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products/Sources/formale Sprachen/GAP/pkg/ctbllib/data/ (GAP Algebra Version 4.15.1^©) Datei vom 1.2.2023 mit Größe 95 kB

Impressum ctborth2.tbl Sprache: unbekannt

Spracherkennung für: .tbl vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]

#############################################################################
##
#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";

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MBT("2.O8+(2)",5,
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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,
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( 40, 41)( 45, 46)( 48, 49)( 51, 52)( 56, 57)( 61, 62)( 64, 65)( 67, 68)
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(115,160)(116,161)(117,162)(118,163)(119,164)(120,165)(121,166)(122,167)
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(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)
(101,146)(102,147)(103,148)(104,149)(105,150)(106,151)(107,152)(108,153)
(109,154)(110,155)(111,156)(112,157)(113,158)(172,173)(175,176)(178,179)
(191,192)(193,194)(200,202)(201,203)
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MBT("O8+(3).(2^2)_{111}",13,
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27,28,29,30,31,32,33,1,2,4,3,34,35,36,37,38,39,40,41,42,43,44,46,45,48,47,1,2,
4,3,50,49,52,51,53,54,55,56,58,57,59,60,62,61,64,63,65,66,68,67,70,69,72,71,73
,74,76,75,77,78,79,80,82,81,83,85,84,86,87,89,88,90,91,93,92,94,95,96,97,99,98
,100,101,103,102,104,105,106,107,108,109,111,110,113,112,114,115,116,117,119,
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155,157,156,159,158,163,162,161,160,165,164,166,167,169,168,170,171,173,172,
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( 41, 42)( 46, 47)( 49, 50)( 52, 53)( 57, 58)( 60, 61)( 63, 64)( 66, 67)
( 69, 70)( 84, 85)( 87, 88)( 90, 91)(103,104)(105,106)(110,111)(114,116)
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MBT("O8+(3).(2^2)_{122}",2,
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MBT("O8+(3).(2^2)_{122}",5,
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MBT("O8+(3).(2^2)_{122}",7,
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91,92,93,94,95,96,97,98,99,100,101,102,103,6,5,8,7,9,6,5,8,7,104,105,106,107,2
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MBT("O8+(3).(2^2)_{122}",13,
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99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118
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MBT("O8+(3).D8",2,
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MBT("O8+(3).S4",5,
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MBT("O8+(3).S4",7,
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MBT("O8+(3).S4",13,
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MBT("2.O8+(3)",3,
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0,
rec(version:=1,
date:="31.08.2018"));

MBT("2^2.O8+(3)",3,
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RootDatumInfo:=[[[2,0,-1,0],[0,2,-1,0],[-1,-1,2,-1],[0,0,-1,2]],[[1,0,0,0],[0,
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version:=1,
date:="31.08.2018"));

MBT("2^2.O8+(3).3",3,
[
"origin: computed as extension of 2^2.O8+(3) mod 3 by 3-singular autom."
],
[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3],
[12],
[[95,96,98,102,103,104,106,108,110,128,129,136,159,161,162,168,170,173]],
[],
[[[1,1,-2,0,0,1,0,-1,0,1,1,1,0,0,1,1,-1,-1],[1,3,-4,0,0,2,0,-2,0,2,2,2,0,0,2,2
,-2,-2],[0,0,9,0,4,-3,-3,1,-4,0,-1,0,0,1,0,0,0,0],[1,2,-7,0,-3,4,2,-2,2,0,0,1,
1,0,1,2,-1,-2],[0,2,2,-1,7,-2,-2,-1,-3,5,5,2,-1,1,2,1,-2,-2],[-3,-4,-1,0,-4,-1
,3,3,4,-4,-3,-4,0,-1,-4,-4,4,4],[-4,-10,6,0,-4,-4,3,6,4,-7,-6,-7,0,-1,-7,-7,7,
7],[1,2,16,-1,7,-5,-5,1,-8,1,-1,1,0,2,1,1,-1,-1],[-1,-6,9,2,-8,-2,1,4,1,-10,-
11,-4,1,-1,-5,-3,5,5],[-2,-6,24,0,8,-11,-6,6,-7,-2,-3,-4,-1,1,-3,-5,3,5],[-2,-
3,-31,1,-12,9,10,-1,15,0,4,-2,0,-3,-2,-2,2,1],[1,-2,-9,2,-8,4,2,0,5,-3,-2,-1,0
,-2,-1,-1,1,2],[-6,-13,-2,1,-11,-2,6,7,9,-11,-9,-9,0,-3,-9,-9,9,10],[2,-3,4,2,
-8,3,-2,1,0,-7,-9,-1,2,-1,-1,0,1,2],[0,-3,15,1,7,-6,-7,2,-6,1,0,0,-2,0,0,-1,0,
2],[-4,-13,37,0,3,-15,-7,10,-9,-12,-15,-8,0,1,-8,-8,8,10],[3,12,-26,-2,4,10,0,
-9,2,12,14,8,0,1,8,8,-8,-10],[2,4,50,-3,21,-17,-16,1,-24,1,-5,3,0,5,4,3,-3,-2]
]],
[["O8+(3).3",0]],
[(13,14)(26,27)(30,31)],
0,
rec(version:=1,
date:="17.12.2018"));

LIBTABLE.LOADSTATUS.ctborth2:="userloaded";

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