Quelle  ctborth2.tbl   Sprache: unbekannt

#############################################################################
##
#W  ctborth2.tbl                GAP table library               Thomas Breuer
##
##  This file contains the Brauer character tables related to the
##  orthogonal groups $O_8^+(2)$ and $O_8^+(3)$ (see file 'ctoorth2.tbl'),
##  modulo all prime divisors of the group order.
##
#H  ctbllib history
#H  ---------------
#H  $Log: ctborth2.tbl,v $
#H  Revision 4.15  2012/03/28 13:02:17  gap
#H  added three missing groups of table automorphisms
#H      TB
#H
#H  Revision 4.14  2011/09/28 12:12:37  gap
#H  removed Revision entries and SET_TABLEFILENAME calls
#H      TB
#H
#H  Revision 4.13  2010/12/01 17:38:05  gap
#H  fixed the table of 2^2.O8+(2).3.2 mod 5
#H  (the old table had been computed with a version of the GS3 construction
#H  that assumed the classes in the ordinary table to be ordered suitably)
#H      TB
#H
#H  Revision 4.12  2010/09/15 08:23:18  gap
#H  do not use `factorblocks' encoding in some Brauer tables where the ordering
#H  of ordinary irreducibles does not fit to that in the factors
#H      TB
#H
#H  Revision 4.11  2009/05/11 16:08:54  gap
#H  more tables of non-bicyclic extensions of ATLAS groups
#H      TB
#H
#H  Revision 4.10  2005/08/10 14:42:21  gap
#H  added modular tables of 2^2.O8+(2)
#H      TB
#H
#H  Revision 4.9  2004/08/31 11:51:19  gap
#H  added 3.A6.2^2 mod 2, 5,
#H        A6.2^2 mod 2, 5,
#H        L2(25).2^2 mod 2, 3, 5, 13,
#H        L2(49).2^2 mod 2, 3, 5,
#H        L2(81).2^2 mod 2, 5, 41,
#H        L2(81).(2x4) mod 2,
#H        3.L3(4).2^2 mod 2, 5, 7,
#H        3.L3(4).3.2_2 mod 2, 5, 7,
#H        L3(4).2^2 mod 2, 3, 5, 7,
#H        L3(4).3.2_2 mod 3, 5, 7,
#H        L3(4).3.2_3 mod 3, 5, 7,
#H        L3(4).D12 mod 2, 3, 5, 7,
#H        L3(9).2^2 mod 2, 3, 5, 7, 13,
#H        O8+(2).3.2 mod 3, 5, 7,
#H        O8+(3).3.2 mod 5, 7, 13,
#H        O8+(3).(2^2)_{111} mod 2, 5, 7, 13,
#H        O8+(3).(2^2)_{122} mod 2, 5, 7, 13,
#H        O8+(3).D8 mod 2, 5, 7, 13,
#H        O8+(3).A4 mod 2, 5, 7, 13,
#H        O8+(3).S4 mod 13,
#H        3_1.U4(3).2_2' mod 2, 5, 7,
#H        3_2.U4(3).2_3' mod 2, 5, 7,
#H        3_2.U4(3).(2^2)_{133} mod 2, 5, 7,
#H        6_2.U4(3).2_3' mod 5, 7,
#H        U4(3).(2^2)_{122} mod 2, 3, 5, 7,
#H        U4(3).(2^2)_{133} mod 2, 3, 5, 7,
#H        U4(3).D8 mod 2, 3, 5, 7,
#H        U6(2).3.2 mod 3, 5, 7, 11,
#H  extended `InfoText' values, added missing table automorphisms
#H      TB
#H
#H  Revision 4.8  2002/07/15 15:17:10  gap
#H  added O8+(2).3.2 mod 2
#H      TB
#H
#H  Revision 4.7  2002/07/08 15:58:02  gap
#H  added O8+(3).S4 mod 7
#H      TB
#H
#H  Revision 4.6  2002/06/13 13:58:57  gap
#H  added tables of $O_8^+(3).S_4$ mod 2 and 5
#H      TB
#H
#H  Revision 4.5  2001/11/06 08:40:46  gap
#H  adjustments that make it easier to use the data under GAP 3
#H      TB
#H
#H  Revision 4.4  2001/10/24 15:39:32  gap
#H  added 2-modular table of O8+(3).3.2
#H      TB
#H
#H  Revision 4.3  2001/05/04 16:46:07  gap
#H  first revision for ctbllib
#H
#H
#H  tbl history (GAP 4)
#H  -------------------
#H  (Rev. 4.3 of ctbllib coincides with Rev. 4.2 of tbl in GAP 4)
#H  
#H  RCS file: /gap/CVS/GAP/4.0/tbl/ctborth2.tbl,v
#H  Working file: ctborth2.tbl
#H  head: 4.2
#H  branch:
#H  locks: strict
#H  access list:
#H  symbolic names:
#H   GAP4R2: 4.2.0.8
#H   GAP4R2PRE2: 4.2.0.6
#H   GAP4R2PRE1: 4.2.0.4
#H   GAP4R1: 4.2.0.2
#H  keyword substitution: kv
#H  total revisions: 3; selected revisions: 3
#H  description:
#H  ----------------------------
#H  revision 4.2
#H  date: 1999/03/09 16:50:08;  author: gap;  state: Exp;  lines: +10 -13
#H  removed warnings about possibly incorrect irreducibles
#H  (J"urgen M"uller proved the existence of the dubious modules)
#H  
#H      TB
#H  ----------------------------
#H  revision 4.1
#H  date: 1997/07/17 15:35:42;  author: fceller;  state: Exp;  lines: +2 -2
#H  for version 4
#H  ----------------------------
#H  revision 1.1
#H  date: 1996/10/21 15:58:39;  author: sam;  state: Exp;
#H  first proposal of the table library
#H  ==========================================================================
##

TEXT1:= "origin: modular ATLAS of finite groups, tests: DEC, TENS";

MBT("2.O8+(2).2",3,
TEXT1,
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[,[[1,3],[2,3]],2],
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MBT("2.O8+(2).2",5,
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[,[[1,3],[2,4],[3,5],[4,5]],2],
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MBT("2.O8+(2).2",7,
TEXT1,
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MBT("2.O8+(2)",3,
TEXT1,
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MBT("2.O8+(2)",5,
TEXT1,
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[,[[1,3],[2,4],[3,5],[4,5]]],
[[[1,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0],[-1,0,1,0,0,0,0,0,0,0],[0,-1,0,
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MBT("2.O8+(2)",7,
TEXT1,
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MBT("2^2.O8+(2)",3,
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MBT("2^2.O8+(2)",5,
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MBT("2^2.O8+(2)",7,
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MBT("2^2.O8+(2).2",3,
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,
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MBT("2^2.O8+(2).2",5,
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],
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MBT("2^2.O8+(2).2",7,
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],
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MBT("O8+(3)",3,
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MBT("O8+(3)",5,
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MBT("O8+(3)",7,
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MBT("O8+(3).2_1",13,
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10,9,16,17,19,18,20,21,22,23,24,25,26,27,28,1,2,4,3,29,30,32,31,34,33,36,35,38
,37,39,40,41,42,44,43,45,46,48,47,50,49,2,1,3,4,4,3,1,2,3,4,2,1,5,6,8,7,10,9,
51,53,52,54,55,57,56,58,59,61,60,62,63,64,65,67,66,69,68,70,71,72,73,75,74,5,6
,8,7,10,9,76,77,78,80,79,40,39,42,41,43,44,82,81,83,84,85,86,87,88,89,91,90,93
,92,95,94,96,97,99,98,101,100,105,104,103,102,1,2,4,3,106,107,108,109,110,111,
112,113,114,115,117,116],
[2,2,2,2,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
],
[[15,20,23,28,58,78,84,87,108,181],[16,19,24,29,57,77,83,88,109,180],[18,21,25
,31,60,80,81,85,110,183],[17,22,26,30,59,79,82,86,111,182]],
[,,,,[[1,3],[2,4],[3,5],[4,5]],5,5,5,5,5,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[[1,2],[2
,3,4]],39,39,39,39,39],
[[[0,1,1,1,-1,-1,0,0,1,0],[1,-1,-1,-1,1,1,0,0,-1,0],[0,0,-1,-1,1,1,0,0,-1,0],[
0,-1,0,-1,1,1,0,0,-1,0],[0,0,0,1,0,0,0,0,0,0],[-1,1,1,2,-1,-2,0,0,2,0],[0,0,0,
-1,0,1,0,0,0,0],[0,0,0,-1,0,0,1,0,0,0],[0,0,0,-1,0,0,0,1,0,0],[0,0,0,1,0,-1,0,
0,0,1]],1,1,1],
0,
[(),( 95, 96)( 97, 98)(134,135)(136,137)(173,174)(175,176),
( 53, 54)( 93, 94)(132,133)(171,172),
(  3,  4)(  8,  9)( 15, 16)( 19, 20)( 23, 24)( 26, 27)( 29, 30)( 38, 39)
( 43, 44)( 46, 47)( 51, 52)( 56, 57)( 59, 60)( 74, 75)( 77, 78)( 88, 89)
( 90, 91)( 97, 98)(100,139)(101,140)(102,141)(103,142)(104,143)(105,144)
(106,145)(107,146)(108,147)(109,148)(110,149)(111,150)(112,151)(113,152)
(114,153)(115,154)(116,155)(117,156)(118,157)(119,158)(120,159)(121,160)
(122,161)(123,162)(124,163)(125,164)(126,165)(127,166)(128,167)(129,168)
(130,169)(131,170)(132,171)(133,172)(134,173)(135,174)(136,175)(137,176)
(138,177)
,
(  2,  3)(  7,  8)( 14, 15)( 18, 19)( 22, 23)( 25, 26)( 28, 29)( 37, 38)
( 42, 43)( 45, 46)( 50, 51)( 55, 56)( 58, 59)( 61,100)( 62,101)( 63,102)
( 64,103)( 65,104)( 66,105)( 67,106)( 68,107)( 69,108)( 70,109)( 71,110)
( 72,111)( 73,112)( 74,113)( 75,114)( 76,115)( 77,116)( 78,117)( 79,118)
( 80,119)( 81,120)( 82,121)( 83,122)( 84,123)( 85,124)( 86,125)( 87,126)
( 88,127)( 89,128)( 90,129)( 91,130)( 92,131)( 93,132)( 94,133)( 95,134)
( 96,135)( 97,136)( 98,137)( 99,138)(152,153)(155,156)(166,167)(168,169)
(175,176)
],
0);

MBT("O8+(3).(2^2)_{111}",7,
[
"constructed using `PossibleCharacterTablesOfTypeGV4"
],
[1,2,4,3,5,6,8,7,10,9,1,2,4,3,11,12,13,14,16,15,18,17,19,20,22,21,23,1,2,4,3,
24,25,26,27,28,29,30,31,33,32,1,2,4,3,34,35,36,37,38,5,6,8,7,10,9,40,39,41,42,
44,43,46,45,47,48,49,50,52,51,53,54,56,55,58,57,59,60,62,61,64,63,66,65,67,68,
70,69,71,72,73,74,76,75,77,79,78,80,81,83,82,84,85,87,86,88,89,90,91,93,92,94,
95,97,96,98,99,100,101,102,103,105,104,107,106,108,109,110,111,113,112,5,6,8,7
,10,9,114,1,2,4,3,115,116,118,117,120,119,122,121,123,124,125,126,128,127,129,
130,131,132,133,134,135,1,2,4,3,137,136,138,139,141,140,142,143,145,144,146,
147,149,148,150,151,153,152,155,154,157,156,159,158,160,161,162,163,164,165,
166,167,168,169,171,170],
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[],
[[[1,2],[2,4],[3,6],[4,5],[5,7],[6,7]],1,1,1,[[1,2],[2,3],[3,4,5]],5,5,5,5,5],
[],
0,
[(),(155,156)(200,201),(112,113)(157,158),(110,111)(202,203),
( 58, 59)(106,107)(151,152)(196,197),
(  3,  4)(  8,  9)( 15, 16)( 19, 20)( 22, 23)( 26, 27)( 29, 30)( 32, 33)
( 40, 41)( 45, 46)( 48, 49)( 51, 52)( 56, 57)( 61, 62)( 64, 65)( 67, 68)
( 82, 83)( 85, 86)( 88, 89)(101,102)(103,104)(110,112)(111,113)(114,159)
(115,160)(116,161)(117,162)(118,163)(119,164)(120,165)(121,166)(122,167)
(123,168)(124,169)(125,170)(126,171)(127,172)(128,173)(129,174)(130,175)
(131,176)(132,177)(133,178)(134,179)(135,180)(136,181)(137,182)(138,183)
(139,184)(140,185)(141,186)(142,187)(143,188)(144,189)(145,190)(146,191)
(147,192)(148,193)(149,194)(150,195)(151,196)(152,197)(153,198)(154,199)
(155,200)(156,201)(157,202)(158,203)
,
(  2,  3)(  7,  8)( 14, 15)( 18, 19)( 21, 22)( 25, 26)( 28, 29)( 31, 32)
( 39, 40)( 44, 45)( 47, 48)( 50, 51)( 55, 56)( 60, 61)( 63, 64)( 66, 67)
( 69,114)( 70,115)( 71,116)( 72,117)( 73,118)( 74,119)( 75,120)( 76,121)
( 77,122)( 78,123)( 79,124)( 80,125)( 81,126)( 82,127)( 83,128)( 84,129)
( 85,130)( 86,131)( 87,132)( 88,133)( 89,134)( 90,135)( 91,136)( 92,137)
( 93,138)( 94,139)( 95,140)( 96,141)( 97,142)( 98,143)( 99,144)(100,145)
--> --------------------

--> maximum size reached

--> --------------------