File: ctoorth2.tbl

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#############################################################################
##
#W  ctoorth2.tbl                GAP table library               Thomas Breuer
##
#H  @(#)$Id: ctoorth2.tbl,v 4.22 2003/09/23 16:30:45 gap Exp $
##
#Y  Copyright (C)  1996,  Lehrstuhl D fuer Mathematik,  RWTH Aachen,  Germany
##
##  This file contains the ordinary character tables related to the
##  orthogonal groups $O_8^+(2)$ and $O_8^+(3)$.
##
Revision.ctoorth2_tbl :=
    "@(#)$Id: ctoorth2.tbl,v 4.22 2003/09/23 16:30:45 gap Exp $";

SET_TABLEFILENAME("ctoorth2");
ALN:= Ignore;

MOT("2.O8+(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[348364800,348364800,110592,92160,92160,46080,46080,3072,155520,155520,155520,
155520,155520,155520,3888,3888,1296,1296,9216,9216,512,384,384,192,192,64,600,
600,600,600,600,600,3456,3456,1728,1728,576,576,288,288,432,432,216,216,216,
144,144,72,72,24,14,14,32,64,64,54,54,54,54,54,54,40,40,20,20,288,288,288,288,
288,288,72,72,48,48,24,24,30,30,30,30,30,30],
[,[1,1,1,1,1,2,2,1,9,9,11,11,13,13,15,15,17,17,3,3,3,4,4,6,7,8,27,27,29,29,31,
31,9,9,11,13,9,9,12,14,15,15,17,17,17,17,17,18,18,17,51,51,19,21,21,56,56,58,
58,60,60,27,27,30,32,33,33,35,35,36,36,41,41,37,37,39,40,78,78,80,80,82,82],[
1,2,3,4,5,6,7,8,1,2,1,2,1,2,1,2,1,2,19,20,21,22,23,24,25,26,27,28,29,30,31,32,
3,3,3,3,4,5,6,7,3,3,3,3,3,4,5,6,7,8,51,52,53,54,55,15,16,15,16,15,16,62,63,64,
65,19,20,19,20,19,20,19,20,22,23,24,25,27,28,29,30,31,32],,[1,2,3,4,5,6,7,8,9,
10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,1,2,1,2,1,2,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,4,5,6,
7,66,67,68,69,70,71,72,73,74,75,76,77,9,10,11,12,13,14],,[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,
36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,1,2,53,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83]],
0,
[( 6, 7)(11,13)(12,14)(24,25)(29,31)(30,32)(35,36)(39,40)(44,45)(48,49)(58,60)
(59,61)(64,65)(68,70)(69,71)(76,77)(80,82)(81,83)],
["ConstructProj",[["O8+(2)",[]],["2.O8+(2)",[]]]]);
ALF("2.O8+(2)","O8+(2)",[1,1,2,3,3,4,5,6,7,7,8,8,9,9,10,10,11,11,12,12,13,
14,14,15,16,17,18,18,19,19,20,20,21,21,22,23,24,24,25,26,27,27,28,29,30,
31,31,32,33,34,35,35,36,37,37,38,38,39,39,40,40,41,41,42,43,44,44,45,45,
46,46,47,47,48,48,49,50,51,51,52,52,53,53]);
ALF("2.O8+(2)","2.O8+(2).2",[1,2,3,4,5,6,6,7,8,9,10,11,10,11,12,13,14,15,
16,17,18,19,20,21,21,22,23,24,25,26,25,26,27,28,29,29,30,31,32,32,33,34,
35,36,36,37,38,39,39,40,41,42,43,44,45,46,47,48,49,48,49,50,51,52,52,53,
54,55,56,55,56,57,58,59,60,61,61,62,63,64,65,64,65]);

MOT("2.O8+(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[696729600,696729600,221184,184320,184320,46080,6144,311040,311040,155520,
155520,7776,7776,2592,2592,18432,18432,1024,768,768,192,128,1200,1200,600,600,
6912,6912,1728,1152,1152,288,864,864,432,216,288,288,72,48,28,28,64,128,128,
108,108,54,54,80,80,20,576,576,288,288,144,144,96,96,24,60,60,30,30,5806080,
5806080,18432,18432,15360,15360,4608,1536,1536,768,256,8640,8640,2592,2592,
576,576,432,432,288,288,144,144,384,384,64,16,120,120,576,576,192,192,72,24,
48,48,28,28,36,36,40,40,48,48,60,60],
[,[1,1,1,1,1,2,1,8,8,10,10,12,12,14,14,3,3,3,4,4,6,7,23,23,25,25,8,8,10,8,8,
11,12,12,14,14,14,14,15,14,41,41,16,18,18,46,46,48,48,23,23,26,27,27,29,29,33,
33,30,30,32,62,62,64,64,1,1,1,1,4,4,4,3,3,5,4,8,8,12,12,8,8,14,14,12,12,14,14,
16,16,18,22,23,23,30,30,30,30,37,38,33,33,41,41,46,46,50,50,53,53,62,62],[1,2,
3,4,5,6,7,1,2,1,2,1,2,1,2,16,17,18,19,20,21,22,23,24,25,26,3,3,3,4,5,6,3,3,3,
3,4,5,6,7,41,42,43,44,45,12,13,12,13,50,51,52,16,17,16,17,16,17,19,20,21,23,
24,25,26,66,67,68,69,70,71,72,73,74,75,76,66,67,66,67,68,69,66,67,68,69,68,69,
89,90,91,92,93,94,72,72,70,71,72,75,73,74,103,104,79,80,107,108,89,90,93,
94],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,1,2,1,2,27,28,
29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,4,5,6,53,54,55,
56,57,58,59,60,61,8,9,10,11,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,
82,83,84,85,86,87,88,89,90,91,92,66,67,95,96,97,98,99,100,101,102,103,104,105,
106,70,71,109,110,77,78],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,1,2,43,44,45,46,
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,
99,100,101,102,66,67,105,106,107,108,109,110,111,112]],
0,
[( 66, 67)( 68, 69)( 70, 71)( 73, 74)( 77, 78)( 79, 80)( 81, 82)( 83, 84)
( 85, 86)( 87, 88)( 89, 90)( 93, 94)( 95, 96)( 97, 98)(101,102)(103,104)
(105,106)(107,108)(109,110)(111,112)],
["ConstructProj",[["O8+(2).2",[]],["2.O8+(2).2",[]]]]);
ALF("2.O8+(2).2","O8+(2).2",[1,1,2,3,3,4,5,6,6,7,7,8,8,9,9,10,10,11,12,12,
13,14,15,15,16,16,17,17,18,19,19,20,21,21,22,23,24,24,25,26,27,27,28,29,
29,30,30,31,31,32,32,33,34,34,35,35,36,36,37,37,38,39,39,40,40,41,41,42,
42,43,43,44,45,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,54,54,55,56,
57,57,58,58,59,59,60,61,62,62,63,63,64,64,65,65,66,66,67,67]);
ALN("2.O8+(2).2",["w(e8)"]);

MOT("2^2.O8+(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[696729600,696729600,696729600,696729600,110592,92160,92160,92160,92160,92160,
92160,3072,311040,311040,311040,311040,311040,311040,311040,311040,311040,
311040,311040,311040,7776,7776,7776,7776,2592,2592,2592,2592,18432,18432,
18432,18432,512,384,384,384,384,384,384,64,1200,1200,1200,1200,1200,1200,1200,
1200,1200,1200,1200,1200,3456,3456,3456,3456,3456,3456,576,576,576,576,576,
576,864,864,864,864,216,216,216,144,144,144,144,144,144,24,28,28,28,28,32,128,
128,128,128,108,108,108,108,108,108,108,108,108,108,108,108,40,40,40,40,40,40,
576,576,576,576,576,576,576,576,576,576,576,576,144,144,144,144,48,48,48,48,
48,48,60,60,60,60,60,60,60,60,60,60,60,60],
[,[1,1,1,1,1,2,2,3,3,4,4,1,13,13,13,13,17,17,17,17,21,21,21,21,25,25,25,25,29,
29,29,29,5,5,5,5,5,6,6,8,8,10,10,12,45,45,45,45,49,49,49,49,53,53,53,53,13,13,
17,17,21,21,14,14,19,19,24,24,25,25,25,25,29,29,29,30,30,31,31,32,32,29,83,83,
83,83,33,37,37,37,37,92,92,92,92,96,96,96,96,100,100,100,100,46,46,51,51,56,
56,57,57,57,57,59,59,59,59,61,61,61,61,69,69,69,69,63,63,65,65,67,67,132,132,
132,132,136,136,136,136,140,140,140,140],[1,2,3,4,5,6,7,8,9,10,11,12,1,2,3,4,
1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
48,49,50,51,52,53,54,55,56,5,5,5,5,5,5,6,7,8,9,10,11,5,5,5,5,5,5,5,6,7,8,9,10,
11,12,83,84,85,86,87,88,89,90,91,25,26,27,28,25,26,27,28,25,26,27,28,104,105,
106,107,108,109,33,34,35,36,33,34,35,36,33,34,35,36,33,34,35,36,38,39,40,41,
42,43,45,46,47,48,49,50,51,52,53,54,55,56],,[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,
41,42,43,44,1,2,3,4,1,2,3,4,1,2,3,4,57,58,59,60,61,62,63,64,65,66,67,68,69,70,
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,
97,98,99,100,101,102,103,6,7,8,9,10,11,110,111,112,113,114,115,116,117,118,
119,120,121,122,123,124,125,126,127,128,129,130,131,13,14,15,16,17,18,19,20,
21,22,23,24],,[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,
77,78,79,80,81,82,1,2,3,4,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,
122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,
141,142,143]],
0,
[(  3,  4)(  8, 10)(  9, 11)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)
( 27, 28)( 31, 32)( 35, 36)( 40, 42)( 41, 43)( 47, 48)( 49, 53)( 50, 54)
( 51, 56)( 52, 55)( 59, 61)( 60, 62)( 65, 67)( 66, 68)( 71, 72)( 74, 75)
( 78, 80)( 79, 81)( 85, 86)( 90, 91)( 94, 95)( 96,100)( 97,101)( 98,103)
( 99,102)(106,108)(107,109)(112,113)(114,118)(115,119)(116,121)(117,120)
(124,125)(128,130)(129,131)(134,135)(136,140)(137,141)(138,143)(139,142),
(  2,  3)(  6,  8)(  7,  9)( 13, 17)( 14, 19)( 15, 18)( 16, 20)( 22, 23)
( 26, 27)( 30, 31)( 34, 35)( 38, 40)( 39, 41)( 45, 49)( 46, 51)( 47, 50)
( 48, 52)( 54, 55)( 57, 59)( 58, 60)( 63, 65)( 64, 66)( 70, 71)( 73, 74)
( 76, 78)( 77, 79)( 84, 85)( 89, 90)( 92, 96)( 93, 98)( 94, 97)( 95, 99)
(101,102)(104,106)(105,107)(110,114)(111,116)(112,115)(113,117)(119,120)
(123,124)(126,128)(127,129)(132,136)(133,138)(134,137)(135,139)(141,142)],
["ConstructV4G","2.O8+(2)",(  2,  3,  4)(  6,  8, 10)
(  7,  9, 11)( 13, 17, 21)( 14, 19, 24)( 15, 20, 22)( 16, 18, 23)( 26, 27,
 28)( 30, 31, 32)( 34, 35, 36)( 38, 40, 42)( 39, 41, 43)( 45, 49, 53)( 46,
 51, 56)( 47, 52, 54)( 48, 50, 55)( 57, 59, 61)( 58, 60, 62)( 63, 65, 67)
( 64, 66, 68)( 70, 71, 72)( 73, 74, 75)( 76, 78, 80)( 77, 79, 81)( 84, 85,
 86)( 89, 90, 91)( 92, 96,100)( 93, 98,103)( 94, 99,101)( 95, 97,102)(104,
106,108)(105,107,109)(110,114,118)(111,116,121)(112,117,119)(113,115,120)
(123,124,125)(126,128,130)(127,129,131)(132,136,140)(133,138,143)(134,139,
141)(135,137,142)]);
ALF("2^2.O8+(2)","O8+(2)",[1,1,1,1,2,3,3,4,4,5,5,6,7,7,7,7,8,8,8,8,9,9,9,
9,10,10,10,10,11,11,11,11,12,12,12,12,13,14,14,15,15,16,16,17,18,18,18,18,
19,19,19,19,20,20,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,27,27,
28,29,30,31,31,32,32,33,33,34,35,35,35,35,36,37,37,37,37,38,38,38,38,39,
39,39,39,40,40,40,40,41,41,42,42,43,43,44,44,44,44,45,45,45,45,46,46,46,
46,47,47,47,47,48,48,49,49,50,50,51,51,51,51,52,52,52,52,53,53,53,53]);
ALF("2^2.O8+(2)","2.O8+(2)",[1,1,2,2,3,4,5,6,6,7,7,8,9,9,10,10,11,11,12,
12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,22,23,24,24,25,25,
26,27,27,28,28,29,29,30,30,31,31,32,32,33,34,35,35,36,36,37,38,39,39,40,
40,41,41,42,42,43,44,45,46,47,48,48,49,49,50,51,51,52,52,53,54,54,55,55,
56,56,57,57,58,58,59,59,60,60,61,61,62,63,64,64,65,65,66,66,67,67,68,68,
69,69,70,70,71,71,72,72,73,73,74,75,76,76,77,77,78,78,79,79,80,80,81,81,
82,82,83,83]);
ALF("2^2.O8+(2)","2^2.O8+(2).2",[1,2,3,3,4,5,6,7,8,7,8,9,10,11,12,12,13,
14,15,16,13,14,16,15,17,18,19,19,20,21,22,22,23,24,25,25,26,27,28,29,30,
29,30,31,32,33,34,34,35,36,37,38,35,36,38,37,39,40,41,42,41,42,43,44,45,
46,45,46,47,48,49,49,50,51,51,52,53,54,55,54,55,56,57,58,59,59,60,61,62,
63,63,64,65,66,66,67,68,69,70,67,68,70,69,71,72,73,74,73,74,75,76,77,77,
78,79,80,81,78,79,81,80,82,83,84,84,85,86,87,88,87,88,89,90,91,91,92,93,
94,95,92,93,95,94]);
ALF("2^2.O8+(2)","2^2.O8+(2).3",[1,2,2,2,3,4,5,4,5,4,5,6,7,8,9,10,7,10,8,
9,7,9,10,8,11,12,12,12,13,14,14,14,15,16,16,16,17,18,19,18,19,18,19,20,21,
22,23,24,21,24,22,23,21,23,24,22,25,26,25,26,25,26,27,28,27,28,27,28,29,
30,30,30,31,31,31,32,33,32,33,32,33,34,35,36,36,36,37,38,39,39,39,40,41,
42,43,40,43,41,42,40,42,43,41,44,45,44,45,44,45,46,47,48,49,46,49,47,48,
46,48,49,47,50,51,51,51,52,53,52,53,52,53,54,55,56,57,54,57,55,56,54,56,
57,55]);

MOT("2^2.O8+(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
[1393459200,1393459200,696729600,221184,184320,184320,92160,92160,6144,622080,
622080,311040,311040,311040,311040,311040,15552,15552,7776,5184,5184,2592,
36864,36864,18432,1024,768,768,384,384,128,2400,2400,1200,1200,1200,1200,1200,
6912,6912,3456,3456,1152,1152,576,576,1728,1728,864,432,216,288,288,144,144,48
,56,56,28,64,256,256,128,216,216,108,108,108,108,108,80,80,40,40,1152,1152,576
,576,576,576,576,288,288,144,96,96,48,48,120,120,60,60,60,60,60,5806080,
5806080,18432,18432,15360,15360,4608,1536,1536,768,256,8640,8640,2592,2592,576
,576,432,432,288,288,144,144,384,384,64,16,120,120,576,576,192,192,72,24,48,48
,28,28,36,36,40,40,48,48,60,60],
[,[1,1,1,1,2,2,3,3,1,10,10,10,13,13,13,13,17,17,17,20,20,20,4,4,4,4,5,5,7,7,9,
32,32,32,35,35,35,35,10,10,13,13,11,11,15,15,17,17,17,20,20,21,21,22,22,20,57,
57,57,23,26,26,26,64,64,64,67,67,67,67,33,33,37,37,39,39,39,41,41,41,41,47,47,
47,43,43,45,45,89,89,89,92,92,92,92,1,2,2,1,5,5,5,4,4,6,5,10,11,17,18,11,10,20
,21,18,17,21,20,24,23,26,31,32,33,43,43,43,43,52,53,47,48,57,58,64,65,71,71,76
,75,89,90],[1,2,3,4,5,6,7,8,9,1,2,3,1,2,3,3,1,2,3,1,2,3,23,24,25,26,27,28,29,
30,31,32,33,34,35,36,37,38,4,4,4,4,5,6,7,8,4,4,4,4,4,5,6,7,8,9,57,58,59,60,61,
62,63,17,18,19,17,18,19,19,71,72,73,74,23,24,25,23,24,25,25,23,24,25,27,28,29,
30,32,33,34,35,36,37,38,96,97,98,99,100,101,102,103,104,105,106,96,97,96,97,98
,99,96,97,98,99,98,99,119,120,121,122,123,124,102,102,100,101,102,105,103,104,
133,134,109,110,137,138,119,120,123,124],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,1,2,3,1,2,3,3,39,40,41,42,43,
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,
70,5,6,7,8,75,76,77,78,79,80,81,82,83,84,85,86,87,88,10,11,12,13,14,15,16,96,
97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,
117,118,119,120,121,122,96,97,125,126,127,128,129,130,131,132,133,134,135,136,
100,101,139,140,107,108],,[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,
47,48,49,50,51,52,53,54,55,56,1,2,3,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
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,
119,120,121,122,123,124,125,126,127,128,129,130,131,132,96,97,135,136,137,138,
139,140,141,142]],
0,
[],
["ConstructMixed","2^2.O8+(2)","2.O8+(2).2",[[84,114],[85,115],[86,116],[87,
117],[88,119],[89,118],[90,120],[91,121],[92,122],[93,124],[94,123],[95,125],
[96,126],[97,128],[98,127],[99,129],[100,130],[101,131],[102,132],[103,133],
[104,135],[105,134],[106,136],[107,137],[108,139],[109,138],[110,140],[111,
141],[112,142],[113,143]],()]);
ALF("2^2.O8+(2).2","2.O8+(2).2",[1,1,2,3,4,5,6,6,7,8,8,9,10,10,11,11,12,
12,13,14,14,15,16,16,17,18,19,20,21,21,22,23,23,24,25,25,26,26,27,28,29,
29,30,31,32,32,33,33,34,35,36,37,38,39,39,40,41,41,42,43,44,44,45,46,46,
47,48,48,49,49,50,51,52,52,53,53,54,55,55,56,56,57,57,58,59,60,61,61,62,
62,63,64,64,65,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,
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]);
ALF("2^2.O8+(2).2","2^2.O8+(2).3.2",[1,2,2,3,4,5,4,5,6,7,8,9,7,9,8,9,10,
11,11,12,13,13,14,15,15,16,17,18,17,18,19,20,21,22,20,22,21,22,23,24,23,
24,25,26,25,26,27,28,28,29,29,30,31,30,31,32,33,34,34,35,36,37,37,38,39,
40,38,40,39,40,41,42,41,42,43,44,45,43,45,44,45,46,47,47,48,49,48,49,50,
51,52,50,52,51,52,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,
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]);
ALF("2^2.O8+(2).2","O8+(2).2",[1,1,1,2,3,3,4,4,5,6,6,6,7,7,7,7,8,8,8,9,9,
9,10,10,10,11,12,12,13,13,14,15,15,15,16,16,16,16,17,17,18,18,19,19,20,20,
21,21,21,22,23,24,24,25,25,26,27,27,27,28,29,29,29,30,30,30,31,31,31,31,
32,32,33,33,34,34,34,35,35,35,35,36,36,36,37,37,38,38,39,39,39,40,40,40,
40,41,41,42,42,43,43,44,45,45,46,47,48,48,49,49,50,50,51,51,52,52,53,53,
54,54,55,56,57,57,58,58,59,59,60,61,62,62,63,63,64,64,65,65,66,66,67,67]);

MOT("2^2.O8+(2).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
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3456,576,576,2592,864,216,144,144,72,84,28,96,384,128,108,108,108,108,40,40,
576,576,576,576,432,144,48,48,60,60,60,60,36288,36288,648,648,576,576,144,144,
72,72,54,54,288,288,144,144,96,96,12,12,18,18,21,21,24,24,24,24],
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,14,13,35,35,15,17,17,40,40,40,40,22,22,25,25,25,25,29,29,27,27,54,54,54,54,59
,58,61,60,59,58,59,58,61,60,69,68,63,62,63,62,63,62,67,66,69,68,81,80,71,70,75
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3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,1,2,2,2,25,26,27,28,29,30,31,32
,33,34,35,36,37,38,39,40,41,42,43,4,5,46,47,48,49,50,51,52,53,7,8,9,10,59,58,
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,,[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,
29,30,31,32,33,34,1,2,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55
,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,58,59
,82,83,84,85]],
0,
[(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),(9,10)(23,24)(42,43)(48,49)(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)
],
["ConstructMixed","2^2.O8+(2)","O8+(2).3",[[54,84,114],[55,85,115],[56,86,
116],[57,87,117],[58,88,118],[59,89,119],[60,90,120],[61,91,121],[62,92,122],
[63,93,123],[64,94,124],[65,95,125],[66,96,126],[67,97,127],[68,98,128],[69,
99,129],[70,100,130],[71,101,131],[72,102,132],[73,103,133],[74,104,134],[75,
105,135],[76,106,136],[77,107,137],[78,108,138],[79,109,139],[80,110,140],[81,
111,141],[82,112,142],[83,113,143]],()]);
ALF("2^2.O8+(2).3","O8+(2).3",[1,1,2,3,3,4,5,5,5,5,6,6,7,7,8,8,9,10,10,11,
12,12,12,12,13,13,14,14,15,15,16,17,17,18,19,19,20,21,21,22,22,22,22,23,
23,24,24,24,24,25,25,26,26,27,27,27,27,28,29,30,31,32,33,34,35,36,37,38,
39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55]);
ALF("2^2.O8+(2).3","2^2.O8+(2).3.2",[1,2,3,4,5,6,7,8,9,9,10,11,12,13,14,
15,16,17,18,19,20,21,22,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,40,41,42,43,44,45,45,46,47,48,49,50,51,52,52,53,53,54,54,55,55,
56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,66,66]);

MOT("2^2.O8+(2).3.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
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15552,15552,5184,110592,36864,3072,768,768,384,2400,2400,1200,6912,6912,1152,
1152,5184,1728,432,288,288,144,168,56,192,768,256,216,216,108,80,80,1152,1152,
576,864,288,96,96,120,120,60,36288,648,576,144,72,54,288,144,96,12,18,21,24,24
,5806080,5806080,18432,18432,15360,15360,4608,1536,1536,768,256,8640,8640,2592
,2592,576,576,432,432,288,288,144,144,384,384,64,16,120,120,576,576,192,192,72
,24,48,48,28,28,36,36,40,40,48,48,60,60],
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58,55,55,55,57,58,64,59,61,1,2,2,1,4,4,4,3,3,5,4,7,8,10,11,8,7,12,13,11,10,13,
12,15,14,16,19,20,21,25,25,25,25,30,31,27,28,33,34,38,39,41,41,44,43,50,51],[1
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95],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,1,2,2,23,24,25,26,27,28,
29,30,31,32,33,34,35,36,37,38,39,40,4,5,43,44,45,46,47,48,49,7,8,9,53,54,55,56
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106,107,71,72,110,111,78,79],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19
,20,21,22,23,24,25,26,27,28,29,30,31,32,1,2,35,36,37,38,39,40,41,42,43,44,45,
46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,53,65,66,67,68,69,70,71,
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,
98,99,100,101,102,103,67,68,106,107,108,109,110,111,112,113]],
0,
[],
["ConstructGS3","2^2.O8+(2).2","2^2.O8+(2).3",[5,6,10,11,15,16,24,25,29,30,32,
33,37,38,40,41,45,46,48,49,51,52,54,55,57,58,68,69,70,71,72,73,74,75,76,77,78,
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],[[2,3],[5,6],[9,10],[13,14],[17,18],
[20,21],[23,24],[27,28],[32,33],[37,38],[45,46],[48,49],[51,52],[54,55]],[[1,
1],[4,3],[8,8],[12,13],[16,18],[19,20],[22,22],[26,27],[31,35],[36,43],[44,
60],[47,62],[50,64],[53,66]],(1,7,28,70,113,67,109,61,104,44,86)(2,8,29,71,
112,66,108,60,102,37,79,32,74,11,35,77,24,54,97,23,53,94,19,49,90,9,33,75,16,
43,85,68,111,64,107,58,100,30,72,3,12,36,78,27,69,110,63,105,45,88,4,13,40,82,
59,101,31,73,6,18,48,91,10,34,76,21,51,93,15,42,84,65,106,57,98,25,55,96,22,
52,95,20,50,92,14,41,83,62,103,38,80,39,81,46,87)(5,17,47,89)(26,56,99)]);
ALF("2^2.O8+(2).3.2","O8+(2).3.2",[1,1,2,3,3,4,5,5,5,6,6,7,7,8,8,9,10,10,
11,12,12,12,13,13,14,14,15,15,16,17,17,18,19,19,20,21,21,22,22,22,23,23,
24,24,24,25,25,26,26,27,27,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
42,42,43,43,44,44,45,46,46,47,48,49,49,50,50,51,51,52,52,53,53,54,54,55,
55,56,57,58,58,59,59,60,60,61,62,63,63,64,64,65,65,66,66,67,67,68,68]);

MOT("O8+(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
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192,192,192,64,300,300,300,1728,1728,1728,288,288,288,216,216,216,216,72,72,
72,24,7,32,32,27,27,27,20,20,20,144,144,144,36,24,24,24,15,15,15],
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11,11,35,12,13,38,39,40,18,19,20,21,22,23,27,24,25,26,51,52,53],[1,2,3,4,5,6,
1,1,1,1,1,12,13,14,15,16,17,18,19,20,2,2,2,3,4,5,2,2,2,2,3,4,5,6,35,36,37,10,
10,10,41,42,43,12,12,12,12,14,15,16,18,19,20],,[1,2,3,4,5,6,7,8,9,10,11,12,13,
14,15,16,17,1,1,1,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,
3,4,5,44,45,46,47,48,49,50,7,8,9],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,1,36,37,38,39,40,41,42,43,
44,45,46,47,48,49,50,51,52,53]],
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1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[28,-4,4,4,4,-4,10,10,10,1,1,8,0,0,0,0,0,3,3,3,
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1,-2,1,-5,1,1,-1,1,-1,0,0,0,0,0,0,0,1,0,-3,3,-3,0,1,-1,1,0,-1,0],[210,-14,10,
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0],[2100,52,20,20,-60,4,-60,-60,75,-6,3,12,-4,0,0,-4,0,0,0,0,4,4,-5,-4,-4,3,
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1,0],[2268,-36,-36,-36,12,12,0,0,81,0,0,-12,4,0,0,-4,0,3,3,-2,0,0,9,0,0,-3,0,
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1,0,0,3,0,0,0,1,0,0,-1,0,0],[2835,-45,-45,51,-45,3,0,-81,0,0,0,3,3,3,-5,3,-1,
0,5,0,0,-9,0,0,3,0,0,0,0,0,0,0,0,0,0,-1,-1,0,0,0,0,1,0,0,3,0,0,0,1,0,0,-1,0],[
2835,-45,-45,-45,51,3,0,0,-81,0,0,3,3,3,3,-5,-1,0,0,5,0,0,-9,0,0,3,0,0,0,0,0,
0,0,0,0,-1,-1,0,0,0,0,0,1,0,0,3,0,0,0,1,0,0,-1],[3200,128,0,0,0,0,-40,-40,-40,
14,-4,0,0,0,0,0,0,0,0,0,8,8,8,0,0,0,2,-4,-4,-4,0,0,0,0,1,0,0,-1,-1,-1,0,0,0,0,
0,0,0,0,0,0,0,0,0],[4096,0,0,0,0,0,64,64,64,-8,-8,0,0,0,0,0,0,-4,-4,-4,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,-1,-1,-1],[4200,-24,40,
40,40,8,-30,-30,-30,15,-3,-8,-8,0,0,0,0,0,0,0,-6,-6,-6,-2,-2,-2,3,3,3,3,1,1,1,
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0,-9,-1,3,3,3,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0]],
[( 4, 5)( 8, 9)(15,16)(19,20)(22,23)(25,26)(29,30)(32,33)(39,40)(42,43)(45,46)
(49,50)(52,53),( 3, 4)( 7, 8)(14,15)(18,19)(21,22)(24,25)(28,29)(31,32)(38,39)
(41,42)(44,45)(48,49)(51,52)]);
ARC("O8+(2)","CAS",[rec(name:="o8p2",
permchars:=(),
permclasses:=(),
text:=Concatenation(
" test:= 1. o.r., sym 2 decompose correctly      \n",
""))]);
ARC("O8+(2)","projectives",["2.O8+(2)",[[8,0,4,0,0,0,5,-4,-4,-1,2,4,0,2,0,0,0,
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1,1],[56,0,-4,0,0,0,11,-16,-16,2,2,12,0,-2,0,0,0,1,-4,-4,3,0,0,-1,0,0,6,0,0,0,
2,0,0,0,0,0,2,-1,-1,-1,1,0,0,3,0,0,0,1,0,0,1,-1,-1],[112,0,24,0,0,0,31,4,4,4,
4,8,0,4,0,0,0,7,2,2,-9,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,-1,0,0,-1,2,2,2,
1,0,0,1,-1,-1],[160,0,16,0,0,0,34,-20,-20,-2,-2,16,0,0,0,0,0,5,0,0,-6,0,0,-2,
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0,-1,1,0],[400,0,40,0,0,0,25,-20,-20,4,10,-8,0,4,0,0,0,0,0,0,9,0,0,1,0,0,0,0,
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0,0,3,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,2,-4,-1,-1,0,0,0,1,-2],[1008,
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0,0,0,0,0,-1,0,0,-1,-4,2,-1,-1,0,0,0,-2,1],[1296,0,-24,0,0,0,81,0,0,0,0,24,0,
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1,0,0],[1400,0,60,0,0,0,-25,20,20,-13,8,-4,0,-2,0,0,0,0,0,0,15,0,0,3,0,0,3,0,
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0],[2800,0,-40,0,0,0,55,-80,-80,-8,10,-24,0,-4,0,0,0,0,0,0,-9,0,0,-1,0,0,0,0,
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-1,0,0],[3584,0,0,0,0,0,-64,80,-64,-16,-4,0,0,0,0,0,0,4,-6,4,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,-1,2,-1,0,0,0,0,0,0,0,0,0,0,1,0,1],[3584,0,0,0,0,0,-64,-64,
80,-16,-4,0,0,0,0,0,0,4,4,-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,2,0,0,0,
0,0,0,0,0,0,0,1,1,0],[4096,0,0,0,0,0,64,64,64,-8,-8,0,0,0,0,0,0,-4,-4,-4,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,-1,-1,-1],[4200,0,20,
0,0,0,-75,60,60,15,6,4,0,2,0,0,0,0,0,0,-3,0,0,-7,0,0,3,0,0,0,2,0,0,0,0,0,-2,0,
0,0,0,0,0,1,-2,-2,1,-1,0,0,0,0,0],[4536,0,60,0,0,0,-81,0,0,0,0,12,0,-2,0,0,0,
-4,6,6,-9,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,3,0,0,0,1,0,0,-1,0,0],[
5600,0,-80,0,0,0,20,20,20,11,2,-16,0,0,0,0,0,0,0,0,-12,0,0,4,0,0,3,0,0,0,-2,0,
0,0,0,0,0,-1,-1,-1,0,0,0,-4,2,2,-1,0,0,0,0,0,0]],]);
ARC("O8+(2)","isSimple",true);
ARC("O8+(2)","extInfo",["2^2","3.2"]);
ARC("O8+(2)","tomfusion",rec(name:="O8+(2)",map:=[1,2,3,4,5,6,8,7,9,10,11,43,
44,46,45,47,48,49,50,51,68,69,67,71,70,72,76,74,73,75,79,78,77,80,81,291,290,
301,302,303,312,311,310,329,330,331,332,334,333,335,409,410,411],text:=[
"fusion map is unique up to table automorphisms, hard to determine"
]));
ALF("O8+(2)","O8+(2).2",[1,2,3,4,4,5,6,7,7,8,9,10,11,12,13,13,14,15,16,16,
17,18,18,19,20,20,21,22,23,23,24,25,25,26,27,28,29,30,31,31,32,33,33,34,
35,35,36,37,38,38,39,40,40],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("O8+(2)","O8+(2).3",[1,2,3,3,3,4,5,5,5,6,7,8,9,10,10,10,11,12,12,12,
13,13,13,14,14,14,15,16,16,16,17,17,17,18,19,20,21,22,22,22,23,23,23,24,
24,24,25,26,26,26,27,27,27],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("O8+(2)","O8+(3)",[1,5,2,3,4,5,7,8,12,16,17,19,23,20,21,22,23,24,25,26,
37,38,42,31,32,36,49,52,51,50,43,44,45,53,55,56,57,71,71,71,72,73,74,78,79,
83,88,89,90,94,100,101,105],[
"fusion map is unique up to table automorphisms,\n",
"the representative is the one mentioned in the ATLAS"
]);
ALN("O8+(2)",["o8p2"]);

MOT("O8+(3)M11",
[
"11th maximal subgroup of O8+(3),\n",
"differs from O8+(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(2)"]]);
ALF("O8+(3)M11","O8+(3)",[1,5,2,3,4,5,7,11,9,15,17,19,23,20,21,22,23,24,25,
26,37,41,39,31,35,33,48,53,50,51,43,44,45,52,55,56,57,70,70,70,72,73,74,78,
82,80,87,89,93,91,100,104,102],[
"fusion map is unique up to table automorphisms,\n",
"equal to the map from O8+(2), mapped under an outer autom.;\n",
"compatible with the ATLAS"
]);

MOT("O8+(3)M12",
[
"12th maximal subgroup of O8+(3),\n",
"differs from O8+(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(2)"]]);
ALF("O8+(3)M12","O8+(3)",[1,5,2,3,4,5,10,8,9,14,17,19,23,20,21,22,23,24,25,
26,40,38,39,34,32,33,47,50,53,52,43,44,45,51,55,56,57,69,69,69,72,73,74,81,
79,80,86,92,90,91,103,101,102],[
"fusion map is unique up to table automorphisms,\n",
"equal to the map from O8+(2), mapped under an outer autom.;\n",
"compatible with the ATLAS"
]);

MOT("O8+(3)M13",
[
"13th maximal subgroup of O8+(3),\n",
"differs from O8+(2) only by fusion map"
],
0,
0,
0,
0,
["ConstructPermuted",["O8+(2)"]]);
ALF("O8+(3)M13","O8+(3)",[1,5,2,3,4,5,10,11,12,13,17,19,23,20,21,22,23,24,
25,26,40,41,42,34,35,36,46,51,52,53,43,44,45,50,55,56,57,68,68,68,72,73,74,
81,82,83,85,92,93,94,103,104,105],[
"fusion map is unique up to table automorphisms,\n",
"equal to the map from O8+(2), mapped under an outer autom.;\n",
"compatible with the ATLAS"
]);

MOT("O8+(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
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128,600,300,3456,1728,576,288,432,432,216,144,72,48,14,64,64,54,27,40,20,288,
144,72,48,24,30,15,2903040,9216,7680,4608,768,768,256,4320,1296,288,216,144,
72,192,64,16,60,288,96,72,24,24,14,18,20,24,30],
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17,18,21,19,20,39,40,1,1,3,3,2,3,3,6,8,6,9,8,9,10,11,14,15,19,19,24,24,21,27,
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[]);
ARC("O8+(2).2","CAS",[rec(name:="o8p2b",
permchars:=( 7, 9, 8)(17,21,20,19,18)(26,36,33,31,41,38,35,32,30,29,28,27)
(34,44,40,37)(39,47,55,51,48,45,42,52,49,46,43)(50,62,58,54)(53,63,59,65,61,57
 )(56,64,60),
permclasses:=(),
text:=Concatenation(
" test:= 1. o.r., sym 2 decompose correctly \n",
""))]);
ARC("O8+(2).2","projectives",["2.O8+(2).2",[[8,0,4,0,0,5,-4,-1,2,4,0,2,0,0,3,
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0,0,0],[4096,0,0,0,0,64,64,-8,-8,0,0,0,0,0,-4,-4,0,0,0,0,0,0,0,0,0,0,1,0,0,1,
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0,0,0,-1,0],[4536,0,60,0,0,-81,0,0,0,12,0,-2,0,0,-4,6,-9,0,3,0,0,0,0,0,0,0,0,
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0,0,0,0,-1,1],[5600,0,-80,0,0,20,20,11,2,-16,0,0,0,0,0,0,-12,0,4,0,3,0,0,-2,0,
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0,0,0,1,0,1,0,0,0]],]);
ALF("O8+(2).2","Fi22",[1,3,3,3,4,5,5,6,7,9,9,13,13,12,14,14,18,18,18,18,
17,23,23,23,23,22,26,28,27,32,32,35,35,39,39,38,46,46,52,52,2,4,10,10,11,
10,13,15,16,20,19,21,24,27,28,30,34,41,41,47,47,45,51,57,59,64,65],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("O8+(2).2","O8+(2).3.2",[1,2,3,3,4,5,5,6,7,8,9,10,10,11,12,12,13,13,
14,14,15,16,16,17,17,18,19,20,21,22,22,23,23,24,24,25,26,26,27,27,42,43,
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],[
"fusion map is unique, equal to that on the CAS table"
]);
ALF("O8+(2).2","S8(2)",[1,3,4,5,7,8,9,11,10,14,15,19,21,23,24,25,27,30,28,
36,35,29,34,37,38,41,42,45,46,49,50,53,54,55,59,63,62,67,69,71,2,6,13,12,
18,17,20,26,31,32,33,40,39,43,44,48,51,56,57,60,65,66,68,74,76,78,80],[
"fusion map is unique"
]);
ALN("O8+(2).2",["f22u4","o8p2b"]);

MOT("O8+(2).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
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144,72,72,54,54,288,288,144,144,96,96,12,12,18,18,21,21,24,24,24,24],
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3,4,1,1,1,8,9,10,11,12,2,3,2,2,3,4,19,20,21,6,23,8,8,10,12,1,1,1,1,2,2,4,4,4,
4,6,6,8,8,8,8,9,9,11,11,15,15,19,19,20,20,21,21],,[1,2,3,4,5,6,7,8,9,10,11,1,
13,14,15,16,17,18,19,20,21,22,3,24,25,26,5,29,28,31,30,33,32,35,34,37,36,39,
38,41,40,43,42,45,44,47,46,49,48,51,50,53,52,55,54],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,18,1,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,28,29,52,53,54,55]],
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[TENSOR,[44,2]],
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[TENSOR,[47,2]],
[TENSOR,[47,3]],[4200,-24,40,8,-30,15,-3,-8,-8,0,0,0,-6,-2,3,3,1,-1,0,0,0,0,0,
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[TENSOR,[50,2]],
[TENSOR,[50,3]],[6075,27,-45,-21,0,0,0,-9,-1,3,3,0,0,0,0,0,0,0,-1,1,1,0,0,0,0,
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[TENSOR,[53,2]],
[TENSOR,[53,3]]],
[(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)]);
ARC("O8+(2).3","CAS",[rec(name:="o8p2d",
permchars:=(),
permclasses:=(),
text:=Concatenation(
"  test:= 1. o.r., sym 2 decompose correctly      \n",
""))]);
ALF("O8+(2).3","O8+(2).3.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,
35,36,36,37,37,38,38,39,39,40,40,41,41]);
ALN("O8+(2).3",["o8p2d"]);

MOT("O8+(2).3.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]"
],
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[]);
ARC("O8+(2).3.2","CAS",[rec(permchars:=( 4, 5)( 6, 8,10, 7,11, 9)(12,15)(13,
14)(16,18,24,28,36,40,44,34,38,30,26,21,23,19,17,25,22,20)(27,31)(29,35,41,43,
47,54,62,64,51,61,49,58,46,42,48,53,63,52,60,50,57,45,33,39,37)(55,67)(56,66),
permclasses:=(10,11)(14,15)(17,18)(28,30,39,64,60,54,44,32,45,33,49,37,59,51,
 40,67,65,61,56,47,34,52,41,66,63,58,50,38,62,57,48,36,55,46,35,53,42)
(29,31,43),
name:="o8p2s3")]);
ALF("O8+(2).3.2","Fi22",[1,3,3,4,5,6,7,9,9,13,12,14,18,18,17,23,23,22,26,
28,27,32,35,39,38,46,52,5,8,18,20,25,31,39,40,39,48,58,60,63,64,2,4,10,10,
11,10,13,15,16,20,19,21,24,27,28,30,34,41,41,47,47,45,51,57,59,64,65],[
"fusion map is unique, equal to that on the CAS table"
]);
ALN("O8+(2).3.2",["O8+(2).S3","O8+(2):S3","o8p2s3","f22m4"]);

MOT("O8+(3)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"
],
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0,0,0,0,0,0],[291200,0,0,0,-128,1544,-400,680,680,680,-400,-400,-76,194,-76,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[291200,0,0,0,-128,
1544,680,680,-400,-400,-400,680,-76,-76,-76,194,-4,-13,0,0,0,0,0,0,0,0,0,0,0,
-8,0,0,0,0,0,0,-8,-8,16,16,16,-8,0,0,0,4,4,4,-2,4,4,4,-8,1,0,0,0,-4,-4,-4,-4,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[332800,1280,1280,1280,0,-1568,160,160,
160,160,160,160,-56,-56,-56,-56,34,16,0,0,0,0,0,0,0,0,-16,-16,-16,0,-16,-16,
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-1,0,0,0,0,0,0,2,2,2,2,2,2,0,0,0],[332800,1280,-1280,-1280,0,-1568,160,160,
160,160,160,160,-56,-56,-56,-56,34,16,0,0,0,0,0,0,0,0,-16,16,16,0,-16,16,16,
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0,0,0,0,2,-2,-2,2,-2,-2,0,0,0],[332800,-1280,1280,-1280,0,-1568,160,160,160,
160,160,160,-56,-56,-56,-56,34,16,0,0,0,0,0,0,0,0,16,-16,16,0,16,-16,16,16,
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0,0,0,-2,2,-2,-2,2,-2,0,0,0],[332800,-1280,-1280,1280,0,-1568,160,160,160,160,
160,160,-56,-56,-56,-56,34,16,0,0,0,0,0,0,0,0,16,16,-16,0,16,16,-16,16,16,-16,
0,0,0,0,0,0,-2,-2,2,0,0,0,0,0,0,0,0,0,-1,0,0,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,1,
1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,0,0,0,0,0,0,-2,
-2,2,-2,-2,2,0,0,0],[419328,896,0,0,0,-576,72,-576,-576,72,-576,-576,72,72,72,
72,-36,18,0,16,0,0,0,-7,8,8,32,0,0,0,-4,0,0,-4,0,0,0,0,0,0,0,0,-4,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,-9,0,0,-9,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,-2,0,0,-2,0,0,0,0,0,0,0,2,-1,-1,2,-1,-1,-1,0,0,-1,0,0,1,0,0],[419328,0,896,
0,0,-576,-576,72,-576,-576,72,-576,72,72,72,72,-36,18,0,0,16,0,0,8,-7,8,0,32,
0,0,0,-4,0,0,-4,0,0,0,0,0,0,0,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-9,0,0,-9,0,0,
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-1,-1,2,-1,0,-1,0,0,-1,0,0,1,0],[419328,0,0,896,0,-576,-576,-576,72,-576,-576,
72,72,72,72,72,-36,18,0,0,0,16,0,8,8,-7,0,0,32,0,0,0,-4,0,0,-4,0,0,0,0,0,0,0,
0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-9,0,0,-9,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,-2,0,0,-2,0,0,0,0,0,-1,-1,2,-1,-1,2,0,0,-1,0,0,-1,0,0,1],[
465920,-1792,0,0,0,-640,656,-640,-640,656,-640,-640,8,8,8,8,8,8,0,0,0,0,0,10,
0,0,-64,0,0,0,8,0,0,8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-10,8,8,
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0,0,0,0,0,0,1,0,0,1,0,0,2,0,0,2,0,0,0,0,0],[465920,0,-1792,0,0,-640,-640,656,
-640,-640,656,-640,8,8,8,8,8,8,0,0,0,0,0,0,10,0,0,-64,0,0,0,8,0,0,8,0,0,0,0,0,
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0,0,0,0],[465920,0,0,-1792,0,-640,-640,-640,656,-640,-640,656,8,8,8,8,8,8,0,0,
0,0,0,0,0,10,0,0,-64,0,0,0,8,0,0,8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,
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0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,2,0,0,2,0,0,0],[491400,-840,-840,-840,200,
-675,540,540,540,540,540,540,54,54,54,54,-27,-27,0,0,0,0,16,0,0,0,-3,-3,-3,
-19,-12,-12,-12,-12,-12,-12,-4,-4,-4,-4,-4,-4,-3,-3,-3,2,2,2,2,-1,-1,-1,-1,-1,
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[531441,729,729,729,81,0,0,0,0,0,0,
0,0,0,0,0,0,0,-27,9,9,9,-3,-9,-9,-9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1],[716800,0,0,
0,0,1408,-320,-320,-320,-320,-320,-320,-104,-104,-104,-104,-32,-14,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,4,4,4,4,
4,4,4,4,4,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
E(13)+E(13)^3+E(13)^4+E(13)^9+E(13)^10+E(13)^12,E(13)^2+E(13)^5+E(13)^6
 +E(13)^7+E(13)^8+E(13)^11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[113,2]]],
[(95,96),(  3,  4)(  8,  9)( 11, 12)( 15, 16)( 21, 22)( 25, 26)( 28, 29)
( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 48, 49)( 52, 53)( 59, 60)
( 62, 63)( 66, 67)( 70, 71)( 73, 74)( 76, 77)( 79, 80)( 82, 83)( 87, 88)
( 90, 91)( 93, 94)( 98, 99)(101,102)(104,105)(107,108)(110,111)(113,114),
(  2,  3)(  7,  8)( 10, 11)( 14, 15)( 20, 21)( 24, 25)( 27, 28)( 31, 32)
( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 47, 48)( 51, 52)( 58, 59)( 61, 62)
( 65, 66)( 69, 70)( 72, 73)( 75, 76)( 78, 79)( 81, 82)( 86, 87)( 89, 90)
( 92, 93)( 97, 98)(100,101)(103,104)(106,107)(109,110)(112,113),(  3,  4)
(  8, 12)(  9, 11)( 13, 14)( 21, 22)( 25, 26)( 28, 29)( 32, 36)( 33, 35)
( 38, 42)( 39, 41)( 44, 45)( 46, 47)( 50, 51)( 59, 63)( 60, 62)( 64, 65)
( 68, 69)( 73, 74)( 76, 77)( 79, 83)( 80, 82)( 85, 86)( 90, 94)( 91, 93)
( 98, 99)(101,105)(102,104)(107,111)(108,110)(113,114)]);
ARC("O8+(3)","CAS",[rec(name:="o8p3",
permchars:=(),
permclasses:=(  6, 13, 20)(  7, 14, 21)(  8, 16, 23, 10, 15, 22)
(  9, 18, 24, 94, 73, 98,111, 92, 69, 37, 53, 65, 35, 46, 59, 29, 42, 58, 27,
  40, 54, 67, 34, 44, 50, 63, 30, 52, 64, 32, 45, 51, 66, 33, 47, 60, 31, 43,
  49, 62, 28, 41, 56, 11, 17, 25, 95,113,101,105,108, 93, 71, 39, 57, 12, 19)
( 26, 96,114,102,107, 91, 72, 97,110, 90, 70, 38, 55,109, 88, 87, 86, 85, 84,
  83, 82, 80, 81, 78, 77, 76, 75, 74, 99,112,100,103,104,106, 89, 68, 36, 48,
  61),
text:=Concatenation(
"names:=o8p3; pom8[3,+]\n",
"               d4[3]     [lie-not.]\n",
"    order: 2^12.3^12.5^2.7.13 = 4,952,179,814,400\n",
"    number of classes: 114\n",
"    source:hunt, d.c.\n",
"          the character table of an eight-dimensional\n",
"          orthogonal group\n",
"          math.comp. 28\n",
"          [1974],659-660\n",
"          loose microfiche suppl. d1-e5\n",
"    test: 1. o.r., sym 2 decompose correctly\n",
"    comments: -\n",
""))]);
ARC("O8+(3)","isSimple",true);
ARC("O8+(3)","extInfo",["2^2","S4"]);
ARC("O8+(3)","maxes",["O7(3)","O8+(3)M2","O8+(3)M3","O8+(3)M4","O8+(3)M5",
"O8+(3)M6","3^6:L4(3)","O8+(3)M8","O8+(3)M9","O8+(2)","O8+(3)M11",
"O8+(3)M12","O8+(3)M13","O8+(3)M14","2.U4(3).(2^2)_{122}","O8+(3)M16",
"O8+(3)M17","(A4xU4(2)):2","O8+(3)M19","O8+(3)M20","O8+(3)M21","O8+(3)M22",
"O8+(3)M23","(A6xA6):2^2","O8+(3)M25","O8+(3)M26","O8+(3)M27"]);
ALF("O8+(3)","O8+(3).2_1",[1,2,3,4,5,6,7,8,9,10,8,9,11,11,12,12,13,14,15,
16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,28,29,31,32,33,34,32,33,35,
36,37,38,38,39,39,40,40,41,41,42,43,44,45,46,47,48,49,47,48,50,50,51,51,
52,52,53,53,54,55,56,57,58,59,60,61,62,63,61,62,64,65,65,66,66,67,68,69,
70,68,69,71,72,73,74,75,76,77,78,79,77,78,80,81,82,83,81,82,84,85,86]);
ALF("O8+(3)","O8+(3).2_2",[1,2,3,3,4,5,6,7,7,8,9,9,10,11,12,12,13,14,15,
16,17,17,18,19,20,20,21,22,22,23,24,25,25,26,27,27,28,29,29,30,31,31,32,
33,33,34,35,36,36,37,38,39,39,40,41,42,43,44,45,45,46,47,47,48,49,50,50,
51,52,53,53,54,55,55,56,57,57,58,59,59,60,61,61,62,63,64,65,65,66,67,67,
68,69,69,70,71,72,73,73,74,75,75,76,77,77,78,79,79,80,81,81,82,83,83]);
ALF("O8+(3)","O8+(3).3",[1,2,2,2,3,4,5,5,5,6,6,6,7,8,8,8,9,10,11,12,12,12,
13,14,14,14,15,15,15,16,17,17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,
23,23,23,24,25,25,25,26,27,28,29,30,30,30,31,31,31,32,33,33,33,34,35,35,
35,36,36,36,37,37,37,38,38,38,39,39,39,40,41,42,42,42,43,43,43,44,44,44,
45,46,47,47,47,48,48,48,49,49,49,50,50,50,51,51,51,52,52,52]);
ALF("O8+(3)","O8+(3).4",[1,2,3,3,4,5,6,7,7,6,7,7,8,8,8,8,9,10,11,12,13,13,
14,15,16,16,17,18,18,19,20,21,21,20,21,21,22,23,23,22,23,23,24,25,25,26,
26,26,26,27,27,27,27,28,29,30,31,32,33,33,32,33,33,34,34,34,34,35,35,35,
35,36,37,37,38,39,39,40,41,41,40,41,41,42,43,43,43,43,44,45,45,44,45,45,
46,47,48,49,49,50,51,51,50,51,51,52,53,53,52,53,53,54,55,55]);
ALF("O8+(3)","B",[1,3,3,3,5,7,6,6,6,6,6,6,7,7,7,7,6,7,12,14,14,14,12,18,
18,18,26,26,26,28,22,22,22,22,22,22,27,27,27,27,27,27,22,22,22,29,29,29,
29,24,24,24,24,28,31,41,41,47,47,47,47,47,47,46,46,46,46,47,47,47,47,49,
49,49,60,60,60,64,64,64,64,64,64,60,68,68,68,68,66,66,66,66,66,66,75,75,
79,79,79,81,81,81,81,81,81,94,94,94,94,94,94,104,104,104],[
"fusion map is unique"
]);
ALN("O8+(3)",["o8p3"]);

MOT("O8+(3).2_1",
[
"origin: ATLAS of finite groups, tests: 1.o.r."
],
[9904359628800,52254720,52254720,52254720,663552,136048896,37791360,18895680,
18895680,37791360,472392,472392,104976,26244,27648,5760,5760,5760,3072,3600,
3600,3600,93312,93312,93312,20736,15552,7776,7776,15552,10368,5184,5184,10368,
1296,1296,1296,648,648,648,648,324,56,64,64,5832,2916,2916,5832,729,729,81,81,
80,80,80,3456,3456,3456,864,432,432,864,384,108,108,144,72,72,144,26,26,56,56,
56,90,45,45,90,216,108,108,216,40,40,40,24261120,1036800,26127360,48384,9216,
768,23328,12960,12960,7776,7776,648,648,324,324,2304,768,768,256,80,80,3600,
100,100,80,46656,7776,7776,864,648,576,288,288,96,72,108,108,40,288,288,96,96,
72,72,26,26,56,56,56,56,90,90,108,108,40,40,40,40],
[,[1,1,1,1,1,6,7,8,9,10,11,12,13,14,5,2,3,4,5,20,21,22,6,6,6,6,7,8,9,10,7,8,9,
10,13,13,13,11,12,13,13,14,43,15,19,46,47,48,49,50,51,52,53,20,21,22,26,26,26,
31,32,33,34,26,38,39,27,28,29,30,72,71,43,43,43,76,77,78,79,46,47,48,49,54,55,
56,1,1,2,2,2,5,6,7,10,7,10,13,13,14,14,15,15,15,15,17,18,20,21,22,20,23,27,30,
23,35,23,27,30,26,35,46,49,54,58,59,58,59,60,63,72,71,73,73,73,73,76,79,80,83,
85,85,86,86],[1,2,3,4,5,1,1,1,1,1,1,1,1,1,15,16,17,18,19,20,21,22,2,3,4,5,2,3,
4,2,5,5,5,5,2,3,4,5,5,5,5,5,43,44,45,6,6,6,6,6,6,11,12,54,55,56,15,15,15,15,
15,15,15,19,15,15,16,17,18,16,71,72,73,74,75,20,21,22,20,23,24,25,23,84,85,86,
87,88,89,90,91,92,87,88,88,87,87,88,88,87,88,102,103,104,105,106,107,108,109,
110,111,89,89,89,90,89,91,91,91,92,90,93,93,124,102,102,103,104,102,102,131,
132,133,134,135,136,108,108,112,112,141,142,143,144],,[1,2,3,4,5,6,7,8,9,10,
11,12,13,14,15,16,17,18,19,1,1,1,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,
38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,2,3,4,57,58,59,60,61,62,63,64,
65,66,67,68,69,70,72,71,73,74,75,7,8,9,10,80,81,82,83,16,17,18,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,88,88,88,87,112,113,
114,115,116,117,118,119,120,121,122,123,89,125,126,127,128,129,130,132,131,
134,133,136,135,94,95,139,140,106,106,107,107],,[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,
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[TENSOR,[123,2]],[419328,896,0,0,0,-576,72,-576,-576,72,72,72,-36,18,0,16,0,0,
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[TENSOR,[133,2]],[465920,0,0,-1792,0,-640,-640,-640,656,-640,8,8,8,8,0,0,0,0,
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[TENSOR,[141,2]],
[GALOIS,[141,2]],
[TENSOR,[143,2]]],
[(143,144),(141,142)(143,144),(133,134)(135,136),( 71, 72)(131,132),(  7, 10)
( 11, 12)( 27, 30)( 31, 34)( 38, 39)( 40, 41)( 46, 49)( 50, 51)( 52, 53)
( 60, 63)( 65, 66)( 67, 70)( 76, 79)( 80, 83)( 94, 95)( 96, 97)( 98, 99)
(113,114)(118,119)(122,123)(129,130)(137,138)(139,140),(  3,  4)(  8,  9)
( 17, 18)( 21, 22)( 24, 25)( 28, 29)( 32, 33)( 36, 37)( 47, 48)( 55, 56)
( 58, 59)( 61, 62)( 68, 69)( 74, 75)( 77, 78)( 81, 82)( 85, 86)(103,104)
(106,107)(109,110)(125,126)(127,128)(135,136)(141,143)(142,144)]);
ALF("O8+(3).2_1","O8+(3).4",[1,2,3,3,4,5,6,7,7,6,8,8,9,10,11,12,13,13,14,
15,16,16,17,18,18,19,20,21,21,20,22,23,23,22,24,25,25,26,26,27,27,28,29,
30,31,32,33,33,32,34,34,35,35,36,37,37,38,39,39,40,41,41,40,42,43,43,44,
45,45,44,46,47,48,49,49,50,51,51,50,52,53,53,52,54,55,55,56,57,58,59,60,
61,62,63,63,64,64,65,65,66,67,68,69,69,70,71,71,72,73,73,74,75,76,76,77,
78,79,80,80,81,82,83,83,84,85,85,86,86,87,87,88,89,90,90,91,92,93,93,94,
94,95,96,95,96]);
ALF("O8+(3).2_1","O8+(3).(2^2)_{111}",[1,2,3,4,5,6,7,8,9,7,10,10,11,12,13,
14,15,16,17,18,19,20,21,22,23,24,25,26,27,25,28,29,30,28,31,32,33,34,34,
35,35,36,37,38,39,40,41,42,40,43,43,44,44,45,46,47,48,49,50,51,52,53,51,
54,55,55,56,57,58,56,59,60,61,62,63,64,65,66,64,67,68,69,67,70,71,72,73,
74,75,76,77,78,79,80,80,81,81,82,82,83,84,85,86,87,88,89,90,91,92,93,94,
95,96,96,97,98,99,100,100,101,102,103,103,104,105,106,107,108,109,109,110,
111,112,113,114,115,116,116,117,117,118,119,120,121]);
ALF("O8+(3).2_1","O8+(3).A4",[1,2,2,2,3,4,5,5,5,5,6,6,7,8,9,10,10,10,11,
12,12,12,13,13,13,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,19,20,21,
22,23,24,24,24,24,25,25,26,26,27,27,27,28,28,28,29,29,29,29,30,31,31,32,
32,32,32,33,34,35,35,35,36,36,36,36,37,37,37,37,38,38,38,39,40,41,42,43,
44,45,46,46,47,47,48,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,62,63,
64,65,66,66,67,68,69,69,70,71,72,73,74,75,75,76,77,78,79,80,81,82,82,83,
83,84,85,86,87]);
ALF("O8+(3).2_1","O8+(3).D8",[1,2,3,3,4,5,6,7,7,6,8,8,9,10,11,12,13,13,14,
15,16,16,17,18,18,19,20,21,21,20,22,23,23,22,24,25,25,26,26,27,27,28,29,
30,31,32,33,33,32,34,34,35,35,36,37,37,38,39,39,40,41,41,40,42,43,43,44,
45,45,44,46,47,48,49,49,50,51,51,50,52,53,53,52,54,55,55,56,57,58,59,60,
61,62,63,63,64,64,65,65,66,67,68,69,69,70,71,71,72,73,73,74,75,76,76,77,
78,79,80,80,81,82,83,83,84,85,85,86,86,87,87,88,89,90,90,91,92,93,93,94,
94,95,96,95,96]);
ALF("O8+(3).2_1","O8+(3).S4",[1,2,2,2,3,4,5,5,5,5,6,6,7,8,9,10,10,10,11,
12,12,12,13,13,13,14,15,15,15,15,16,16,16,16,17,17,17,18,18,19,19,20,21,
22,23,24,24,24,24,25,25,26,26,27,27,27,28,28,28,29,29,29,29,30,31,31,32,
32,32,32,33,34,35,35,35,36,36,36,36,37,37,37,37,38,38,38,39,40,41,42,43,
44,45,46,46,47,47,48,48,49,50,51,52,52,53,54,54,55,56,56,57,58,59,59,60,
61,62,63,63,64,65,66,66,67,68,68,69,69,70,70,71,72,73,73,74,75,76,76,77,
77,78,79,78,79]);

MOT("O8+(3).2_2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"
],
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1296,648,1296,1296,648,324,56,64,64,5832,2916,5832,2916,1458,1458,729,162,162,
81,80,40,3456,1728,864,432,864,432,384,216,216,108,144,72,144,72,26,26,56,28,
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1259712,349920,279936,155520,34992,34992,15552,5832,5184,3888,3888,2916,2592,
648,324,192,64,240,240,2592,864,864,432,288,288,288,72,72,72,72,28,648,324,
216,54,54,54,54,40,24,26,26,28,30,30,36],
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90,90,96,94,95,96,96,128,105,130,131,132,107,108,109],,[1,2,3,4,5,6,7,8,9,10,
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37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,2,3,56,57,58,59,60,61,62,
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112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,86,129,131,
130,132,91,93,135],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
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49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,71,70,2,3,74,
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,
119,84,121,122,123,124,125,126,127,128,129,131,130,87,133,134,135],,,,,,[1,2,
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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,
57,58,59,60,61,62,63,64,65,66,67,68,69,1,1,72,73,74,75,76,77,78,79,80,81,82,
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,
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ALF("O8+(3).2_2","O8+(3).D8",[1,2,3,4,5,6,7,6,7,8,8,8,9,10,11,12,13,14,15,
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"fusion map is unique up to table automorphisms"
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ALF("O8+(3).2_2","O8+(3).S4",[1,2,2,3,4,5,5,5,5,6,6,6,7,8,9,10,10,11,12,
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MOT("O8+(3).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"
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ALF("O8+(3).3","O8+(3).3.2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
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ALF("O8+(3).3","O8+(3).A4",[1,2,3,4,5,5,6,6,7,8,9,10,11,12,13,14,15,15,16,
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ALF("O8+(3).3","O8+(3).S4",[1,2,3,4,5,5,6,6,7,8,9,10,11,12,13,14,15,15,16,
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MOT("O8+(3).3.2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13]"
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[( 45, 46)( 72, 73)(120,121)]);
ALF("O8+(3).3.2","Fi23",[1,3,4,6,7,5,6,8,7,8,10,11,10,13,17,19,24,16,25,
22,24,21,28,20,26,27,29,30,31,34,35,33,36,34,37,39,43,49,44,43,46,54,55,
50,57,58,60,62,61,70,71,75,5,8,22,28,33,36,36,35,48,44,54,69,72,68,76,84,
82,87,93,95,96,2,4,9,9,11,12,15,14,18,20,15,23,21,18,26,19,27,23,22,25,28,
31,30,38,40,45,42,45,51,50,47,53,51,55,52,56,59,66,67,68,67,73,69,72,74,
82,85,86,88,90,91,94],[
"fusion map is unique up to table automorphisms"
]);
ALN("O8+(3).3.2",["O8+(3).S3","o8+(3):s3"]);

MOT("O8+(3).4",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13],\n",
"2nd power map determined only up to matrix automorphism (141,143)(142,144)"
],
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[(133,135)(134,136),( 95, 96)(133,135)(134,136),( 91, 92)(141,143)(142,144),
( 91, 92)( 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)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144),( 46, 47)( 88, 89)(137,139)(138,140),( 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)(127,128)(129,130)(131,132)(133,134)
(135,136)(137,138)(139,140)(141,144)(142,143)]);
ALF("O8+(3).4","O8+(3).D8",[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,
91,92,93,94,95,96,193,193,194,194,195,195,196,196,197,197,198,198,199,199,
200,200,201,201,202,202,203,203,204,204,205,205,206,206,207,207,208,208,
209,209,210,210,211,211,212,212,213,213,214,214,215,216,216,215]);
ALF("O8+(3).4","O8+(3).S4",[1,2,2,3,4,5,5,6,7,8,9,10,10,11,12,12,13,13,14,
15,15,16,16,17,17,18,19,20,21,22,23,24,24,25,26,27,27,28,28,29,29,30,31,
32,32,33,34,35,35,36,36,37,37,38,38,39,40,41,42,43,44,45,46,47,48,49,50,
51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,
75,76,77,78,79,148,148,149,149,150,150,151,151,152,152,153,153,154,154,
155,155,156,156,157,157,158,158,159,159,160,160,161,161,162,162,163,163,
164,164,165,165,166,166,167,167,168,168,169,169,170,171,171,170]);

MOT("O8+(3).(2^2)_{111}",
[
"table of the normal subgroup O8+(3).V4 in O8+(3).S4,\n",
"constructed by T. Breuer using the tables of O8+(3), O8+(3).2_1"
],
[19808719257600,104509440,104509440,104509440,1327104,272097792,37791360,
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ALF("O8+(3).(2^2)_{111}","O8+(3).D8",[1,2,3,3,4,5,6,7,7,8,9,10,11,12,13,
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MOT("O8+(3).D8",
[
"constructed (by accident) in April 2003 using Dixon's algorithm and\n",
"character theoretic methods"
],
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MOT("O8+(3).A4",
[
"origin: constructed by T. Breuer using the tables of O8+(3), O8+(3).3,\n",
"O8+(3).(2^2)_{111},\n",
"tests: 1.o.r., pow[2,3,5,7,13,]"
],
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ALF("O8+(3).A4","O8+(3).S4",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
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81,82,82,83,83,84,84,85,85,86,86,87,87,88,88,89,89,90,90,91,91,92,92,93,
93,94,94,95,95,96,96,97,97,98,98,99,99,100,100]);

MOT("O8+(3).S4",
[
"origin: constructed by T. Breuer using the tables of O8+(3), O8+(3).A4,\n",
"O8+(3).2_2, O8+(3).4, B\n",
"tests: 1.o.r., pow[2,3,5,7,13,]"
],
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[GALOIS,[162,2]],
[GALOIS,[164,2]],
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[GALOIS,[166,2]],
[TENSOR,[170,1]]],
[( 78, 79)(166,167),( 74, 75)(170,171),( 33, 34)( 71, 72)( 99,100)(142,143)
(168,169)]);
ALF("O8+(3).S4","B",[1,3,5,7,6,7,6,7,12,14,12,18,26,28,22,27,22,29,24,28,
31,41,41,47,46,47,49,60,64,60,68,66,75,75,79,81,94,104,4,4,9,10,13,17,30,
25,25,25,30,30,38,38,38,43,50,50,50,56,55,67,58,69,63,72,61,97,102,121,
121,122,129,129,132,133,133,139,156,164,164,6,7,27,29,46,46,46,47,64,64,
68,96,96,95,109,123,123,131,158,160,160,2,5,11,11,14,15,23,20,21,24,23,29,
21,24,28,23,27,27,29,41,41,48,52,65,59,65,62,66,71,70,62,66,73,77,92,93,
95,93,96,103,123,130,130,135,138,141,157,16,16,32,33,37,40,45,45,74,74,74,
106,119,124,118,114,126,127,161,161,176,176,178,179]);
ALN("O8+(3).S4",["BM12"]);

LIBTABLE.LOADSTATUS.ctoorth2:="userloaded";
ALN:= NotifyCharTableName;

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