#############################################################################
##
#W  ctoconja.tbl                GAP table library               Thomas Breuer
##
#H  @(#)$Id: ctoconja.tbl,v 4.21 2004/03/30 08:05:55 gap Exp $
##
#Y  Copyright (C)  1996,  Lehrstuhl D fuer Mathematik,  RWTH Aachen,  Germany
##
##  This file contains the ordinary character tables related to the
##  Conway and Janko groups.  These are the tables of $Co_1$, $Co_2$, $Co_3$,
##  $2.Co_1$, $J_1$, $J_2$, $2.J_2$, $J_2.2$, $2.J_2.2$, $J_3$, $3.J_3$,
##  $J_3.2$, $3.J_3.2$ and $J_4$.
##
Revision.ctoconja_tbl :=
    "@(#)$Id: ctoconja.tbl,v 4.21 2004/03/30 08:05:55 gap Exp $";

SET_TABLEFILENAME("ctoconja");
ALN:= Ignore;

MOT("2.Co1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13,23]"
],
[8315553613086720000,8315553613086720000,178362777600,178362777600,2012774400,
389283840,2690072985600,2690072985600,117573120,117573120,25194240,25194240,
1088640,1088640,743178240,743178240,1179648,1474560,1474560,294912,48384,
15360,6048000,6048000,72000,72000,30000,30000,19906560,19906560,483840,311040,
311040,311040,311040,41472,41472,31104,31104,3456,1440,576,35280,35280,2352,
2352,92160,6144,12288,12288,2048,1536,1536,768,3888,3888,972,972,972,972,
19200,19200,1200,1200,1200,1200,1200,1200,160,132,132,276480,276480,9216,4608,
5184,5184,3456,3456,864,576,576,576,576,576,288,576,576,72,48,312,312,168,112,
112,10800,10800,1800,1800,360,360,180,180,60,60,64,128,128,432,432,108,108,
108,108,960,960,40,40,40,504,504,126,126,42,42,44,44,46,46,46,46,576,384,384,
144,96,48,48,48,52,56,56,56,56,240,240,60,60,60,60,60,60,66,66,70,70,72,72,78,
78,78,78,80,80,84,120,120],
[,[1,1,1,1,2,1,7,7,9,9,11,11,13,13,4,4,4,3,3,3,5,6,23,23,25,25,27,27,7,7,8,9,
9,11,11,9,9,11,11,9,14,13,43,43,45,45,16,15,17,17,17,18,18,20,55,55,57,57,59,
59,23,23,24,26,25,25,27,27,25,70,70,30,30,30,29,39,39,37,37,31,37,34,34,36,36,
36,39,39,41,42,91,91,44,45,45,96,96,98,98,100,100,102,102,104,104,49,51,51,55,
55,57,57,59,59,62,62,69,67,67,120,120,122,122,124,124,70,70,128,128,130,130,
73,74,74,79,75,78,82,82,92,95,95,93,93,96,96,99,101,102,102,104,104,153,153,
155,155,110,110,159,159,161,161,116,116,121,146,146],[1,2,3,4,5,6,1,2,1,2,1,2,
1,2,15,16,17,18,19,20,21,22,23,24,25,26,27,28,3,4,5,3,4,3,4,3,4,3,4,6,5,6,43,
44,45,46,47,48,49,50,51,52,53,54,11,12,11,12,11,12,61,62,63,64,65,66,67,68,69,
70,71,15,16,17,20,15,16,15,16,21,17,18,19,18,19,20,17,17,21,22,91,92,93,94,95,
23,24,25,26,23,24,25,26,27,28,106,107,108,38,39,38,39,38,39,115,116,117,118,
119,43,44,43,44,45,46,126,127,128,129,130,131,47,49,50,47,54,48,52,53,140,141,
142,143,144,61,62,64,63,65,66,67,68,70,71,155,156,76,77,91,92,91,92,163,164,
93,115,116],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,2,1,
2,1,2,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,
53,54,55,56,57,58,59,60,3,4,5,5,3,4,3,4,6,70,71,72,73,74,75,76,77,78,79,80,81,
82,83,84,85,86,87,88,89,90,91,92,93,94,95,7,8,7,8,13,14,9,10,11,12,106,107,
108,109,110,111,112,113,114,15,16,22,18,19,120,121,122,123,124,125,126,127,
130,131,128,129,132,133,134,135,136,137,138,139,140,141,142,143,144,29,30,31,
41,32,33,34,35,153,154,43,44,157,158,159,160,161,162,47,47,165,72,73],,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,38,39,40,41,42,1,2,1,2,47,48,49,50,51,52,53,54,55,56,57,58,
59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
85,86,87,88,89,90,91,92,5,3,4,96,97,98,99,100,101,102,103,104,105,106,107,108,
109,110,111,112,113,114,115,116,117,118,119,7,8,9,10,13,14,127,126,130,131,
128,129,132,133,134,135,136,137,138,139,140,15,16,21,21,145,146,147,148,149,
150,151,152,153,154,23,24,157,158,161,162,159,160,163,164,31,166,167],,,,[1,2,
3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,
57,58,59,60,61,62,63,64,65,66,67,68,69,1,2,72,73,74,75,76,77,78,79,80,81,82,
83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,
125,6,6,130,131,128,129,132,133,134,135,136,137,138,139,140,141,142,144,143,
145,146,147,148,149,150,151,152,7,8,155,156,157,158,159,160,161,162,164,163,
165,166,167],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,
77,78,79,80,81,82,83,84,85,86,87,88,89,90,1,2,93,94,95,96,97,98,99,100,101,
102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,
121,122,123,124,125,127,126,128,129,130,131,132,133,134,135,136,137,138,139,5,
141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,7,8,7,
8,164,163,165,166,167],,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,123,124,125,126,127,1,2,1,2,132,133,134,135,136,137,
138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,
157,158,161,162,159,160,163,164,165,166,167]],
0,
[(163,164),(159,161)(160,162),(143,144),(143,144)(163,164),(128,130)(129,131),
(126,127)],
["ConstructProj",[["Co1",[]],["2.Co1",[]]]]);
ALF("2.Co1","Co1",[1,1,2,2,3,4,5,5,6,6,7,7,8,8,9,9,10,11,11,12,13,14,15,
15,16,16,17,17,18,18,19,20,20,21,21,22,22,23,23,24,25,26,27,27,28,28,29,
30,31,31,32,33,33,34,35,35,36,36,37,37,38,38,39,40,41,41,42,42,43,44,44,
45,45,46,47,48,48,49,49,50,51,52,52,53,53,54,55,55,56,57,58,58,59,60,60,
61,61,62,62,63,63,64,64,65,65,66,67,67,68,68,69,69,70,70,71,71,72,73,73,
74,74,75,75,76,76,77,77,78,78,79,79,80,81,81,82,83,84,85,85,86,87,87,88,
88,89,89,90,91,92,92,93,93,94,94,95,95,96,96,97,97,98,98,99,99,100,101,
101]);
ALN("2.Co1",["2.F2-"]);

MOT("2.J2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[1209600,1209600,3840,3840,240,2160,2160,72,72,192,192,600,600,600,600,100,
100,100,100,48,48,12,14,14,16,16,20,20,20,20,20,20,24,24,30,30,30,30],
[,[1,1,1,1,2,6,6,8,8,3,3,14,14,12,12,18,18,16,16,6,6,9,23,23,11,11,15,13,18,
18,16,16,20,20,37,37,35,35],[1,2,3,4,5,1,2,1,2,10,11,14,15,12,13,18,19,16,17,
3,4,5,23,24,26,25,28,27,31,32,29,30,10,11,14,15,12,13],,[1,2,3,4,5,6,7,8,9,10,
11,1,2,1,2,1,2,1,2,20,21,22,23,24,25,26,5,5,3,4,3,4,33,34,6,7,6,7],,[1,2,3,4,
5,6,7,8,9,10,11,14,15,12,13,18,19,16,17,20,21,22,1,2,26,25,28,27,31,32,29,30,
33,34,37,38,35,36]],
0,
[(25,26),(12,14)(13,15)(16,18)(17,19)(27,28)(29,31)(30,32)(35,37)(36,38)],
["ConstructProj",[["J2",[]],["2.J2",[]]]]);
ALF("2.J2","J2",[1,1,2,2,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,13,13,
14,14,15,16,17,17,18,18,19,19,20,20,21,21]);
ALF("2.J2","2.J2.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,12,13,14,15,14,15,16,
17,18,19,20,21,21,22,22,23,24,23,24,25,26,27,28,27,28]);
ARC("2.J2","maxes",["2xU3(3)","(2x3.A6).2","2^{1+4}_-:2A5","2^{3+4}:(3xS3)",
"2A4xA5","2A5xD10","(2xL3(2)).2","2.J2M8","2.A5"]);
ALN("2.J2",["2.HJ","2.F5-"]);

MOT("2.J2.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[2419200,2419200,7680,7680,480,4320,4320,144,144,384,384,600,600,100,100,96,
96,24,28,28,16,20,20,20,48,48,30,30,672,96,48,48,12,192,192,32,24,24,24,24,28,
28,48,48,48,48],
[,[1,1,1,1,2,6,6,8,8,3,3,12,12,14,14,6,6,9,19,19,11,13,14,14,16,16,27,27,2,4,
5,5,9,11,11,11,17,17,18,18,20,20,26,26,26,26],[1,2,3,4,5,1,2,1,2,10,11,12,13,
14,15,3,4,5,19,20,21,22,23,24,10,11,12,13,29,30,32,31,29,35,34,36,30,30,32,31,
41,42,35,34,35,34],,[1,2,3,4,5,6,7,8,9,10,11,1,2,1,2,16,17,18,19,20,21,5,3,4,
25,26,6,7,29,30,32,31,33,35,34,36,38,37,40,39,42,41,44,43,46,45],,[1,2,3,4,5,
6,7,8,9,10,11,12,13,14,15,16,17,18,1,2,21,22,23,24,25,26,27,28,29,30,31,32,33,
34,35,36,38,37,39,40,29,29,45,46,43,44]],
0,
[(41,42),(37,38)(43,45)(44,46),(37,38)(41,42)(43,45)(44,46),(31,32)(34,35)
(37,38)(39,40)(41,42)(43,44)(45,46),(31,32)(34,35)(39,40)(43,46)(44,45)],
["ConstructProj",[["J2.2",[]],["2.J2.2",[]]]]);
ALF("2.J2.2","J2.2",[1,1,2,2,3,4,4,5,5,6,6,7,7,8,8,9,9,10,11,11,12,13,14,
14,15,15,16,16,17,18,19,19,20,21,21,22,23,23,24,24,25,25,26,26,27,27]);
ALF("2.J2.2","2.Suz",[1,2,3,4,5,6,7,10,11,13,12,19,20,17,18,21,22,29,30,
31,32,42,40,41,46,45,63,64,5,15,16,16,29,32,32,32,49,49,50,51,58,58,76,75,
75,76],[
"fusion map is unique up to table automorphisms,\n",
"compatible with Brauer tables"
]);
ALN("2.J2.2",["2.HJ.2","2.F5-.2"]);

MOT("3.J3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17,19]"
],
[150698880,150698880,150698880,5760,5760,5760,3240,3240,3240,243,288,288,288,
90,90,90,90,90,90,72,72,72,24,24,24,27,27,27,30,30,30,30,30,30,36,36,36,45,45,
45,45,45,45,51,51,51,51,51,51,57,57,57,57,57,57],
[,[1,3,2,1,3,2,7,9,8,10,4,6,5,17,19,18,14,16,15,7,9,8,11,13,12,27,28,26,17,19,
18,14,16,15,20,22,21,41,43,42,38,40,39,44,46,45,47,49,48,53,55,54,50,52,51],[
1,1,1,4,4,4,1,1,1,1,11,11,11,17,17,17,14,14,14,4,4,4,23,23,23,10,10,10,32,32,
32,29,29,29,11,11,11,17,17,17,14,14,14,47,47,47,44,44,44,53,53,53,50,50,50],,[
1,3,2,4,6,5,7,9,8,10,11,13,12,1,3,2,1,3,2,20,22,21,23,25,24,28,26,27,4,6,5,4,
6,5,35,37,36,7,9,8,7,9,8,47,49,48,44,46,45,50,52,51,53,55,54],,,,,,,,,,,,[1,3,
2,4,6,5,7,9,8,10,11,13,12,17,19,18,14,16,15,20,22,21,23,25,24,26,27,28,32,34,
33,29,31,30,35,37,36,41,43,42,38,40,39,1,3,2,1,3,2,50,52,51,53,55,54],,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,1,2,3,1,2,3]],
0,
[(50,53)(51,54)(52,55),(44,47)(45,48)(46,49),(26,27,28),(14,17)(15,18)(16,19)
(29,32)(30,33)(31,34)(38,41)(39,42)(40,43),( 2, 3)( 5, 6)( 8, 9)(12,13)(15,16)
(18,19)(21,22)(24,25)(26,27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)
(48,49)(51,52)(54,55),( 2, 3)( 5, 6)( 8, 9)(12,13)(15,16)(18,19)(21,22)(24,25)
(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)],
["ConstructProj",[["J3",[]],,["3.J3",[11,11,11,11,-1,11,11,-1,35,35,-37,-37,
-1,-1,-1,-1,-1]]]]);
ALF("3.J3","J3",[1,1,1,2,2,2,3,3,3,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,11,
12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,19,19,19,20,20,
20,21,21,21]);
ALF("3.J3","3.J3.2",[1,2,2,3,4,4,5,6,6,7,8,9,9,10,11,12,10,12,11,13,14,14,
15,16,16,17,18,19,20,21,22,20,22,21,23,24,24,25,26,27,25,27,26,28,29,29,
30,31,31,32,33,34,32,34,33]);

MOT("3.J3.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17,19]"
],
[301397760,150698880,11520,5760,6480,3240,486,576,288,90,90,90,144,72,48,24,
54,54,54,30,30,30,72,36,45,45,45,102,51,102,51,57,57,57,4896,96,18,96,32,12,
18,18,18,24,24,34,34],
[,[1,2,1,2,5,6,7,3,4,10,11,12,5,6,8,9,18,19,17,10,11,12,13,14,25,26,27,28,29,
30,31,32,33,34,1,3,7,8,8,13,18,19,17,23,23,28,30],[1,1,3,3,1,1,1,8,8,10,10,10,
3,3,15,15,7,7,7,20,20,20,8,8,10,10,10,30,30,28,28,32,32,32,35,36,35,38,39,36,
37,37,37,38,38,47,46],,[1,2,3,4,5,6,7,8,9,1,2,2,13,14,15,16,19,17,18,3,4,4,23,
24,5,6,6,30,31,28,29,32,34,33,35,36,37,38,39,40,43,41,42,44,45,47,
46],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,
24,25,26,27,1,2,1,2,32,34,33,35,36,37,38,39,40,41,42,43,45,44,35,35],,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
1,2,2,35,36,37,38,39,40,41,42,43,44,45,46,47]],
0,
[(44,45),(33,34),(28,30)(29,31)(46,47),(11,12)(21,22)(26,27),(11,12)(17,18,19)
(21,22)(26,27)(33,34)(41,42,43)(44,45),(17,18,19)(41,42,43),(17,19,18)
(41,43,42)],
["ConstructMixed","3.J3","J3.2",[[22,25],[23,24],[26,29],[27,28],[30,31],[32,
35],[33,34],[36,37],[38,39],[40,41],[42,45],[43,44],[46,47],[48,49],[50,51],
[52,53],[54,55]],()]);
ALF("3.J3.2","J3.2",[1,1,2,2,3,3,4,5,5,6,6,6,7,7,8,8,9,10,11,12,12,12,13,
13,14,14,14,15,15,16,16,17,17,17,18,19,20,21,22,23,24,25,26,27,28,29,30]);

MOT("Co1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13,23]"
],
[4157776806543360000,89181388800,2012774400,389283840,1345036492800,58786560,
12597120,544320,371589120,1179648,737280,294912,48384,15360,3024000,36000,
15000,9953280,483840,155520,155520,20736,15552,3456,1440,576,17640,1176,92160,
6144,6144,2048,768,768,1944,486,486,9600,1200,1200,600,600,160,66,138240,9216,
4608,2592,1728,864,576,288,288,288,288,72,48,156,168,56,5400,900,180,90,30,64,
64,216,54,54,480,40,20,252,63,21,22,23,23,576,192,144,96,48,24,52,28,28,120,
60,60,30,30,33,35,36,39,39,40,84,60],
[,[1,1,1,1,5,6,7,8,2,2,2,2,3,4,15,16,17,5,5,6,7,6,7,6,8,8,27,28,9,9,10,10,11,
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ARC("Co1","CAS",[rec(name:="c1",
permchars:=(94,95),
permclasses:=(20,21)(30,31)(36,37)(39,40)(41,42)(52,55)(66,67)(90,91),
text:=Concatenation(
"names:=c1; co1; .1; conway.1\n",
"    order:  2^21.3^9.5^4.7^2.11.13.23  =  4,157,776,806,543,360,000\n",
"    number  of  classes:  101\n",
"    source:private communication of compound table\n",
"           from cambridge group atlas project  1980/81\n",
"    origin:conway, j. - guy, m.\n",
"           -unpublished- \n",
""))]);
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ARC("Co1","isSimple",true);
ARC("Co1","extInfo",["2",""]);
ALN("Co1",["F2-"]);
ARC("Co1","maxes",["Co2","3.Suz.2","2^11:M24","Co3","2^(1+8)+.O8+(2)",
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MOT("Co2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,23]"
],
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[(53,54),(46,47)(59,60),(43,44)]);
ARC("Co2","CAS",[rec(name:="c2",
permchars:=(16,17)(38,39)(46,48)(52,53),
permclasses:=(35,36)(55,56)(59,60),
text:=Concatenation(
"names:=c2; co2; .2; conway.2\n",
"    order: 2^18.3^6.5^3.7.11.23 = 42,305,421,312,000\n",
"    number of classes: 60\n",
"    source:private communication of compound table\n",
"           from cambridge group atlas project  1980/81\n",
"    origin:conway, j. - guy, m.\n",
"           -unpublished- \n",
""))]);
ARC("Co2","isSimple",true);
ARC("Co2","extInfo",["",""]);
ALF("Co2","Co1",[1,2,2,4,7,6,9,11,11,10,11,12,14,17,16,21,23,20,22,22,24,
28,30,33,31,32,33,33,37,42,41,43,44,48,52,49,53,55,53,52,54,60,60,60,64,
65,65,67,66,70,73,72,78,79,84,85,87,92,93,93],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ARC("Co2","maxes",["U6(2).2","2^10:m22:2","McL","2^1+8:s6f2","HS.2",
"2^1+4+6.a8","U4(3).D8","2^(4+10)(S5xS3)","M23","3^1+4:2^1+4.s5",
"5^(1+2):4S4"]);

MOT("Co3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,23]"
],
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1,2,-4,1,0,0,0,1,-1,1,0,-1,0,0,-1,-1,0,0,0,0,0,-1,1,1],[9625,105,-55,40,-5,7,
5,-3,0,0,0,6,3,-1,-1,0,3,-1,-1,-2,1,0,0,0,0,2,0,-1,0,0,0,0,0,0,0,0,0,
E(23)+E(23)^2+E(23)^3+E(23)^4+E(23)^6+E(23)^8+E(23)^9+E(23)^12+E(23)^13
 +E(23)^16+E(23)^18,E(23)^5+E(23)^7+E(23)^10+E(23)^11+E(23)^14+E(23)^15
 +E(23)^17+E(23)^19+E(23)^20+E(23)^21+E(23)^22,0,2,0],
[GALOIS,[16,5]],[20608,0,-16,-128,-20,7,0,0,8,3,0,0,0,2,-1,0,0,0,0,-2,-2,0,-1,
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[GALOIS,[18,2]],[23000,280,120,50,5,8,40,8,0,0,10,10,1,3,0,-2,0,0,0,-1,2,0,0,
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9,9,0,0,0,0,2,2,-2,0,0,-1,1,1,1,-3,1,0,0,1,0,0,-1,-1,0,1,1,0,0,-1,-1,-1],[
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-1,-1,-1,1,1,1,-1,-1,0,0,0,0,-5,-1,1,1,0,0,-1,0,0,-1,0,0,0,0,1,1,0],[31625,
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0,1,0,0,-1,0,0,0,0,1,-1,0],[31878,294,-66,45,45,0,46,-2,3,3,-3,-3,-3,-3,0,0,2,
2,-2,0,0,-1,-1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0,0,-1,-1,2],[40250,-70,10,-115,
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-1,0,0,1,1,0],[57960,168,120,126,45,0,-40,-8,10,0,6,6,-3,3,0,0,0,0,0,0,0,-2,0,
1,1,2,-2,-1,0,1,0,0,0,0,0,-1,-1,0,0,0,0,1],[63250,210,-110,-65,-20,22,-30,2,0,
0,15,3,0,-2,-2,-2,2,2,2,4,1,0,0,0,0,3,-1,0,0,0,0,0,0,0,1,0,0,0,0,-1,-1,0],[
73600,0,144,160,16,13,0,0,0,-5,0,0,0,0,-3,2,0,0,0,4,1,0,-1,-1,-1,0,0,0,0,0,1,
0,0,0,-1,1,1,0,0,0,0,0],[80960,-448,0,176,50,8,0,0,10,0,-16,-16,2,0,0,-2,0,0,
0,-1,2,2,0,0,0,0,0,0,0,1,0,-1,0,0,1,0,0,0,0,0,0,-1],[91125,405,45,0,0,27,45,
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0],[93312,0,-144,0,0,27,0,0,12,-3,0,0,0,0,3,2,0,0,0,0,0,0,1,-1,-1,0,0,0,0,0,0,
0,0,0,-1,-1,-1,1,1,0,0,0],[129536,-512,0,-64,44,8,0,0,-14,-4,16,-8,4,0,0,1,0,
0,0,-1,-1,-2,0,0,0,0,0,0,-1,1,-1,1,0,0,1,0,0,0,0,0,0,1],[129536,512,0,-64,44,
8,0,0,-14,-4,-16,8,-4,0,0,1,0,0,0,-1,-1,2,0,0,0,0,0,0,1,1,-1,-1,0,0,1,0,0,0,0,
0,0,-1],[177100,140,44,-20,-29,-14,-20,12,0,-5,20,-4,-1,-1,2,0,0,0,0,-5,1,0,
-1,0,0,4,0,1,0,0,1,-1,0,0,0,0,0,0,0,0,0,0],[184437,405,-99,0,0,-27,45,-3,12,
-3,0,0,0,0,-3,1,-3,-3,1,0,0,0,1,0,0,0,0,0,-1,0,0,0,0,0,1,0,0,0,0,0,0,0],[
221375,735,55,-160,-25,-7,-25,-9,0,0,0,-12,3,1,1,0,3,3,-1,2,2,0,0,0,0,-4,0,-1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[226688,0,-176,320,-40,-7,0,0,-12,3,0,0,0,4,1,0,
0,0,0,2,-1,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[246400,0,176,160,-56,
7,0,0,0,5,0,0,0,-4,-1,0,0,0,0,-2,-2,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,1,0,0,
0],[249480,-504,0,-81,0,0,-24,8,5,0,-9,9,0,0,0,0,-4,4,0,0,0,1,0,0,0,-3,-1,0,0,
-1,0,0,1,1,0,0,0,-1,-1,-1,1,1],[253000,-440,0,-125,10,-8,40,8,0,0,-5,1,-2,0,0,
-1,4,-4,0,1,1,0,0,0,0,1,-1,-2,1,0,0,1,0,0,-1,0,0,0,0,1,-1,0],[255024,-336,0,
-126,36,0,-16,-16,-1,4,-6,6,0,0,0,0,0,0,0,0,0,-1,0,0,0,2,2,2,0,-1,1,0,-1,-1,0,
0,0,0,0,0,0,-1]],
[(38,39),(33,34),(24,25)(36,37)]);
ARC("Co3","CAS",[rec(name:="c3",
permchars:=( 3, 4)(22,23,24)(33,34),
permclasses:=(14,15)(40,41),
text:=Concatenation(
"names:=c3; co3; .3; conway.3\n",
"    order: 2^10.3^7.5^3.7.11.23 = 495,766,656,000\n",
"    number of classes: 42\n",
"    source / origin:\n",
"           fendel, d.\n",
"           a characterization of conway's group.3\n",
"           j.algebra 24\n",
"           [1973],159-196 \n",
""))]);
ARC("Co3","isSimple",true);
ARC("Co3","extInfo",["",""]);
ARC("Co3","tomfusion",rec(name:="Co3",map:=[1,2,3,4,5,6,7,8,12,13,21,22,23,24,
25,26,48,47,49,57,58,62,63,64,64,82,83,84,91,92,93,206,214,214,215,218,218,
219,219,241,240,292],text:=[
"fusion map is unique"
]));
ALF("Co3","Co1",[1,2,4,7,6,8,11,11,17,16,21,23,22,24,26,28,33,33,33,36,37,
42,43,44,44,52,52,53,60,65,64,69,73,73,76,77,77,78,79,85,85,93],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ARC("Co3","maxes",["McL.2","HS","U4(3).(2^2)_{133}","M23","3^5:(2xm11)",
"2.S6(2)","U3(5).3.2","3^1+4:4s6","2^4.a8","psl(3,4):d12","2xm12",
"2^2.(2^7.3^2).s3","s3xpsl(2,8).3","a4xs5"]);

MOT("J1",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,19]"
],
[175560,120,30,30,30,6,7,10,10,11,15,15,19,19,19],
[,[1,1,3,5,4,3,7,5,4,10,12,11,14,15,13],[1,2,1,5,4,2,7,9,8,10,5,4,14,15,13],,[
1,2,3,1,1,6,7,2,2,10,3,3,14,15,13],,[1,2,3,5,4,6,1,9,8,10,12,11,13,14,15],,,,[
1,2,3,4,5,6,7,8,9,1,11,12,13,14,15],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,1,1,
1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[56,0,2,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,
0,0,0,0,1,E(5)+E(5)^4,E(5)^2+E(5)^3,-1,-1,-1],
[GALOIS,[2,2]],[76,4,1,1,1,1,-1,-1,-1,-1,1,1,0,0,0],[76,-4,1,1,1,-1,-1,1,1,-1,
1,1,0,0,0],[77,5,-1,2,2,-1,0,0,0,0,-1,-1,1,1,1],[77,-3,2,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,E(5)+E(5)^4,E(5)^2+E(5)^3,1,1,
1],
[GALOIS,[7,2]],[120,0,0,0,0,0,1,0,0,-1,0,0,E(19)+E(19)^7+E(19)^8+E(19)^11
 +E(19)^12+E(19)^18,E(19)^2+E(19)^3+E(19)^5+E(19)^14+E(19)^16+E(19)^17,
E(19)^4+E(19)^6+E(19)^9+E(19)^10+E(19)^13+E(19)^15],
[GALOIS,[9,4]],
[GALOIS,[9,2]],[133,5,1,-2,-2,-1,0,0,0,1,1,1,0,0,0],[133,-3,-2,-E(5)-E(5)^4,
-E(5)^2-E(5)^3,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,
0,0],
[GALOIS,[13,2]],[209,1,-1,-1,-1,1,-1,1,1,0,-1,-1,0,0,0]],
[(13,14,15),( 4, 5)( 8, 9)(11,12)]);
ARC("J1","CAS",[rec(name:="j1",
permchars:=( 7, 8)( 9,11),
permclasses:=( 4, 5)( 8, 9)(14,15),
text:=Concatenation(
"names:=j1\n",
"    order: 2^3.3.5.7.11.19 = 175,560\n",
"    number of classes: 15\n",
"    source:mckay, john\n",
"           the non-abelian simple groups g,\n",
"           ord[g]<10^6 - character tables\n",
"           comm.algebra 7\n",
"           [1979],1407-1445\n",
"    origin:janko, z.\n",
"           a new finite simple group with abelian\n",
"           sylow 2-subgroups and its characterization\n",
"           j.algebra 3\n",
"           [1966], 147-186 \n",
""))]);
ARC("J1","isSimple",true);
ARC("J1","extInfo",["",""]);
ARC("J1","tomfusion",rec(name:="J1",map:=[1,2,3,5,5,8,9,13,13,14,18,18,19,
19,19],text:=[
"fusion map is unique"
]));
ALF("J1","ON",[1,2,3,6,6,7,9,12,12,13,16,17,22,23,24],[
"fusion map is unique up to table automorphisms"
]);
ARC("J1","maxes",["L2(11)","2^3.7.3","2xA5","19:6","11:10","D6xD10","7:6"]);

MOT("J2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[604800,1920,240,1080,36,96,300,300,50,50,24,12,7,8,20,20,10,10,12,15,15],
[,[1,1,1,4,5,2,8,7,10,9,4,5,13,6,8,7,10,9,11,21,20],[1,2,3,1,1,6,8,7,10,9,2,3,
13,14,16,15,18,17,6,8,7],,[1,2,3,4,5,6,1,1,1,1,11,12,13,14,3,3,2,2,19,4,4],,[
1,2,3,4,5,6,8,7,10,9,11,12,1,14,16,15,18,17,19,21,20]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[14,-2,2,5,-1,2,-3*E(5)-3*E(5)^4,
-3*E(5)^2-3*E(5)^3,-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,-2*E(5)-E(5)^2-E(5)^3
 -2*E(5)^4,1,-1,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,
0,0],
[GALOIS,[2,2]],[21,5,-3,3,0,1,-3*E(5)-4*E(5)^2-4*E(5)^3-3*E(5)^4,
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-1,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,1,-E(5)^2-E(5)^3,-E(5)-E(5)^4],
[GALOIS,[4,2]],[36,4,0,9,0,4,-4,-4,1,1,1,0,1,0,0,0,-1,-1,1,-1,-1],[63,15,-1,0,
3,3,3,3,-2,-2,0,-1,0,1,-1,-1,0,0,0,0,0],[70,-10,-2,7,1,2,-5*E(5)-5*E(5)^4,
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E(5)+E(5)^4,E(5)^2+E(5)^3],
[GALOIS,[8,2]],[90,10,6,9,0,-2,5,5,0,0,1,0,-1,0,1,1,0,0,1,-1,-1],[126,14,6,-9,
0,2,1,1,1,1,-1,0,0,0,1,1,-1,-1,-1,1,1],[160,0,4,16,1,0,-5,-5,0,0,0,1,-1,0,-1,
-1,0,0,0,1,1],[175,15,-5,-5,1,-1,0,0,0,0,3,1,0,-1,0,0,0,0,-1,0,0],[189,-3,-3,
0,0,-3,-3*E(5)-3*E(5)^4,-3*E(5)^2-3*E(5)^3,-E(5)-2*E(5)^2-2*E(5)^3-E(5)^4,
-2*E(5)-E(5)^2-E(5)^3-2*E(5)^4,0,0,0,1,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,0,0],
[GALOIS,[14,2]],[224,0,-4,8,-1,0,3*E(5)-E(5)^2-E(5)^3+3*E(5)^4,
-E(5)+3*E(5)^2+3*E(5)^3-E(5)^4,2*E(5)+2*E(5)^4,2*E(5)^2+2*E(5)^3,0,-1,0,0,1,1,
0,0,0,-E(5)^2-E(5)^3,-E(5)-E(5)^4],
[GALOIS,[16,2]],[225,-15,5,0,3,-3,0,0,0,0,0,-1,1,-1,0,0,0,0,0,0,0],[288,0,4,0,
-3,0,3,3,-2,-2,0,1,1,0,-1,-1,0,0,0,0,0],[300,-20,0,-15,0,4,0,0,0,0,1,0,-1,0,0,
0,0,0,1,0,0],[336,16,0,-6,0,0,-4,-4,1,1,-2,0,0,0,0,0,1,1,0,-1,-1]],
[( 7, 8)( 9,10)(15,16)(17,18)(20,21)]);
ARC("J2","CAS",[rec(name:="j2",
permchars:=( 2, 3)( 8, 9)(14,15),
permclasses:=( 9,10)(15,16),
text:=Concatenation(
"names:=j2; hj; hjw\n",
"    order: 2^7.3^3.5^2.7 = 604,800\n",
"    number of classes: 21\n",
"    source:mckay, john\n",
"           the non-abelian simple groups g,\n",
"           ord[g]<10^6 - character tables\n",
"           comm.algebra 7\n",
"           [1979],1407-1445\n",
"    origin:hall, m; wales, d.\n",
"           the simple group of order 604,800\n",
"           j.algebra 9\n",
"           [1968], 417-450\n",
" maximal subgroup   index\n",
" a4xa5              840\n",
""))]);
ARC("J2","projectives",["2.J2",[[6,-2,0,-3,0,2,-2*E(5)-2*E(5)^4,
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 ,1,0,-1,0,0,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,E(5)+E(5)^4,E(5)^2+E(5)^3],
[GALOIS,[1,2]],[14,6,0,-4,2,2,4,4,-1,-1,0,0,0,0,0,0,1,1,2,1,1],[50,10,0,5,2,2,
0,0,0,0,1,0,1,2*E(4),0,0,0,0,-1,0,0],
[GALOIS,[4,3]],[56,-8,0,2,2,0,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,
E(5)+2*E(5)^2+2*E(5)^3+E(5)^4,2*E(5)+E(5)^2+E(5)^3+2*E(5)^4,-2,0,0,0,0,0,
E(5)+E(5)^4,E(5)^2+E(5)^3,0,E(5)+E(5)^4,E(5)^2+E(5)^3],
[GALOIS,[6,2]],[64,0,0,-8,-2,0,-2*E(5)-6*E(5)^2-6*E(5)^3-2*E(5)^4,
-6*E(5)-2*E(5)^2-2*E(5)^3-6*E(5)^4,2*E(5)+2*E(5)^4,2*E(5)^2+2*E(5)^3,0,0,1,0,
0,0,0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3],
[GALOIS,[8,2]],[84,4,0,-15,0,4,-6,-6,-1,-1,1,0,0,0,0,0,-1,-1,1,0,0],[126,-10,
0,-9,0,2,2*E(5)-4*E(5)^2-4*E(5)^3+2*E(5)^4,-4*E(5)+2*E(5)^2+2*E(5)^3-4*E(5)^4,
-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,-1,0,0,0,0,0,0,0,-1,1,1],
[GALOIS,[11,2]],[216,24,0,0,0,0,6,6,1,1,0,0,-1,0,0,0,-1,-1,0,0,0],[252,-20,0,
9,0,4,2,2,2,2,1,0,0,0,0,0,0,0,1,-1,-1],[336,16,0,-6,0,0,-4,-4,1,1,-2,0,0,0,0,
0,1,1,0,-1,-1],[350,-10,0,-10,2,-6,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0],[448,0,0,16,
-2,0,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,1,1]],]);
ARC("J2","isSimple",true);
ARC("J2","extInfo",["2","2"]);
ARC("J2","tomfusion",rec(name:="J2",map:=[1,2,3,4,5,10,11,11,12,12,16,17,
18,25,31,31,32,32,40,45,45],text:=[
"fusion map is unique"
]));
ALF("J2","J2.2",[1,2,3,4,5,6,7,7,8,8,9,10,11,12,13,13,14,14,15,16,16]);
ALF("J2","G2(4)",[1,2,3,4,5,6,9,10,11,12,13,14,15,16,20,21,18,19,22,27,28],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("J2","S6(5)",[1,2,3,5,6,9,18,18,21,22,26,28,29,31,54,54,51,50,61,77,
77],[
"fusion map is unique up to table automorphisms"
]);
ARC("J2","maxes",["U3(3)","3.A6.2_2","2^1+4b:a5","2^2+4.3xs3","a4xa5",
"a5xd10","L3(2).2","5^2:D12","A5"]);
ALN("J2",["HJ","F5-"]);

MOT("J2.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[1209600,3840,480,2160,72,192,300,50,48,24,14,16,20,10,24,15,672,96,24,12,96,
32,12,12,14,24,24],
[,[1,1,1,4,5,2,7,8,4,5,11,6,7,8,9,16,1,2,3,5,6,6,9,10,11,15,15],[1,2,3,1,1,6,
7,8,2,3,11,12,13,14,6,7,17,18,19,17,21,22,18,19,25,21,21],,[1,2,3,4,5,6,1,1,9,
10,11,12,3,2,15,4,17,18,19,20,21,22,23,24,25,26,27],,[1,2,3,4,5,6,7,8,9,10,1,
12,13,14,15,16,17,18,19,20,21,22,23,24,17,27,26]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[28,-4,4,10,-2,4,3,3,2,-2,0,0,
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0,0,0,0,0,0,0,0],[36,4,0,9,0,4,-4,1,1,0,1,0,0,-1,1,-1,6,-2,0,0,2,2,1,0,-1,-1,
-1],
[TENSOR,[5,2]],[63,15,-1,0,3,3,3,-2,0,-1,0,1,-1,0,0,0,7,3,-1,1,-3,1,0,-1,0,0,
0],
[TENSOR,[7,2]],[140,-20,-4,14,2,4,5,0,-2,2,0,0,1,0,-2,-1,0,0,0,0,0,0,0,0,0,0,
0],[90,10,6,9,0,-2,5,0,1,0,-1,0,1,0,1,-1,6,2,0,0,4,0,-1,0,-1,1,1],
[TENSOR,[10,2]],[126,14,6,-9,0,2,1,1,-1,0,0,0,1,-1,-1,1,0,4,0,0,2,-2,1,0,0,-1,
-1],
[TENSOR,[12,2]],[160,0,4,16,1,0,-5,0,0,1,-1,0,-1,0,0,1,8,0,2,-1,0,0,0,-1,1,0,
0],
[TENSOR,[14,2]],[175,15,-5,-5,1,-1,0,0,3,1,0,-1,0,0,-1,0,7,-1,1,1,-1,-1,-1,1,
0,-1,-1],
[TENSOR,[16,2]],[378,-6,-6,0,0,-6,3,3,0,0,0,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,
0],[448,0,-8,16,-2,0,-2,-2,0,-2,0,0,2,0,0,1,0,0,0,0,0,0,0,0,0,0,0],[225,-15,5,
0,3,-3,0,0,0,-1,1,-1,0,0,0,0,1,-3,-1,1,3,-1,0,-1,1,0,0],
[TENSOR,[20,2]],[288,0,4,0,-3,0,3,-2,0,1,1,0,-1,0,0,0,8,0,-2,-1,0,0,0,1,1,0,
0],
[TENSOR,[22,2]],[300,-20,0,-15,0,4,0,0,1,0,-1,0,0,0,1,0,6,-2,0,0,-2,-2,1,0,-1,
1,1],
[TENSOR,[24,2]],[336,16,0,-6,0,0,-4,1,-2,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,
E(24)-E(24)^11-E(24)^17+E(24)^19,-E(24)+E(24)^11+E(24)^17-E(24)^19],
[TENSOR,[26,2]]],
[(26,27)]);
ARC("J2.2","CAS",[rec(name:="j2.2",
permchars:=( 4, 6, 5)( 9,13,12,11,10)(18,26,24,22,20)(19,27,25,23,21),
permclasses:=(),
text:=Concatenation(
"names:=     j2.2, j2.z2, autj2\n",
"    order:     2^8.3^3.5^2.7 = 1,209,600\n",
"    number of classes:  27\n",
"    source:    private communication of atlas compound table\n",
"               from cambridge 1980/81\n",
"    comments:  extension of j2 with an outer\n",
"               automorphism of order 2\n",
"    test:      orth.1, min, sym[3]     \n",
""))]);
ARC("J2.2","projectives",["2.J2.2",[[12,-4,0,-6,0,4,2,-3,2,0,-2,0,0,1,-2,-1,0,
0,0,0,0,0,0,0,0,0,0],[14,6,0,-4,2,2,4,-1,0,0,0,0,0,1,2,1,0,0,E(8)-E(8)^3,0,
-2*E(8)+2*E(8)^3,0,0,E(8)-E(8)^3,0,E(8)-E(8)^3,E(8)-E(8)^3],[100,20,0,10,4,4,
0,0,2,0,2,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0],[112,-16,0,4,4,0,2,-3,-4,0,0,0,0,
-1,0,-1,0,0,0,0,0,0,0,0,0,0,0],[128,0,0,-16,-4,0,8,-2,0,0,2,0,0,0,0,-1,0,0,0,
0,0,0,0,0,0,0,0],[84,4,0,-15,0,4,-6,-1,1,0,0,0,0,-1,1,0,0,0,0,0,0,0,
-E(12)^7+E(12)^11,0,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11],[252,-20,0,-18,0,4,
2,2,-2,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0,0],[216,24,0,0,0,0,6,1,0,0,-1,0,0,
-1,0,0,0,0,0,0,0,0,0,0,E(28)^3-E(28)^11-E(28)^15+E(28)^19-E(28)^23+E(28)^27,0,
0],[252,-20,0,9,0,4,2,2,1,0,0,0,0,0,1,-1,0,0,0,0,0,0,-E(12)^7+E(12)^11,0,0,
E(12)^7-E(12)^11,-E(12)^7+E(12)^11],[336,16,0,-6,0,0,-4,1,-2,0,0,0,0,1,0,-1,0,
0,0,0,4*E(8)-4*E(8)^3,0,0,0,0,E(8)-E(8)^3,E(8)-E(8)^3],[350,-10,0,-10,2,-6,0,
0,2,0,0,0,0,0,0,0,0,0,E(8)-E(8)^3,0,2*E(8)-2*E(8)^3,0,0,E(8)-E(8)^3,0,
-E(8)+E(8)^3,-E(8)+E(8)^3],[448,0,0,16,-2,0,-2,-2,0,0,0,0,0,0,0,1,0,0,
2*E(8)-2*E(8)^3,0,0,0,0,-E(8)+E(8)^3,0,0,0]],]);
ARC("J2.2","maxes",["J2","U3(3).2","3.A6.2^2","2^(1+4).S5","2^(2+4):(S3xS3)",
"(A4xA5):2","(A5xD10).2","L3(2).2x2","5^2:(4xS3)","A5.2"]);
ARC("J2.2","tomfusion",rec(name:="J2.2",map:=[1,2,4,5,6,13,16,17,23,24,26,41,
53,54,63,79,3,14,15,25,39,40,65,64,76,141,141],text:=[
"fusion map is unique"
]));
ALF("J2.2","Suz",[1,2,3,4,6,7,12,11,13,17,18,19,25,24,27,37,3,9,10,17,19,
19,29,30,34,43,43],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("J2.2","J2.2x2",[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,
39,41,43,45,47,49,51,53],[
"fusion map is unique up to table automorphisms"
]);
ALN("J2.2",["HJ.2","F5-.2"]);

MOT("J3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17,19]"
],
[50232960,1920,1080,243,96,30,30,24,8,27,27,27,10,10,12,15,15,17,17,19,19],
[,[1,1,3,4,2,7,6,3,5,11,12,10,7,6,8,17,16,18,19,21,20],[1,2,1,1,5,7,6,2,9,4,4,
4,14,13,5,7,6,19,18,21,20],,[1,2,3,4,5,1,1,8,9,12,10,11,2,2,15,3,3,19,18,20,
21],,,,,,,,,,,,[1,2,3,4,5,7,6,8,9,10,11,12,14,13,15,17,16,1,1,20,21],,[1,2,3,
4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[85,5,-5,4,1,0,0,-1,-1,1,1,1,0,0,
1,0,0,0,0,E(19)+E(19)^4+E(19)^5+E(19)^6+E(19)^7+E(19)^9+E(19)^11+E(19)^16
 +E(19)^17,E(19)^2+E(19)^3+E(19)^8+E(19)^10+E(19)^12+E(19)^13+E(19)^14
 +E(19)^15+E(19)^18],
[GALOIS,[2,2]],[323,3,8,-1,3,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,-1,-1,-1,-1,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0],
[GALOIS,[4,2]],[324,4,9,0,4,-1,-1,1,0,0,0,0,-1,-1,1,-1,-1,1,1,1,1],[646,-10,7,
-2,2,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,-1,0,1,1,1,0,0,-1,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,0,0,0],
[GALOIS,[7,2]],[816,-16,6,6,0,1,1,2,0,0,0,0,-1,-1,0,1,1,0,0,-1,-1],[1140,20,
15,6,-4,0,0,-1,0,0,0,0,0,0,-1,0,0,1,1,0,0],[1215,15,0,0,3,0,0,0,1,0,0,0,0,0,0,
0,0,E(17)+E(17)^2+E(17)^4+E(17)^8+E(17)^9+E(17)^13+E(17)^15+E(17)^16,
E(17)^3+E(17)^5+E(17)^6+E(17)^7+E(17)^10+E(17)^11+E(17)^12+E(17)^14,-1,-1],
[GALOIS,[11,3]],[1615,15,-5,-5,-1,0,0,3,-1,1,1,1,0,0,-1,0,0,0,0,0,0],[1920,0,
0,3,0,0,0,0,0,-E(9)^2+E(9)^4+E(9)^5-E(9)^7,-E(9)^2-2*E(9)^4-2*E(9)^5-E(9)^7,
2*E(9)^2+E(9)^4+E(9)^5+2*E(9)^7,0,0,0,0,0,-1,-1,1,1],
[GALOIS,[14,4]],
[GALOIS,[14,2]],[1938,2,3,-6,-2,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,0,0,0,0,
E(5)+E(5)^4,E(5)^2+E(5)^3,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,0,0],
[GALOIS,[17,2]],[2432,0,-16,2,0,2,2,0,0,-1,-1,-1,0,0,0,-1,-1,1,1,0,0],[2754,
-14,9,0,-2,-1,-1,1,0,0,0,0,1,1,1,-1,-1,0,0,-1,-1],[3078,-10,-9,0,2,-2,-2,-1,0,
0,0,0,0,0,-1,1,1,1,1,0,0]],
[(20,21),(18,19),(10,11,12),( 6, 7)(13,14)(16,17)]);
ARC("J3","CAS",[rec(name:="j3",
permchars:=( 4, 5)( 7, 8)(14,15,16)(17,18),
permclasses:=(),
text:=Concatenation(
"names:=j3; hjm\n",
"    order: 2^7.3^5.5.17.19 = 50,232,960\n",
"    number of classes: 21\n",
"    source:private communication\n",
"           by olsson, j.b.\n",
"           univ. of dortmund [1980]\n",
"    origin:janko, z.\n",
"           some new simple groups of finite order i,\n",
"           symp. math. 1\n",
"           [1967/68], 25-64 \n",
""))]);
ARC("J3","projectives",["3.J3",[[18,2,3,0,-2,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,0,
0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,1,1,-1,-1],
[GALOIS,[1,2]],[153,-7,3,0,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,-1,1,0,0,0,
-E(5)-E(5)^4,-E(5)^2-E(5)^3,1,-E(5)-E(5)^4,-E(5)^2-E(5)^3,0,0,1,1],
[GALOIS,[3,2]],[171,11,6,0,3,1,1,2,-1,0,0,0,1,1,0,1,1,1,1,0,0],[171,-5,-3,0,
-1,-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,1,1,0,0,0,0,0,-1,E(5)+E(5)^4,
E(5)^2+E(5)^3,1,1,0,0],
[GALOIS,[6,2]],[324,4,9,0,4,-1,-1,1,0,0,0,0,-1,-1,1,-1,-1,1,1,1,1],[1215,15,0,
0,3,0,0,0,1,0,0,0,0,0,0,0,0,E(17)+E(17)^2+E(17)^4+E(17)^8+E(17)^9+E(17)^13
 +E(17)^15+E(17)^16,E(17)^3+E(17)^5+E(17)^6+E(17)^7+E(17)^10+E(17)^11+E(17)^12
 +E(17)^14,-1,-1],
[GALOIS,[9,3]],[1530,10,-15,0,-2,0,0,1,0,0,0,0,0,0,1,0,0,0,0,
-E(19)-E(19)^4-E(19)^5-E(19)^6-E(19)^7-E(19)^9-E(19)^11-E(19)^16-E(19)^17,
-E(19)^2-E(19)^3-E(19)^8-E(19)^10-E(19)^12-E(19)^13-E(19)^14-E(19)^15-E(19)^18
 ],
[GALOIS,[11,2]],[2736,-16,6,0,0,1,1,2,0,0,0,0,-1,-1,0,1,1,-1,-1,0,0],[2754,
-14,9,0,-2,-1,-1,1,0,0,0,0,1,1,1,-1,-1,0,0,-1,-1],[2907,-5,-6,0,3,2,2,-2,-1,0,
0,0,0,0,0,-1,-1,0,0,0,0],[3060,20,15,0,-4,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0,1,1],[
3078,-10,-9,0,2,-2,-2,-1,0,0,0,0,0,0,-1,1,1,1,1,0,0]],]);
ARC("J3","isSimple",true);
ARC("J3","extInfo",["3","2"]);
ARC("J3","tomfusion",rec(name:="J3",map:=[1,2,3,4,7,8,8,11,17,20,20,20,23,
23,28,30,30,40,40,44,44],text:=[
"fusion map is unique"
]));
ALF("J3","J3.2",[1,2,3,4,5,6,6,7,8,9,10,11,12,12,13,14,14,15,16,17,17]);
ARC("J3","maxes",["L2(16).2","L2(19)","J3M3","j3m4","L2(17)","j3m6",
"3^2.3^(1+2):8","2^1+4b:a5","2^2+4.3xs3"]);

MOT("J3.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,17,19]"
],
[100465920,3840,2160,486,192,30,48,16,54,54,54,10,24,15,34,34,19,4896,96,18,
96,32,12,18,18,18,24,24,34,34],
[,[1,1,3,4,2,6,3,5,10,11,9,6,7,14,15,16,17,1,2,4,5,5,7,10,11,9,13,13,15,16],[
1,2,1,1,5,6,2,8,4,4,4,12,5,6,16,15,17,18,19,18,21,22,19,20,20,20,21,21,30,
29],,[1,2,3,4,5,1,7,8,11,9,10,2,13,3,16,15,17,18,19,20,21,22,23,26,24,25,27,
28,30,29],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,1,1,17,18,19,20,21,22,
23,24,25,26,28,27,18,18],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,18,19,20,
21,22,23,24,25,26,27,28,29,30]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[170,10,-10,8,2,0,
-2,-2,2,2,2,0,2,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[646,6,16,-2,6,1,0,-2,-2,
-2,-2,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[324,4,9,0,4,-1,1,0,0,0,0,-1,1,
-1,1,1,1,18,2,0,-2,-2,-1,0,0,0,1,1,1,1],
[TENSOR,[5,2]],[1292,-20,14,-4,4,2,-2,0,2,2,2,0,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[816,-16,6,6,0,1,2,0,0,0,0,-1,0,1,0,0,-1,0,0,0,0,0,0,0,0,0,
E(24)-E(24)^11-E(24)^17+E(24)^19,-E(24)+E(24)^11+E(24)^17-E(24)^19,0,0],
[TENSOR,[8,2]],[1140,20,15,6,-4,0,-1,0,0,0,0,0,-1,0,1,1,0,18,2,0,2,2,-1,0,0,0,
-1,-1,1,1],
[TENSOR,[10,2]],[1215,15,0,0,3,0,0,1,0,0,0,0,0,0,E(17)+E(17)^2+E(17)^4+E(17)^8
 +E(17)^9+E(17)^13+E(17)^15+E(17)^16,E(17)^3+E(17)^5+E(17)^6+E(17)^7+E(17)^10
 +E(17)^11+E(17)^12+E(17)^14,-1,9,-3,0,3,-1,0,0,0,0,0,0,-E(17)-E(17)^2-E(17)^4
 -E(17)^8-E(17)^9-E(17)^13-E(17)^15-E(17)^16,-E(17)^3-E(17)^5-E(17)^6-E(17)^7
 -E(17)^10-E(17)^11-E(17)^12-E(17)^14],
[TENSOR,[12,2]],
[GALOIS,[12,3]],
[TENSOR,[14,2]],[1615,15,-5,-5,-1,0,3,-1,1,1,1,0,-1,0,0,0,0,17,1,-1,1,1,1,-1,
-1,-1,1,1,0,0],
[TENSOR,[16,2]],[1920,0,0,3,0,0,0,0,-E(9)^2+E(9)^4+E(9)^5-E(9)^7,
-E(9)^2-2*E(9)^4-2*E(9)^5-E(9)^7,2*E(9)^2+E(9)^4+E(9)^5+2*E(9)^7,0,0,0,-1,-1,
1,16,0,1,0,0,0,E(9)^2+E(9)^4+E(9)^5+E(9)^7,-E(9)^2-E(9)^7,-E(9)^4-E(9)^5,0,0,
-1,-1],
[TENSOR,[18,2]],
[GALOIS,[18,4]],
[TENSOR,[20,2]],
[GALOIS,[18,2]],
[TENSOR,[22,2]],[3876,4,6,-12,-4,1,-2,0,0,0,0,-1,2,1,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],[2432,0,-16,2,0,2,0,0,-1,-1,-1,0,0,-1,1,1,0,16,0,-2,0,0,0,1,1,1,0,0,
-1,-1],
[TENSOR,[25,2]],[2754,-14,9,0,-2,-1,1,0,0,0,0,1,1,-1,0,0,-1,0,4,0,2,-2,1,0,0,
0,-1,-1,0,0],
[TENSOR,[27,2]],[3078,-10,-9,0,2,-2,-1,0,0,0,0,0,-1,1,1,1,0,18,-2,0,-4,0,1,0,
0,0,-1,-1,1,1],
[TENSOR,[29,2]]],
[(27,28),(15,16)(29,30),( 9,10,11)(24,25,26)(27,28),( 9,10,11)(24,25,26),
( 9,11,10)(24,26,25)]);
ARC("J3.2","CAS",[rec(name:="j3.2",
permchars:=( 4, 6, 5)( 7,15,14,13,12,11,10, 9, 8)(24,30,29,28,27,26,25),
permclasses:=(24,26)(29,30),
text:=Concatenation(
"names:=     j3.2, j3.z2, autj3\n",
"    order:     2^8.3^5.5.7.17 = 100,465,920\n",
"    number of classes:  30\n",
"    source:    private communication of atlas compound table\n",
"               from cambridge 1980/81\n",
"    comments:  extension of j3 with an outer\n",
"               automorphism of order 2\n",
"    test:      orth.1, min, sym[3]     \n",
""))]);
ARC("J3.2","maxes",["J3","L2(16).4","2^4:(3xA5).2","L2(17)x2","(3xM10):2",
"3^2.3^(1+2):8.2","2^(1+4).S5","2^(2+4):(S3xS3)","19:18"]);
ARC("J3.2","tomfusion",rec(name:="J3.2",map:=[1,3,4,5,9,11,16,22,37,37,37,40,
50,52,83,83,92,2,10,17,21,23,51,91,91,91,109,109,150,150],text:=[
"fusion map is unique"
]));

MOT("J4",
[
"origin: ATLAS of finite groups, tests: 1.o.r.,\n",
"pow[2,3,5,7,11,23,29,31,37,43]"
],
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56,30,32,160,160,42,42,264,22,23,48,48,28,28,29,30,31,31,31,66,66,35,35,37,37,
37,40,40,42,42,43,43,43,44,66,66],
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17,32,33,19,20,36,22,22,26,27,41,28,43,44,45,46,47,48,49,51,52,50,31,30,32,33,
57,58,59,34,46,47],[1,2,3,1,5,6,7,8,2,2,3,13,12,14,15,16,17,18,19,20,5,6,7,25,
24,27,26,8,29,31,30,13,12,34,35,36,15,15,40,39,41,17,45,43,44,19,19,49,48,52,
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33,2,3,36,37,38,39,40,41,42,44,45,43,4,4,48,49,50,51,52,53,54,55,56,57,58,59,
5,9,9],,,,,,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,29,31,30,32,33,34,35,1,37,38,39,40,41,42,43,44,45,47,46,48,
49,50,51,52,54,53,55,56,58,59,57,60,62,61],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,38,37,
39,40,1,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,59,57,58,60,61,62],,[1,2,
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31,33,32,34,35,36,38,37,40,39,41,42,1,1,1,46,47,49,48,50,51,52,53,54,56,55,58,
59,57,60,61,62],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,31,30,32,33,34,35,36,37,38,39,40,41,42,45,43,44,46,47,
48,49,1,1,1,54,53,55,56,58,59,57,60,61,62],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,31,30,32,33,34,35,36,38,37,
39,40,41,42,45,43,44,47,46,48,49,50,51,52,54,53,55,56,1,1,1,60,62,61]],
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0,0,0,E(43)+E(43)^2+E(43)^4+E(43)^8+E(43)^11+E(43)^16+E(43)^21+E(43)^22
 +E(43)^27+E(43)^32+E(43)^35+E(43)^39+E(43)^41+E(43)^42,
E(43)^3+E(43)^5+E(43)^6+E(43)^10+E(43)^12+E(43)^19+E(43)^20+E(43)^23+E(43)^24
 +E(43)^31+E(43)^33+E(43)^37+E(43)^38+E(43)^40,E(43)^7+E(43)^9+E(43)^13
 +E(43)^14+E(43)^15+E(43)^17+E(43)^18+E(43)^25+E(43)^26+E(43)^28+E(43)^29
 +E(43)^30+E(43)^34+E(43)^36,1,0,0],
[GALOIS,[46,7]],
[GALOIS,[46,3]],[1509863773,-5027,-7139,-176,-99,45,-27,-7,-176,16,16,5,5,1,
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0,0,0,0,1,1,-1,-1,0,0,0,0,0,0],[1579061136,31632,4752,-384,528,-48,-48,-14,
384,0,0,-5,-5,0,0,0,2,2,4,4,0,0,0,-1,-1,-1,-1,1,0,-2,-2,1,1,-4,0,0,0,0,1,1,0,
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1981808640,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-24,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,
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 -E(37)^14-E(37)^23-E(37)^26-E(37)^27-E(37)^29-E(37)^31-E(37)^36,
-E(37)^2-E(37)^9-E(37)^12-E(37)^15-E(37)^16-E(37)^17-E(37)^20-E(37)^21
 -E(37)^22-E(37)^25-E(37)^28-E(37)^35,-E(37)^3-E(37)^4-E(37)^5-E(37)^7
 -E(37)^13-E(37)^18-E(37)^19-E(37)^24-E(37)^30-E(37)^32-E(37)^33-E(37)^34,0,0,
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[GALOIS,[53,3]],
[GALOIS,[53,2]],[2001151845,-10395,-10395,0,165,-27,21,0,0,0,0,0,0,5,-3,5,0,0,
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 +E(31)^15+E(31)^16+E(31)^23+E(31)^27+E(31)^29+E(31)^30,
E(31)^5+E(31)^9+E(31)^10+E(31)^11+E(31)^13+E(31)^18+E(31)^20+E(31)^21+E(31)^22
 +E(31)^26,E(31)^3+E(31)^6+E(31)^7+E(31)^12+E(31)^14+E(31)^17+E(31)^19
 +E(31)^24+E(31)^25+E(31)^28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[56,3]],
[GALOIS,[56,5]],[2267824128,-49152,0,384,0,0,0,8,384,0,0,-4,-4,0,0,0,8,0,20,
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[(57,58,59),(57,59,58),(50,51,52),(46,47)(61,62),(43,45,44),(37,38),(37,38)
(46,47)(61,62),(30,31)(53,54),(12,13)(24,25)(26,27)(32,33)(39,40)(48,49)
(55,56),(50,52,51)]);
ARC("J4","CAS",[rec(name:="j4",
permchars:=(19,20)(33,34)(43,44)(53,55)(57,58),
permclasses:=(21,22)(24,25)(39,40)(44,45)(51,52)(55,56),
text:=Concatenation(
"names:=j4;\n",
"     order: 2^21.3^3.5.7.11^3.23.29.31.37.43\n",
"          = 86,775,571,046,077,562,880\n",
"     number of classes: 62\n",
"     source:private communication of compound table\n",
"            from cambridge group atlas project 1980/81\n",
"     origin:conway, j. - norton, s. - janko, z.\n",
"            -unpublished- \n",
""))]);
ARC("J4","isSimple",true);
ARC("J4","extInfo",["",""]);
ARC("J4","maxes",["mx1j4","c2aj4","2^10:L5(2)","J4M4","U3(11).2","M22.2",
"11+^(1+2):(5x2S4)","L2(32).5","L2(23).2","U3(3)","frob","43:14","37:12"]);

LIBTABLE.LOADSTATUS.ctoconja:="userloaded";
ALN:= NotifyCharTableName;

#############################################################################
##
#E