,d^2,b^-1*d^-1*b*d, e^2,a^-1*d^-1*a*d,a^-1*e^-1*a*e, b^-1*e^-1*b*e,w^2,x^2,y^2,z^2,(w*x)^2*e, (w*y)^2*e,(w*z)^2*e,(x*y)^2*e,(x*z)^2*e,(y*z)^2*e, 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, d^-1*w^-1*d*w,d^-1*x^-1*d*x, d^-1*y^-1*d*y,d^-1*z^-1*d*z, 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,b],[a*b,w]]]; end, [32,24]], "A5 2^1 x ( 2^4' C 2^1 )",[1,6,7,7],4, 1,[32,24]] ]; PERFGRP[25]:=[# 4080.1 [[1,"abc", function(a,b,c) return [[c^15,b^2,c^(-1*4)*b*c^3*b*c*b^-1,a^2,(a*c)^2, (a*b)^3],[[b,c]]]; end, [17]], "L2(16)",22,-1, 10,17] ]; PERFGRP[26]:=[# 4860.1 [[1,"abwxyz", function(a,b,w,x,y,z) return [[a^2,b^3,(a*b)^5,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], [[b,a*b*a*b^-1*a,w*x^-1]]]; end, [15]], "A5 3^4'",[2,4,1],1, 1,15], # 4860.2 [[1,"abwxyz", function(a,b,w,x,y,z) return [[a^2,b^3*z^-1,(a*b)^5,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], [[b,w*x^-1]]]; end, [60]], "A5 N 3^4'",[2,4,2],1, 1,60] ]; PERFGRP[27]:=[# 4896.1 [[1,"abcd", function(a,b,c,d) return [[a^2*d^-1,b^17,c^8*d^-1,(a*b)^3,(a*c)^2*d^(-1 *1),d^2,d^-1*b^-1*d*b, d^-1*c^-1*d*c,c^-1*b*c*b^(-1*9), b^5*a*b^-1*a*b^2*a*b^6*a*c^-1],[[b]]]; end, [288]], "L2(17) 2^1 = SL(2,17)",[21,1,1],-2, 7,288] ]; PERFGRP[28]:=[# 5040.1 [[1,"abd", function(a,b,d) return [[a^2*d,b^4*d,(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,d*a*d*a^-1,d*b*d*b^-1], [[a*b,b*a*b*a*b^2*a*b^-1*a*b*a*b^-1*a*b*a *b^2*d]]]; end, [240]], "A7 2^1",[23,1,1],-2, 8,240] ]; PERFGRP[29]:=[# 5376.1 [[1,"abdxyze", function(a,b,d,x,y,z,e) 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, e^2,e^-1*x^-1*e*x,e^-1*y^-1*e*y, e^-1*z^-1*e*z,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, 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^-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], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,e], [a,b]]]; end, [16,16]], "L3(2) 2^1 x ( 2^3 E 2^1 )",[8,5,1],4, 2,[16,16]] ]; PERFGRP[30]:=[# 5616.1 [[1,"ab", function(a,b) 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],[[b,a*b*a*b^-1*a]]]; end, [13]], "L3(3)",[24,0,1],-1, 11,13] ]; PERFGRP[31]:=[# 5760.1 [[1,"abcstuv", function(a,b,c,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^-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)^-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],[[b,c]]]; end, [16]], "A6 2^4",[13,4,1],1, 3,16] ]; PERFGRP[32]:=[# 6048.1 [[1,"ab", function(a,b) 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], [[a,(b*a)^3*b^3]]]; end, [28]], "U3(3)",[25,0,1],-1, 12,28] ]; PERFGRP[33]:=[# 6072.1 [[1,"abc", function(a,b,c) return [[c^11,c*b^3*c^-1*b^-1,b^23,a^2,c*a*c*a^-1, (b*a)^3],[[b,c]]]; end, [24]], "L2(23)",22,-1, 13,24] ]; PERFGRP[34]:=[# 6840.1 [[1,"abc", function(a,b,c) return [[c^9*a^2,c*b^4*c^-1*b^-1,b^19,a^2*b^-1 *a^2*b,a^2*c^-1*a^2*c,a^4,c*a*c*a^-1, (b*a)^3],[[b,c^2]]]; end, [40]], "L2(19) 2^1 = SL(2,19)",22,-2, 9,40] ]; PERFGRP[35]:=[# 7200.1 [[1,"abcd", function(a,b,c,d) return [[a^2,b^3,(a*b)^5,c^4,d^3,(c*d)^5,c^2*d*c^2*d^-1, a^-1*c^-1*a*c,a^-1*d^-1*a*d, b^-1*c^-1*b*c,b^-1*d^-1*b*d], [[a*b*a*b^-1*a,b,c,d],[a,b,c*d]]]; end, [5,24]], "A5 2^1 x A5",[29,1,1,30],2, [1,1],[5,24]], # 7200.2 [[1,"abcd", function(a,b,c,d) return [[a^4,b^3,(a*b)^5,c^2*a^2,d^3,(c*d)^5,a^-1*c^-1 *a*c,a^-1*d^-1*a*d,b^-1*c^-1*b*c, b^-1*d^-1*b*d],[[a*b,c*d]]]; end, [288]], "( A5 N x A5 N ) 2^1",[29,1,2,30],2, [1,1],288] ]; PERFGRP[36]:=[# 7500.1 [[1,"abxyz", function(a,b,x,y,z) return [[a^2,b^3,(a*b)^5,x^5,y^5,z^5,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, b^-1*z*b*(x*y^(-1*2)*z)^-1], [[a*b,b*a*b*a*b^-1*a*b^-1,y]]]; end, [30]], "A5 5^3",[3,3,1],1, 1,30], # 7500.2 [[1,"abxyz", function(a,b,x,y,z) return [[a^2,b^3,(a*b)^5*z^-1,x^5,y^5,z^5,x^-1*y^(-1 *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, b^-1*z*b*(x*y^(-1*2)*z)^-1], [[a*b,b*a*b*a*b^-1*a*b^-1,y]]]; end, [30]], "A5 N 5^3",[3,3,2],1, 1,30] ]; PERFGRP[37]:=[# 7560.1 [[1,"ab", function(a,b) 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], [[a^3,(b^-1*a)^2*(b*a)^2*b^2*a*b*a]]]; end, [45]], "A7 3^1",[23,0,1],-3, 8,45] ]; PERFGRP[38]:=[# 7680.1 [[1,"abstuvef", function(a,b,s,t,u,v,e,f) return [[a^2,b^3,(a*b)^5,e^4,f^2,e^-1*a^-1*e*a,e^(-1 *1)*b^-1*e*b,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*u^-1*e*u, e^-1*v^-1*e*v,e^-1*f^-1*e*f, f^-1*a^-1*f*a,f^-1*b^-1*f*b, f^-1*s^-1*f*s,f^-1*t^-1*f*t, f^-1*u^-1*f*u,f^-1*v^-1*f*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*f^-1)^-1, b^-1*t*b*(s*t*u*v*f)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1], [[a*b,b*a*b*a*b^-1*a*b^-1,s*f,e],[a,b,f]]]; end, [12,64]], "A5 ( 2^4 E ( 2^1 A x 2^1 ) ) C 2^1",[1,7,1],8, 1,[12,64]], # 7680.2 [[1,"abstuvde", function(a,b,s,t,u,v,d,e) return [[a^2*d,b^3,(a*b)^5,d^2,e^4,d^-1*a^-1*d*a,d ^-1*b^-1*d*b,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, e^-1*a^-1*e*a,e^-1*b^-1*e*b, 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*d)^-1 ,b^-1*t*b*(s*t*u*v*d)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1], [[a*b,s*d,e],[a,b]]]; end, [24,64]], "A5 ( 2^4 E ( 2^1 A x N 2^1 ) ) C 2^1 I",[1,7,2],8, 1,[24,64]], # 7680.3 [[1,"abstuvde", function(a,b,s,t,u,v,d,e) return [[a^2*d,b^3,(a*b)^5,d^2,e^4,d^-1*a^-1*d*a,d ^-1*b^-1*d*b,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, e^-1*a^-1*e*a,e^-1*b^-1*e*b, 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*d*e^-1)^-1, b^-1*t*b*(s*t*u*v*d*e^2)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1], [[a*b,s*d,e],[a*e^-1,b*u]]]; end, [24,64]], "A5 ( 2^4 E ( 2^1 A x N 2^1 ) ) C 2^1 II",[1,7,3],8, 1,[24,64]], # 7680.4 [[1,"abdstuve", function(a,b,d,s,t,u,v,e) return [[a^2*d,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b,e^4,d ^-1*a^-1*d*a,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, e^-1*a^-1*e*a,e^-1*b^-1*e*b, 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], [[a*b,s,e],[a,b]]]; end, [24,64]], "A5 2^1 x ( 2^4 E 2^1 A ) C 2^1",[1,7,4],8, 1,[24,64]], # 7680.5 [[1,"abdstuvef", function(a,b,d,s,t,u,v,e,f) return [[a^2*d,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b,e^2,f^2, d^-1*a^-1*d*a,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, d^-1*f^-1*d*f,e^-1*a^-1*e*a, e^-1*b^-1*e*b,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*u^-1*e*u, e^-1*v^-1*e*v,e^-1*f^-1*e*f, f^-1*a^-1*f*a,f^-1*b^-1*f*b, f^-1*s^-1*f*s,f^-1*t^-1*f*t, f^-1*u^-1*f*u,f^-1*v^-1*f*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*f)^-1 ,b^-1*t*b*(s*t*u*v*f)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1], [[a*b,s,e,f],[a*b,b*a*b*a*b^-1*a*b^-1,s*f]] ]; end, [24,24]], "A5 2^1 x ( 2^4 E ( 2^1 x 2^1 ) )",[1,7,5],8, 1,[24,24]] ]; ############################################################################# ## #E perf1.grp . . . . . . . . . . . . . . . . . . . . . . . . . ends here ##