|
#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Volkmar Felsch, Alexander Hulpke.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains the perfect groups of sizes 190080-345600
## All data is based on Holt/Plesken: Perfect Groups, OUP 1989
##
PERFGRP[159]:=[# 190080.1
[[1,"abd",
function(a,b,d)
return
[[a^2,b^3,(a*b)^11*d^-1,(a^-1*b^-1*a*b)^6,
(a*b*a*b*a*b^-1)^6*d^-1,
(a*b*a*b*a*b^-1*a*b^-1)^5,d^2,
a^-1*d*a*d^-1,b^-1*d*b*d^-1],
[[a,b*a*b^-1*a*(b^-1*a*b*a)^2]]];
end,
[24]],
"M12 2^1",28,-2,
31,24]
];
PERFGRP[160]:=[# 192000.1
[[4,7680,4,3000,2,120,4,1],
"A5 # 2^7 5^2 [1]",6,4,
1,[24,64,25]],
# 192000.2
[[4,7680,5,3000,2,120,5,1],
"A5 # 2^7 5^2 [2]",6,4,
1,[24,24,25]]
];
PERFGRP[161]:=[# 194472.1
[[1,"abc",
function(a,b,c)
return
[[c^36,c*b^25*c^-1*b^-1,b^73,a^2,c*a*c*a^-1
,(b*a)^3,
c^(-1*10)*b^2*c*b*c*a*b*c^2*b*a*b^2*c*b*a],
[[b,c]]];
end,
[74],[0,3,5,3]],
"L2(73)",22,-1,
39,74]
];
PERFGRP[162]:=[# 201720.1
[[1,"abyz",
function(a,b,y,z)
return
[[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^41,z^41,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*16))^-1,
b^-1*z*b*y^(-1*18)],[[a*b,a^2,y]]];
end,
[492],[0,0,2,2]],
"A5 2^1 41^2",[5,2,1],1,
1,492]
];
PERFGRP[163]:=[# 205200.1
[[2,60,1,3420,1],
"A5 x L2(19)",40,1,
[1,9],[5,20]]
];
PERFGRP[164]:=[# 205320.1
[[1,"abc",
function(a,b,c)
return
[[c^29*a^2,c*b^4*c^-1*b^-1,b^59,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,
[120]],
"L2(59) 2^1 = SL(2,59)",22,-2,
32,120]
];
PERFGRP[165]:=[# 216000.1
[[2,60,1,3600,1],
"A5 x A5 x A5",40,1,
[1,1,1],[5,5,5]]
];
PERFGRP[166]:=[# 221760.1
[[2,336,1,660,1],
"( L3(2) x L2(11) ) 2^1 [1]",[39,1,1],2,
[2,5],[16,11]],
# 221760.2
[[2,168,1,1320,1],
"( L3(2) x L2(11) ) 2^1 [2]",[39,1,2],2,
[2,5],[7,24]],
# 221760.3
[[3,336,1,1320,1,"d1","d2"],
"( L3(2) x L2(11) ) 2^1 [3]",[39,1,3],2,
[2,5],192]
];
PERFGRP[167]:=[# 223608.1
[[1,"abxyz",
function(a,b,x,y,z)
return
[[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,x^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*(y^4*z^-1)^-1,
b^-1*y*b*(x^5*y*z^(-1*5))^-1,
b^-1*z*b*(x^(-1*5)*y^3*z^-1)^-1],
[[b*a*b^-1,b^-1*a*b,z]]];
end,
[231]],
"L3(2) 11^3",[11,3,1],1,
2,231]
];
PERFGRP[168]:=[# 225792.1
[[2,168,1,1344,1],
"( L3(2) x L3(2) ) # 2^3 [1]",[34,3,1],1,
[2,2],[7,8]],
# 225792.2
[[2,168,1,1344,2],
"( L3(2) x L3(2) ) # 2^3 [2]",[34,3,2],1,
[2,2],[7,14]]
];
PERFGRP[169]:=[# 226920.1
[[1,"abc",
function(a,b,c)
return
[[c^30*a^2,c*b^4*c^-1*b^-1,b^61,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*4)*(b*c)^3*c*a*b^2*a*c*b^2*a],[[b,c^4]]];
end,
[248]],
"L2(61) 2^1 = SL(2,61)",22,-2,
33,248]
];
PERFGRP[170]:=[# 230400.1
[[2,1920,1,120,1],
"( A5 x A5 ) # 2^6 [1]",[29,6,1],4,
[1,1],[12,24]],
# 230400.2
[[2,1920,2,120,1],
"( A5 x A5 ) # 2^6 [2]",[29,6,2],4,
[1,1],[24,24]],
# 230400.3
[[2,1920,3,120,1],
"( A5 x A5 ) # 2^6 [3]",[29,6,3],4,
[1,1],[16,24,24]],
# 230400.4
[[2,1920,4,120,1],
"( A5 x A5 ) # 2^6 [4]",[29,6,4],2,
[1,1],[80,24]],
# 230400.5
[[2,1920,5,120,1],
"( A5 x A5 ) # 2^6 [5]",[29,6,5],4,
[1,1],[10,24,24]],
# 230400.6
[[2,1920,6,120,1],
"( A5 x A5 ) # 2^6 [6]",[29,6,6],4,
[1,1],[80,24]],
# 230400.7
[[2,1920,7,120,1],
"( A5 x A5 ) # 2^6 [7]",[29,6,7],4,
[1,1],[32,24]],
# 230400.8
[[2,3840,1,60,1],
"( A5 x A5 ) # 2^6 [8]",[29,6,8],4,
[1,1],[64,5]],
# 230400.9
[[2,3840,2,60,1],
"( A5 x A5 ) # 2^6 [9]",[29,6,9],4,
[1,1],[64,5]],
# 230400.10
[[2,3840,3,60,1],
"( A5 x A5 ) # 2^6 [10]",[29,6,10],4,
[1,1],[24,5]],
# 230400.11
[[2,3840,4,60,1],
"( A5 x A5 ) # 2^6 [11]",[29,6,11],4,
[1,1],[48,5]],
# 230400.12
[[2,3840,5,60,1],
"( A5 x A5 ) # 2^6 [12]",[29,6,12],4,
[1,1],[24,12,5]],
# 230400.13
[[2,3840,6,60,1],
"( A5 x A5 ) # 2^6 [13]",[29,6,13],2,
[1,1],[48,5]],
# 230400.14
[[2,3840,7,60,1],
"( A5 x A5 ) # 2^6 [14]",[29,6,14],4,
[1,1],[32,24,5]],
# 230400.15
[[3,3840,1,120,1,"e1","e1","d2"],
"( A5 x A5 ) # 2^6 [15]",[29,6,15],4,
[1,1],768],
# 230400.16
[[3,3840,2,120,1,"e1","e1","d2"],
"( A5 x A5 ) # 2^6 [16]",[29,6,16],4,
[1,1],768],
# 230400.17
[[3,3840,3,120,1,"e1","d2"],
"( A5 x A5 ) # 2^6 [17]",[29,6,17],4,
[1,1],288],
# 230400.18
[[3,3840,4,120,1,"e1","d2"],
"( A5 x A5 ) # 2^6 [18]",[29,6,18],4,
[1,1],576],
# 230400.19
[[3,3840,4,120,1,"d1","d2"],
"( A5 x A5 ) # 2^6 [19]",[29,6,19],4,
[1,1],576],
# 230400.20
[[3,3840,5,120,1,"d1","d2"],
"( A5 x A5 ) # 2^6 [20]",[29,6,20],4,
[1,1],[288,144]],
# 230400.21
[[3,3840,5,120,1,"e1","d2"],
"( A5 x A5 ) # 2^6 [21]",[29,6,21],4,
[1,1],[288,144]],
# 230400.22
[[3,3840,5,120,1,"d1","e1","d2"],
"( A5 x A5 ) # 2^6 [22]",[29,6,22],4,
[1,1],[288,144]],
# 230400.23
[[3,3840,6,120,1,"e1","d2"],
"( A5 x A5 ) # 2^6 [23]",[29,6,23],2,
[1,1],576],
# 230400.24
[[3,3840,7,120,1,"d1","d2"],
"( A5 x A5 ) # 2^6 [24]",[29,6,24],4,
[1,1],[384,288]],
# 230400.25
[[3,3840,7,120,1,"e1","d2"],
"( A5 x A5 ) # 2^6 [25]",[29,6,25],4,
[1,1],[384,288]],
# 230400.26
[[3,3840,7,120,1,"d1","e1","d2"],
"( A5 x A5 ) # 2^6 [26]",[29,6,26],4,
[1,1],[384,288]]
];
PERFGRP[171]:=[# 232320.1
[[4,1920,3,14520,2,120,3,1],
"A5 # 2^5 11^2 [1]",6,1,
1,[16,24,121]],
# 232320.2
[[4,1920,4,14520,2,120,4,1],
"A5 # 2^5 11^2 [2]",6,1,
1,[80,121]],
# 232320.3
[[4,1920,5,14520,2,120,5,1],
"A5 # 2^5 11^2 [3]",6,1,
1,[10,24,121]]
];
PERFGRP[172]:=[# 233280.1
[[1,"abwxyzrstuv",
function(a,b,w,x,y,z,r,s,t,u,v)
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,r^3,s^3,t^3,u^3,v^3,
r^-1*s^-1*r*s,r^-1*t^-1*r*t,
r^-1*u^-1*r*u,r^-1*v^-1*r*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,
a^-1*r*a*u^-1,a^-1*s*a*s^-1,
a^-1*t*a*v^-1,a^-1*u*a*r^-1,
a^-1*v*a*t^-1,b^-1*r*b*s^-1,
b^-1*s*b*t^-1,b^-1*t*b*r^-1,
b^-1*u*b*u^-1,b^-1*v*b*v^-1,
w^-1*r*w*r^-1,w^-1*s*w*s,
w^-1*t*w*t,w^-1*u*w*u,w^-1*v*w*v,
x^-1*r*x*r,x^-1*s*x*s^-1,
x^-1*t*x*t,x^-1*u*x*u,x^-1*v*x*v,
y^-1*r*y*r,y^-1*s*y*s,
y^-1*t*y*t^-1,y^-1*u*y*u,
y^-1*v*y*v,z^-1*r*z*r,z^-1*s*z*s,
z^-1*t*z*t,z^-1*u*z*u^-1,
z^-1*v*z*v],[[b,a*b*a*b^-1*a,w,r]]];
end,
[15]],
"A5 2^4' 3^5",[7,5,2],1,
1,15],
# 233280.2
[[4,960,1,14580,1,60],
"A5 # 2^4 3^5 [1]",6,3,
1,[16,18]],
# 233280.3
[[4,960,2,14580,1,60],
"A5 # 2^4 3^5 [2]",6,3,
1,[10,18]]
];
PERFGRP[173]:=[# 237600.1
[[2,360,1,660,1],
"A6 x L2(11)",40,1,
[3,5],[6,11]]
];
PERFGRP[174]:=[# 240000.1
[[4,1920,1,7500,1,60],
"A5 # 2^5 5^3 [1]",6,2,
1,[12,30]],
# 240000.2
[[4,1920,2,7500,1,60],
"A5 # 2^5 5^3 [2]",6,2,
1,[24,30]],
# 240000.3
[[4,1920,3,7500,1,60],
"A5 # 2^5 5^3 [3]",6,2,
1,[16,24,30]],
# 240000.4
[[4,1920,4,7500,1,60],
"A5 # 2^5 5^3 [4]",6,1,
1,[80,30]],
# 240000.5
[[4,1920,5,7500,1,60],
"A5 # 2^5 5^3 [5]",6,2,
1,[10,24,30]],
# 240000.6
[[4,1920,6,7500,1,60],
"A5 # 2^5 5^3 [6]",6,2,
1,[80,30]],
# 240000.7
[[4,1920,7,7500,1,60],
"A5 # 2^5 5^3 [7]",6,2,
1,[32,30]],
# 240000.8
[[4,1920,1,7500,2,60],
"A5 # 2^5 5^3 [8]",6,2,
1,[12,30]],
# 240000.9
[[4,1920,2,7500,2,60],
"A5 # 2^5 5^3 [9]",6,2,
1,[24,30]],
# 240000.10
[[4,1920,3,7500,2,60],
"A5 # 2^5 5^3 [10]",6,2,
1,[16,24,30]],
# 240000.11
[[4,1920,4,7500,2,60],
"A5 # 2^5 5^3 [11]",6,1,
1,[80,30]],
# 240000.12
[[4,1920,5,7500,2,60],
"A5 # 2^5 5^3 [12]",6,2,
1,[10,24,30]],
# 240000.13
[[4,1920,6,7500,2,60],
"A5 # 2^5 5^3 [13]",6,2,
1,[80,30]],
# 240000.14
[[4,1920,7,7500,2,60],
"A5 # 2^5 5^3 [14]",6,2,
1,[32,30]],
# 240000.15
[[4,1920,3,15000,4,120,3,3],
"A5 # 2^5 5^3 [15]",6,5,
1,[16,24,125]],
# 240000.16
[[4,1920,4,15000,4,120,4,3],
"A5 # 2^5 5^3 [16]",6,5,
1,[80,125]],
# 240000.17
[[4,1920,5,15000,4,120,5,3],
"A5 # 2^5 5^3 [17]",6,5,
1,[10,24,125]]
];
PERFGRP[175]:=[# 241920.1
[[1,"abdwxyz",
function(a,b,d,w,x,y,z)
return
[[a^6*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*a^2*d,
a^2*d*b*(a^2*d)^-1*b^-1,d^2,
d^-1*a^-1*d*a,d^-1*b^-1*d*b,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],
[a*b,
b*a*b*a*b^2*a*b^-1*a*b*a*b^-1*a*b*a
*b^2*d,a^2*d,w]]];
end,
[45,16,240]],
"A7 3^1 x 2^1 x 2^4",[23,5,1],6,
8,[45,16,240]],
# 241920.2
[[1,"abdef",
function(a,b,d,e,f)
return
[[a^2,b^4,(a*b)^7*d^-1*e,(a^-1*b^-1*a*b)^5,
(a*b^2)^5*(e*f)^-1,(a*b*a*b*a*b^3)^5*f,
(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,
f^2,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^2*a*b^-1*a*b*a*b^2*a*b*d],
[a*e,b*a*b*a*b^-1*a*b^2*f^-1]]];
end,
[63,224],[[1,2]]],
"L3(4) 3^1 x 2^1 x 2^1",[27,2,1],-12,
20,[63,224]],
# 241920.3
[[1,"abdf",
function(a,b,d,f)
return
[[a^2,b^4*f^(-1*2),(a*b)^7*d^-1,(a^-1*b^-1*a
*b)^5*f^(-1*2),(a*b^2)^5*f^-1,
(a*b*a*b*a*b^3)^5*f,
(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,f^4,
a^-1*f*a*f^-1,b^-1*f*b*f^-1],
[[a*b*a,b^2*a*b^-1*a*b*a*b^2*a*b*d],
[a,b*a*b*a*b^-1*a*b^2*f^-1]]];
end,
[63,224],[[1,2]]],
"L3(4) 3^1 x 2^1 A 2^1 I",[27,2,2],-12,
20,[63,224]],
# 241920.4
[[1,"abde",
function(a,b,d,e)
return
[[a^2,b^4*e^(-1*2),(a*b)^7*d^-1*e,(a^-1*b^-1
*a*b)^5*e^(-1*2),(a*b^2)^5*e^-1,
(a*b*a*b*a*b^3)^5*e^(-1*2),
(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,
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^2,b^-1*a*b^-1*a*b*a*b^2]]];
end,
[63,224],[[1,2]]],
"L3(4) 3^1 x 2^1 A 2^1 II",[27,2,3],-12,
20,[63,224]],
# 241920.5
[[2,336,1,720,1],
"( L3(2) x A6 ) 2^2",[37,2,1],4,
[2,3],[16,80]]
];
PERFGRP[176]:=[# 243000.1
[[4,9720,4,3000,2,120,3,1],
"A5 2^1 # 3^4 5^2",6,1,
1,[45,25]],
# 243000.2
[[1,"abstuvwxyz",
function(a,b,s,t,u,v,w,x,y,z)
return
[[t^2,u^3,v^3,x^3,s^-2*t,a^3,w^3,b^-2*t,x^-1*w^-1*x*w,u*a^-1*v^-1*a,
(t*y)^2,s^-1*u^-1*s*v^-1,w^-1*y*w*y^-1,u*v*u^-1*v^-1,s^-1*v*s*u,
b^-1*w^-1*b*x^-1,b^-1*x^-1*b*w^-1,(t*z)^2,u*x^-1*u^-1*x,a*s^-1*a*s,
t*u^-1*t*u,a^-1*x*a*x^-1,t*v^-1*t*v,u^-1*z*u*z^-1,x^-1*z*x*z^-1,
v*x^-1*v^-1*x,u^-1*w*u*w^-1,a*t*a^-1*t,v^-1*y*v*y^-1,v*w^-1*v^-1*w,
s^-1*x^-1*s*x^-1,u^-1*y*u*y^-1,x^-1*y*x*y^-1,y^-1*z^-1*y*z,t*w^-1*t*w,
w^-1*z*w*z^-1,v^-1*z*v*z^-1,t*x^-1*t*x,x*w*s^-1*w^-1*s,s^-1*z*s*y^-1*z^-1,
a*u*v*a^-1*u,a^-1*w*v*a*w^-1,s^-1*y*z*s*z,y^5,z^5,b^-1*y*b*y^-2,
b^-1*z*b*z^2,a^-1*z*a*y^-1*z^-1*y^-1,a^-1*y*a*y*z^-1*y,
x^-1*b^-1*u^-1*b*v^-1*w^-1,b^-1*x^-1*v^-1*b*u^-1*x,b^-1*s^-1*b*s*b*s^-1,
a^-1*b^-1*(a^-1*b)^2],
[[t,u,v,w,y,z,a^-1*x*u^-1,s^-1*b*s^-1],[a,b,s,t,u,v,w,x]]];
end,
[15,25]],
"PG243000.2",[0,0,0],1,1,[15,25]],
# 243000.3
[[1,"abstuvwxyz",
function(a,b,s,t,u,v,w,x,y,z)
return
[[t^2,u^3,v^3,x^3,w^3,t*u^-1*t*u,v*u^-1*v^-1*u,w^-1*u^-1*w*u,v*x^-1*v^-1*x,
(t*z)^2,a*w^-1*a^-1*w,a*t*a^-1*t,s^-1*w*s*w,v^-1*z*v*z^-1,s^-1*t*s*t,
u^-1*y*u*y^-1,t*x^-1*t*x,v^-1*y*v*y^-1,w^-1*y*w*y^-1,w*v*w^-1*v^-1,
w*x^-1*w^-1*x,(t*y)^2,u^-1*z*u*z^-1,t*v^-1*t*v,b^-1*t*b*t,y^-1*z^-1*y*z,
x^-1*y*x*y^-1,u*x^-1*u^-1*x,x^-1*z*x*z^-1,w^-1*z*w*z^-1,t*w^-1*t*w,
a*w^-1*u*a^-1*v,b^-1*y*z*b*z,a^-1*w^-1*v*a*u,b^-1*t*u*b^-1*u,
x*a^-1*x^-1*a*v^-1,b^-1*x^-1*b*v*u^-1,b^-1*u^-1*v*b*x^-1,b^-1*z*b*y^-1*z^-1,
s^-1*w*v^-1*s*u,b^-1*u*b*w^-1*v^-1,s^-1*w^-1*u*s*v^-1,t*a^-3*w,z^5,
a*s^-1*a*s*v,y^5,s^-1*z*s*z^2,a^-1*s^-1*a^-1*v*s,s^-1*y*s*y^-2,
b^-1*x^-1*w^-1*b*w^-1*x^-1,w*a^-1*u*a*u*v^-1,a^-1*z*a*y^-1*z^2,
a*w^-1*v^-1*a^-1*u*v^-1,s^-1*x*s*u^-1*v*x^-1,b^-1*x*w*b*w*x,t*s^-2*v*w*x^-1,
a^-1*y*a*b^-1*y^-1*b*y,s^-1*b^-1*s^-1*b*w^-1*s*b*v,x*u^-1*a*b^-1*w*b*u*a^-1,
(b^-1*a^-1)^2*b*a^-1*x*v],
[[a,b,s,t,u,v,w,x],[t,v,w,x,y,z,t^-1*a*s,(u^-1*b)^a]]];
end,
[25,30]],
"PG243000.3",[0,0,0],1,1,[25,30]]
];
PERFGRP[177]:=[# 244800.1
[[2,60,1,4080,1],
"A5 x L2(16)",40,1,
[1,10],[5,17]]
];
PERFGRP[178]:=[# 244944.1
[[1,"abuvwxyz",
function(a,b,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,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,b*a*b^-1*a*b^-1*a*b*a*b^-1,u],
[a,b^-1*a*b,z]]];
end,
[16,63]],
"L3(2) 2^1 x 3^6",[9,6,1],2,
2,[16,63]],
# 244944.2
[[1,"abuvwxyz",
function(a,b,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,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],
[[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,u],
[b,a*b^-1*a*b*a,x*y^-1*z]]];
end,
[16,21]],
"L3(2) 2^1 x 3^6'",[9,6,2],2,
2,[16,21]]
];
PERFGRP[179]:=fail;
PERFGRP[180]:=[# 246480.1
[[1,"abc",
function(a,b,c)
return
[[c^39,c*b^9*c^-1*b^-1,b^79,a^2,c*a*c*a^-1,
(b*a)^3],[[b,c]]];
end,
[80],[0,3,3,4,0,2]],
"L2(79)",22,-1,
40,80]
];
PERFGRP[181]:=[# 254016.1
[[2,504,1,504,1],
"L2(8) x L2(8)",40,1,
[4,4],[9,9]]
];
PERFGRP[182]:=[# 258048.1
[[1,"abcuvwxyzdef",
function(a,b,c,u,v,w,x,y,z,d,e,f)
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,
f^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,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*e^-1*v*e,
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*e^-1*w*e,
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*e^-1*x*e,x^-1*f^-1*x*f,
y^-1*z^-1*y*z,y^-1*d^-1*y*d,
y^-1*e^-1*y*e,y^-1*f^-1*y*f,
z^-1*d^-1*z*d,z^-1*e^-1*z*e,
z^-1*f^-1*z*f,d^-1*e^-1*d*e,
d^-1*f^-1*d*f,e^-1*f^-1*e*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*e*a*e^-1,
a^-1*f*a*f^-1,b^-1*u*b*(x*y*d)^-1,
b^-1*v*b*(y*z*e)^-1,
b^-1*w*b*(x*y*z*f)^-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,b^-1*f*b*f^-1,
c^-1*u*c*(v*d*f)^-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*f)^-1,
c^-1*d*c*d^-1,c^-1*e*c*e^-1,
c^-1*f*c*f^-1],
[[b^-1*c,u*d,e,f],[b^-1*c,u*e,d,f],
[b^-1*c,u*f,d,e]]];
end,
[112,112,112],[[1,2]]],
"L2(8) 2^6 E ( 2^1 x 2^1 x 2^1 )",[16,9,1],8,
4,[112,112,112]],
# 258048.2
[[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*f^2)^-1,d^2,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*d^-1*u*d,
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*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*f^2,
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*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*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*f^2)^-1,
b^-1*w*b*(x*y*z*d*f^2)^-1,
b^-1*x*b*(v*w*x)^-1,
b^-1*y*b*(u*v*w*y*d*f^2)^-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],
[[c^-1*x^-1*a, c*b]]];
end,
[576],[[1,2],[11,11]]],
"L2(8) N ( 2^6 E ( 2^1 x 2^1 A ) ) C 2^1",[16,9,2],8,
4,[576]],
# 258048.3
[[1,"abcuvwxyzdef",
function(a,b,c,u,v,w,x,y,z,d,e,f)
return
[[a^2*(e*f^-1)^-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,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*e^-1*u*e,
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*e^-1*v*e,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*e^-1*w*e,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*e^-1*x*e,
x^-1*f^-1*x*f,y^-1*z^-1*y*z,
y^-1*d^-1*y*d,y^-1*e^-1*y*e,
y^-1*f^-1*y*f,z^-1*d^-1*z*d,
z^-1*e^-1*z*e,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*e*a*e^-1,
a^-1*f*a*f^-1,
b^-1*u*b*(x*y*e*f^-1)^-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*f^-1)^-1,
b^-1*d*b*d^-1,b^-1*e*b*e^-1,
b^-1*f*b*f^-1,
c^-1*u*c*(v*d*e*f^-1)^-1,
c^-1*v*c*(w*d*f^-1)^-1,
c^-1*w*c*(u*v*e*f)^-1,
c^-1*x*c*(x*z*d*e*f)^-1,
c^-1*y*c*(x*d*f)^-1,
c^-1*z*c*(y*e*f^-1)^-1,
c^-1*d*c*d^-1,c^-1*e*c*e^-1,
c^-1*f*c*f^-1],
[[b^-1*c,u*f,d,e],[b^-1*c*d,u*d,e,f],
[b^-1*c*e,u,d,f]]];
end,
[112,112,112],[[1,2]]],
"L2(8) N 2^6 E ( 2^1 x 2^1 x 2^1 )",[16,9,3],8,
4,[112,112,112]],
# 258048.4
[[1,"abcstuvwxyzd",
function(a,b,c,s,t,u,v,w,x,y,z,d)
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,d^2,s^2,t^2,u^2,v^2,w^2,x^2,y^2,z^2,
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*w^-1*d*w,d^-1*x^-1*d*x,
d^-1*y^-1*d*y,d^-1*z^-1*d*z,
s^-1*t^-1*s*t*d,s^-1*u^-1*s*u*d,
s^-1*v^-1*s*v*d,s^-1*w^-1*s*w*d,
s^-1*x^-1*s*x*d,s^-1*y^-1*s*y*d,
s^-1*z^-1*s*z*d,t^-1*u^-1*t*u*d,
t^-1*v^-1*t*v*d,t^-1*w^-1*t*w*d,
t^-1*x^-1*t*x*d,t^-1*y^-1*t*y*d,
t^-1*z^-1*t*z*d,u^-1*v^-1*u*v*d,
u^-1*w^-1*u*w*d,u^-1*x^-1*u*x*d,
u^-1*y^-1*u*y*d,u^-1*z^-1*u*z*d,
v^-1*w^-1*v*w*d,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*d,w^-1*y^-1*w*y*d,
w^-1*z^-1*w*z*d,x^-1*y^-1*x*y*d,
x^-1*z^-1*x*z*d,y^-1*z^-1*y*z*d,
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,
a^-1*d*a*d^-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,
b^-1*d*b*d^-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,c^-1*d*c*d^-1],
[[a,b]]];
end,
[512]],
"L2(8) 2^8 C 2^1",[16,9,4],2,
4,512]
];
PERFGRP[183]:=[# 259200.1
[[2,120,1,2160,1],
"( A5 x A6 3^1 ) 2^2",[33,2,1],12,
[1,3],[24,18,80]],
# 259200.2
[[2,360,1,720,1],
"( A6 x A6 ) 2^1 [1]",40,2,
[3,3],[6,80]],
# 259200.3
[[3,720,1,720,1,"d1","d2"],
"( A6 x A6 ) 2^1 [2]",40,2,
[3,3],3200]
];
PERFGRP[184]:=[# 262080.1
[[1,"abc",
function(a,b,c)
return
[[c^63,b^2,c^(-1*7)*b*c^2*b*c^2*b*c^3*b,c^(-1*6)*b*c
*b*c^3*b*c*b*c*b,a^2,c*a*c*a^-1,
(a*b)^3,
c^3*a*(b*c*b*c^2)^2*b*c^-1*b*c^(-1*2)*b*a],
[[b,c]]];
end,
[65]],
"L2(64)",22,-1,
41,65],
# 262080.2
[[2,120,1,2184,1],
"( A5 x L2(13) ) 2^2",40,4,
[1,6],[24,56]]
];
PERFGRP[185]:=[# 262440.1
[[1,"abuvwxyzd",
function(a,b,u,v,w,x,y,z,d)
return
[[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,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^-1,
u^-1*w^-1*u*w*d,u^-1*x^-1*u*x,
u^-1*y^-1*u*y*d^-1,
u^-1*z^-1*u*z*d,v^-1*w^-1*v*w,
v^-1*x^-1*v*x*d^-1,
v^-1*y^-1*v*y*d,v^-1*z^-1*v*z
*d^-1,w^-1*x^-1*w*x,
w^-1*y^-1*w*y*d,w^-1*z^-1*w*z
*d^-1,x^-1*y^-1*x*y,
x^-1*z^-1*x*z,y^-1*z^-1*y*z*d,
a^-1*u*a*(v*d^-1)^-1,
a^-1*v*a*(u^-1*d)^-1,
a^-1*w*a*(u^-1*x*d^-1)^-1,
a^-1*x*a*(v*w^-1)^-1,
a^-1*y*a*(u*w^-1*x^-1*y^-1*z^-1)
^-1,
a^-1*z*a*(w^-1*y^-1*z*d^-1)^-1,
b^-1*u*b*(u^-1*v^-1*w)^-1,
b^-1*v*b*(u^-1*v*w)^-1,
b^-1*w*b*u^-1,b^-1*x*b*(w*y)^-1,
b^-1*y*b*(u^-1*w*x*y*z)^-1,
b^-1*z*b*(w*y*z^-1)^-1],[[a,b]]];
end,
[2187]],
"A5 2^1 3^6' C 3^1",[2,7,1],3,
1,2187],
# 262440.2
[[1,"abcuvwxyz",
function(a,b,c,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,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],
[[b,c*a*b*c,y,z,w,x]]];
end,
[90]],
"A6 3^6",[14,6,1],1,
3,90],
# 262440.3
[[1,"abcuvwxyz",
function(a,b,c,u,v,w,x,y,z)
return
[[a^2*(v^-1*w*x*y^-1)^-1,b^3*z^-1,c^3*v
,(b*c)^4*(v*x^-1*y^-1)^-1,
(b*c^-1)^5*(v*x^-1*y)^-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
],[[b,c*a*b*c,y,z,w,x]]];
end,
[90]],
"A6 N 3^6",[14,6,2],1,
3,90],
# 262440.4
[[1,"abcdwxyze",
function(a,b,c,d,w,x,y,z,e)
return
[[a^2*d^-1,b^3,c^3*(w*x*y^-1)^-1,(b*c)^4,
(b*c^-1)^5,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],
[[a*b,b*a*b*a*b^-1*a*b^-1,w*e]]];
end,
[324]],
"A6 ( 3^1 E 3^4' E 3^1 ) A",[14,6,3],3,
3,324],
# 262440.5
[[1,"abcwxyzef",
function(a,b,c,w,x,y,z,e,f)
return
[[a^2,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1*b^-1*c
*b*c*b^-1*c*b*c^-1,w^3,x^3,y^3,
z^3,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],
[[a,b,w],[a,c,w]]];
end,
[18,18]],
"A6 3^4' E ( 3^1 x 3^1 )",[14,6,4],9,
3,[18,18]],
# 262440.6
[[1,"abcwxyzdf",
function(a,b,c,w,x,y,z,d,f)
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,
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],[[a,b,w],[a*d,c*d,w]]];
end,
[18,18]],
"A6 3^1 x ( 3^4' E 3^1 ) I",[14,6,5],9,
3,[18,18]],
# 262440.7
[[1,"abcwxyzde",
function(a,b,c,w,x,y,z,d,e)
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,
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],
[[a*b,b*a*b*a*b^-1*a*b^-1,w*e,d],
[a*d,c*d,w]]];
end,
[108,18]],
"A6 3^1 x ( 3^4' E 3^1 ) II",[14,6,6],9,
3,[108,18]]
];
PERFGRP[186]:=[# 263424.1
[[4,5376,1,16464,2,336,1,1],
"L3(2) # 2^5 7^2",12,2,
2,[16,16,49]]
];
PERFGRP[187]:=[# 265680.1
[[1,"abc",
function(a,b,c)
return
[[c^40,b^3,c^(-1*12)*b*c*b*c^11*b^-1,c^20*b*c^20
*b^(-1*2),a^2,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]]];
end,
[82],[0,0,3,2]],
"L2(81)",22,-1,
42,82]
];
PERFGRP[188]:=[# 276480.1
[[4,92160,1,1080,2,360,1,1],
"A6 3^1 x 2^4 x 2^4",[13,8,1],3,
3,[16,16,18]],
# 276480.2
[[4,92160,2,1080,2,360,2,1],
"A6 3^1 x 2^4 x 2^4'",[13,8,2],3,
3,[16,16,18]]
];
PERFGRP[189]:=[# 285852.1
[[1,"abc",
function(a,b,c)
return
[[c^41,c*b^4*c^-1*b^-1,b^83,a^2,c*a*c*a^-1,
(b*a)^3],[[b,c]]];
end,
[84]],
"L2(83)",22,-1,
43,84]
];
PERFGRP[190]:=[# 288120.1
[[1,"abwxyz",
function(a,b,w,x,y,z)
return
[[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,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],
[[a*b,w],[b,a*b*a*b^-1*a,w*x^-1]]];
end,
[24,35]],
"A5 2^1 x 7^4",[4,4,1],2,
1,[24,35]],
# 288120.2
[[1,"abwxyz",
function(a,b,w,x,y,z)
return
[[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,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*(w^(-1*3)*x)^-1,
a^-1*x*a*(w^(-1*3)*x^3)^-1,
a^-1*y*a*(w^(-1*2)*x*y^(-1*2)*z^3)^-1,
a^-1*z*a*(x^(-1*2)*y^3*z^2)^-1,
b^-1*w*b*(w^(-1*3)*y^2)^-1,
b^-1*x*b*(w^(-1*3)*x^-1*y^(-1*3))^-1,
b^-1*y*b*(w^2*x*y^(-1*3))^-1,
b^-1*z*b*(w^2*x*y^3*z)^-1],
[[b,a*b*a*b^-1*a,y*z^-1]]];
end,
[245]],
"A5 2^1 7^4'",[4,4,2],1,
1,245],
# 288120.3
[[1,"abwxyz",
function(a,b,w,x,y,z)
return
[[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,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*y,a^-1*x*a*z,
a^-1*y*a*w^-1,a^-1*z*a*x^-1,
b^-1*w*b*w^(-1*2),b^-1*x*b*x^(-1*2),
b^-1*y*b*(w^3*x^(-1*2)*y^(-1*3))^-1,
b^-1*z*b*(w^-1*x^(-1*2)*z^(-1*3))^-1],
[[b,a*b*a*b^-1*a,w]]];
end,
[245]],
"A5 2^1 7^4''",[4,4,3],1,
1,245]
];
PERFGRP[191]:=[# 291600.1
[[2,60,1,4860,1],
"( A5 x A5 ) # 3^4 [1]",[30,4,1],1,
[1,1],[5,15]],
# 291600.2
[[2,60,1,4860,2],
"( A5 x A5 ) # 3^4 [2]",[30,4,2],1,
[1,1],[5,60]]
];
PERFGRP[192]:=[# 293760.1
[[2,60,1,4896,1],
"( A5 x L2(17) ) 2^1 [1]",40,2,
[1,7],[5,288]],
# 293760.2
[[2,120,1,2448,1],
"( A5 x L2(17) ) 2^1 [2]",40,2,
[1,7],[24,18]],
# 293760.3
[[3,120,1,4896,1,"d1","d2"],
"( A5 x L2(17) ) 2^1 [3]",40,2,
[1,7],3456]
];
PERFGRP[193]:=[# 300696.1
[[1,"abc",
function(a,b,c)
return
[[c^33*a^2,c*b^4*c^-1*b^-1,b^67,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,
[136]],
"L2(67) 2^1 = SL(2,67)",22,-2,
35,136]
];
PERFGRP[194]:=[# 302400.1
[[2,60,1,5040,1],
"( A5 x A7 ) 2^1 [1]",40,2,
[1,8],[5,240]],
# 302400.2
[[2,120,1,2520,1],
"( A5 x A7 ) 2^1 [2]",40,2,
[1,8],[24,7]],
# 302400.3
[[3,120,1,5040,1,"d1","d2"],
"( A5 x A7 ) 2^1 [3]",40,2,
[1,8],2880]
];
PERFGRP[195]:=[# 311040.1
[[1,"abdwxyzstuv",
function(a,b,d,w,x,y,z,s,t,u,v)
return
[[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,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,s],[a,b,w]]];
end,
[24,81]],
"A5 2^1 x ( 2^4' C 2^1 ) 3^4",[7,4,1],2,
1,[24,81]],
# 311040.2
[[4,3840,1,4860,1,60],
"A5 # 2^6 3^4 [1]",6,4,
1,[64,15]],
# 311040.3
[[4,3840,2,4860,1,60],
"A5 # 2^6 3^4 [2]",6,4,
1,[64,15]],
# 311040.4
[[4,3840,3,4860,1,60],
"A5 # 2^6 3^4 [3]",6,4,
1,[24,15]],
# 311040.5
[[4,3840,4,4860,1,60],
"A5 # 2^6 3^4 [4]",6,4,
1,[48,15]],
# 311040.6
[[4,3840,5,4860,1,60],
"A5 # 2^6 3^4 [5]",6,4,
1,[24,12,15]],
# 311040.7
[[4,3840,6,4860,1,60],
"A5 # 2^6 3^4 [6]",6,2,
1,[48,15]],
# 311040.8
[[4,3840,7,4860,1,60],
"A5 # 2^6 3^4 [7]",6,4,
1,[32,24,15]],
# 311040.9
[[4,3840,1,4860,2,60],
"A5 # 2^6 3^4 [8]",6,4,
1,[64,60]],
# 311040.10
[[4,3840,2,4860,2,60],
"A5 # 2^6 3^4 [9]",6,4,
1,[64,60]],
# 311040.11
[[4,3840,3,4860,2,60],
"A5 # 2^6 3^4 [10]",6,4,
1,[24,60]],
# 311040.12
[[4,3840,4,4860,2,60],
"A5 # 2^6 3^4 [11]",6,4,
1,[48,60]],
# 311040.13
[[4,3840,5,4860,2,60],
"A5 # 2^6 3^4 [12]",6,4,
1,[24,12,60]],
# 311040.14
[[4,3840,6,4860,2,60],
"A5 # 2^6 3^4 [13]",6,2,
1,[48,60]],
# 311040.15
[[4,3840,7,4860,2,60],
"A5 # 2^6 3^4 [14]",6,4,
1,[32,24,60]],
# 311040.16
[[4,3840,5,9720,4,120,5,3],
"A5 # 2^6 3^4 [15]",6,2,
1,[24,12,45]],
# 311040.17
[[4,3840,6,9720,4,120,6,3],
"A5 # 2^6 3^4 [16]",6,2,
1,[48,45]],
# 311040.18
[[4,3840,7,9720,4,120,7,3],
"A5 # 2^6 3^4 [17]",6,2,
1,[32,24,45]]
];
PERFGRP[196]:=[# 320760.1
[[1,"abvwxyz",
function(a,b,v,w,x,y,z)
return
[[a^4,b^3,(a*b)^11,(a*b)^4*(a*b^-1)^5*(a*b)^4*(a
*b^-1)^5*a^2,a^2*b*a^2*b^-1,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)],
[[a*b,(b*a)^2*(b^-1*a)^4*b^-1*a^2,v],
[b,a*b*a*b^-1*a,y*z]]];
end,
[24,33]],
"L2(11) 2^1 3^5",[18,5,1],2,
5,[24,33]]
];
PERFGRP[197]:=[# 322560.1
[[1,"abduvwxyz",
function(a,b,d,u,v,w,x,y,z)
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,
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^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],
[[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],
[a*b,b*a*b*a*b^2*a*b^-1*a*b*a*b^-1*a*b
*a*b^2*d,u]]];
end,
[14,240],[[1,-2]]],
"A7 2^1 x 2^6",[23,7,1],2,
8,[14,240]],
# 322560.2
[[1,"abuvwxyze",
function(a,b,u,v,w,x,y,z,e)
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,e^2,
u^-1*e*u*e^-1,v^-1*e*v*e^-1,
w^-1*e*w*e^-1,x^-1*e*x*e^-1,
y^-1*e*y*e^-1,z^-1*e*z*e^-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]]];
end,
[128]],
"A7 2^6 C 2^1",[23,7,2],2,
8,128],
# 322560.3
[[1,"abduvwxyz",
function(a,b,d,u,v,w,x,y,z)
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,
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^2*d^-1,v^2*d^-1,w^2*d^-1,
x^2*d^-1,y^2*d^-1,z^2*d^-1,
u^-1*v^-1*u*v*d^-1,
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*d^-1,
v^-1*w^-1*v*w*d^-1,
v^-1*x^-1*v*x*d^-1,
v^-1*y^-1*v*y*d^-1,
v^-1*z^-1*v*z*d^-1,
w^-1*x^-1*w*x*d^-1,
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^-1,
y^-1*z^-1*y*z*d^-1,
a^-1*u*a*u^-1,a^-1*v*a*v^-1,
a^-1*w*a*(y*d)^-1,a^-1*x*a*x^-1,
a^-1*y*a*(w*d)^-1,
a^-1*z*a*(u*v*w*x*y*z*d)^-1,
b^-1*u*b*w^-1,b^-1*v*b*z^-1,
b^-1*w*b*v^-1,b^-1*x*b*(y*d)^-1,
b^-1*y*b*(x*d)^-1,b^-1*z*b*u^-1],
[[a*b,
b*a*b*a*b^2*a*b^-1*a*b*a*b^-1*a*b*a
*b^2*d,x*y*z*d]]];
end,
[1920]],
"A7 2^6 C N 2^1",[23,7,3],2,
8,1920],
# 322560.4
[[1,"abwxyz",
function(a,b,w,x,y,z)
return
[[a^2,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,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]]];
end,
[16]],
"A8 2^4",[26,4,1],1,
19,16],
# 322560.5
[[1,"abwxyz",
function(a,b,w,x,y,z)
return
[[a^2*(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,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]]];
end,
[30],[[1,2],[7,7]]],
"A8 N 2^4",[26,4,2],1,
19,30],
# 322560.6
[[1,"abef",
function(a,b,e,f)
return
[[a^2,b^4*(e^2*f^2)^-1,(a*b)^7*e,(a*b^2)^5*(e*f)
^-1,(a^-1*b^-1*a*b)^5*(e^2*f^2)^-1
,(a*b*a*b*a*b^3)^5*(e^2*f^-1)^-1,
(a*b*a*b*a*b^2*a*b^-1)^5,e^4,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,
[224,224],[[1,2]]],
"L3(4) ( 2^1 A 2^1 ) x ( 2^1 A 2^1 )",[27,4,1],-16,
20,[224,224]],
# 322560.7
[[2,60,1,5376,1],
"( A5 x L3(2) ) # 2^5 [1]",[31,5,1],4,
[1,2],[5,16,16]],
# 322560.8
[[2,120,1,2688,1],
"( A5 x L3(2) ) # 2^5 [2]",[31,5,2],4,
[1,2],[24,8,16]],
# 322560.9
[[2,120,1,2688,2],
"( A5 x L3(2) ) # 2^5 [3]",[31,5,3],4,
[1,2],[24,16]],
# 322560.10
[[2,120,1,2688,3],
"( A5 x L3(2) ) # 2^5 [4]",[31,5,4],4,
[1,2],[24,16,14]],
# 322560.11
[[3,120,1,5376,1,"d1","d2"],
"( A5 x L3(2) ) # 2^5 [5]",[31,5,5],4,
[1,2],[192,192]],
# 322560.12
[[3,120,1,5376,1,"d1","e2"],
"( A5 x L3(2) ) # 2^5 [6]",[31,5,6],4,
[1,2],[192,192]],
# 322560.13
[[2,1920,1,168,1],
"( A5 x L3(2) ) # 2^5 [7]",[31,5,7],2,
[1,2],[12,7]],
# 322560.14
[[2,1920,2,168,1],
"( A5 x L3(2) ) # 2^5 [8]",[31,5,8],2,
[1,2],[24,7]],
# 322560.15
[[2,1920,3,168,1],
"( A5 x L3(2) ) # 2^5 [9]",[31,5,9],2,
[1,2],[16,24,7]],
# 322560.16
[[2,1920,4,168,1],
"( A5 x L3(2) ) # 2^5 [10]",[31,5,10],1,
[1,2],[80,7]],
# 322560.17
[[2,1920,5,168,1],
"( A5 x L3(2) ) # 2^5 [11]",[31,5,11],2,
[1,2],[10,24,7]],
# 322560.18
[[2,1920,6,168,1],
"( A5 x L3(2) ) # 2^5 [12]",[31,5,12],2,
[1,2],[80,7]],
# 322560.19
[[2,1920,7,168,1],
"( A5 x L3(2) ) # 2^5 [13]",[31,5,13],2,
[1,2],[32,7]],
# 322560.20
[[2,960,1,336,1],
"( A5 x L3(2) ) # 2^5 [14]",[31,5,14],2,
[1,2],[16,16]],
# 322560.21
[[2,960,2,336,1],
"( A5 x L3(2) ) # 2^5 [15]",[31,5,16],2,
[1,2],[10,16]],
# 322560.22
[[3,1920,1,336,1,"e1","d2"],
"( A5 x L3(2) ) # 2^5 [16]",[31,5,16],2,
[1,2],96],
# 322560.23
[[3,1920,2,336,1,"d1","d2"],
"( A5 x L3(2) ) # 2^5 [17]",[31,5,17],2,
[1,2],192],
# 322560.24
[[3,1920,3,336,1,"d1","d2"],
"( A5 x L3(2) ) # 2^5 [18]",[31,5,18],2,
[1,2],[128,192]],
# 322560.25
[[3,1920,5,336,1,"d1","d2"],
"( A5 x L3(2) ) # 2^5 [19]",[31,5,19],2,
[1,2],[80,192]],
# 322560.26
[[3,1920,6,336,1,"d1","d2"],
"( A5 x L3(2) ) # 2^5 [20]",[31,5,20],2,
[1,2],640],
# 322560.27
[[3,1920,7,336,1,"e1","d2"],
"( A5 x L3(2) ) # 2^5 [21]",[31,5,21],2,
[1,2],256]
];
PERFGRP[198]:=[# 332640.1
[[2,504,1,660,1],
"L2(8) x L2(11)",40,1,
[4,5],[9,11]]
];
PERFGRP[199]:=[# 336960.1
[[2,60,1,5616,1],
"A5 x L3(3)",40,1,
[1,11],[5,13]]
];
PERFGRP[200]:=fail;
PERFGRP[201]:=[# 345600.1
[[2,60,1,5760,1],
"( A5 x A6 ) # 2^4 [1]",[33,4,1],1,
[1,3],[5,16]],
# 345600.2
[[2,960,1,360,1],
"( A5 x A6 ) # 2^4 [2]",[33,4,2],1,
[1,3],[16,6]],
# 345600.3
[[2,960,2,360,1],
"( A5 x A6 ) # 2^4 [3]",[33,4,3],1,
[1,3],[10,6]]
];
[ Dauer der Verarbeitung: 0.13 Sekunden
(vorverarbeitet)
]
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