Quelle ctbline3.tbl
Sprache: unbekannt
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#############################################################################
##
#W ctbline3.tbl GAP table library Thomas Breuer
##
## This file contains the Brauer character tables related to the linear
## group $L_3(4)$ of the ATLAS modulo all prime divisors of the group order.
##
#H ctbllib history
#H ---------------
#H $Log: ctbline3.tbl,v $
#H Revision 4.12 2012/03/21 16:50:16 gap
#H added many automatically constructed Brauer tables
#H TB
#H
#H Revision 4.11 2011/09/28 12:12:36 gap
#H removed Revision entries and SET_TABLEFILENAME calls
#H TB
#H
#H Revision 4.10 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 4.9 2009/05/11 16:08:53 gap
#H more tables of non-bicyclic extensions of ATLAS groups
#H TB
#H
#H Revision 4.8 2005/09/12 08:46:37 gap
#H added modular tables of (2^2x3).L3(4).2_2, (2^2x3).L3(4).2_3,
#H 2^2.L3(4).2_2, 2^2.L3(4).2_3
#H TB
#H
#H Revision 4.7 2005/08/10 14:41:38 gap
#H added modular tables of 2^2.L3(4) and (2^2x3).L3(4)
#H TB
#H
#H Revision 4.6 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 4.5 2002/07/15 15:16:45 gap
#H added L3(4).3.2_2 and L3(4).3.2_3 mod 2
#H TB
#H
#H Revision 4.4 2001/05/04 16:56:35 gap
#H first revision for ctbllib
#H
#H
#H tbl history (GAP 4)
#H -------------------
#H (Rev. 4.4 of ctbllib coincides with Rev. 4.3 of tbl in GAP 4)
#H
#H RCS file: /gap/CVS/GAP/4.0/tbl/ctbline3.tbl,v
#H Working file: ctbline3.tbl
#H head: 4.3
#H branch:
#H locks: strict
#H access list:
#H symbolic names:
#H GAP4R2: 4.3.0.8
#H GAP4R2PRE2: 4.3.0.6
#H GAP4R2PRE1: 4.3.0.4
#H GAP4R1: 4.3.0.2
#H keyword substitution: kv
#H total revisions: 4; selected revisions: 4
#H description:
#H ----------------------------
#H revision 4.3
#H date: 1999/07/14 11:39:37; author: gap; state: Exp; lines: +4 -3
#H cosmetic changes for the release ...
#H
#H TB
#H ----------------------------
#H revision 4.2
#H date: 1999/05/25 15:34:50; author: gap; state: Exp; lines: +3 -3
#H fixed table of 12_2.L3(4)mod7
#H (was consistent but wrong,
#H the faithful characters with b5 irrationalities were not
#H closed under the conjugation with *7)
#H
#H TB
#H ----------------------------
#H revision 4.1
#H date: 1997/07/17 15:35:05; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 15:58:28; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
TEXT1:= "origin: modular ATLAS of finite groups, tests: DEC, TENS";
MBT("12_1.L3(4).2_1",5,
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rec(version:=1,
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,
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MBT("2.L3(4).2_1",5,
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MBT("2.L3(4).2_2",3,
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MBT("2.L3(4).2_2",5,
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MBT("2.L3(4).2_2",7,
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MBT("2.L3(4).2_3",3,
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MBT("2.L3(4).2_3",5,
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[,[[1,2,4],[3,4]],2],
[],
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0);
MBT("2.L3(4).2_3",7,
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MBT("2.L3(4)",3,
TEXT1,
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MBT("2.L3(4)",5,
TEXT1,
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MBT("2.L3(4)",7,
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MBT("2.L3(4).(2^2)_{123}",3,
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MBT("2.L3(4).(2^2)_{123}",5,
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MBT("2.L3(4).(2^2)_{123}",7,
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MBT("2.L3(4).(2^2)_{123*}",3,
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MBT("2.L3(4).(2^2)_{123*}",5,
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MBT("2.L3(4).(2^2)_{123*}",7,
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"constructed using `PossibleCharacterTablesOfTypeGV4'"
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MBT("2.L3(4).(2^2)_{12*3}",3,
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MBT("2.L3(4).(2^2)_{12*3}",5,
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[(23,24),(21,22)(27,28),(16,17)(21,22)],
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MBT("2.L3(4).(2^2)_{12*3}",7,
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MBT("2.L3(4).(2^2)_{1*23}",3,
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MBT("2.L3(4).(2^2)_{1*23}",5,
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"constructed using `PossibleCharacterTablesOfTypeGV4'"
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MBT("2.L3(4).(2^2)_{1*23}",7,
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[(28,29),(21,22)(25,26),(16,17)(25,26)],
0);
MBT("2.L3(4).(2^2)_{12*3*}",3,
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"constructed using `PossibleCharacterTablesOfTypeGV4'"
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[(16,17)(28,29),(14,15)(25,26)(30,31),(14,15)(16,17)(18,19)(20,21)(23,24)],
0);
MBT("2.L3(4).(2^2)_{12*3*}",5,
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"constructed using `PossibleCharacterTablesOfTypeGV4'"
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[(18,19)(34,35),(14,15)(16,17)(29,30)(31,32),
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MBT("2.L3(4).(2^2)_{12*3*}",7,
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"constructed using `PossibleCharacterTablesOfTypeGV4'"
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[(14,15)(16,17)(18,19)(27,28)(29,30)(32,33)(34,35),
(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)],
0);
MBT("2.L3(4).(2^2)_{1*23*}",3,
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"constructed using `PossibleCharacterTablesOfTypeGV4'"
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[[23,24,25,26,31]],
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[["L3(4).2^2",0]],
[(16,17)(28,29),(14,15)(25,26)(30,31),(14,15)(16,17)(18,19)(20,21)(23,24)],
0);
MBT("2.L3(4).(2^2)_{1*23*}",5,
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"constructed using `PossibleCharacterTablesOfTypeGV4'"
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[],
[["L3(4).2^2",0]],
[(18,19)(34,35),(14,15)(16,17)(29,30)(31,32),
(14,15)(16,17)(20,21)(22,23)(24,25)(27,28)(34,35)],
0);
MBT("2.L3(4).(2^2)_{1*23*}",7,
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"constructed using `PossibleCharacterTablesOfTypeGV4'"
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[["L3(4).2^2",0]],
[(14,15)(16,17)(18,19)(27,28)(29,30)(32,33)(34,35),
(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)],
0);
MBT("2.L3(4).(2^2)_{1*2*3}",3,
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
],
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[[23,24,25,26,31]],
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[[[1,0,1,0,-1],[1,0,0,0,0],[0,1,0,0,0],[-1,0,0,0,1],[-1,0,-1,1,1]]],
[["L3(4).2^2",0]],
[(16,17)(28,29),(14,15)(25,26)(30,31),(14,15)(16,17)(18,19)(20,21)(23,24)],
0);
MBT("2.L3(4).(2^2)_{1*2*3}",5,
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"constructed using `PossibleCharacterTablesOfTypeGV4'"
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[(18,19)(34,35),(14,15)(16,17)(29,30)(31,32),
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0);
MBT("2.L3(4).(2^2)_{1*2*3}",7,
[
"constructed using `PossibleCharacterTablesOfTypeGV4'"
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[["L3(4).2^2",0]],
[(14,15)(16,17)(18,19)(27,28)(29,30)(32,33)(34,35),
(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)],
0);
MBT("2.L3(4).(2^2)_{1*2*3*}",3,
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],[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[-1,-1,0,-1,0,0,1,1],[0,0,0,1,1,0,-1,-1]
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0);
MBT("2.L3(4).(2^2)_{1*2*3*}",5,
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[(23,24),(21,22)(27,28),(16,17)(21,22)],
0);
MBT("2.L3(4).(2^2)_{1*2*3*}",7,
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[["L3(4).2^2",0]],
[(28,29),(21,22)(25,26),(16,17)(25,26)],
0);
MBT("(2^2x3).L3(4)",5,
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26,25,26,27,28,29,30,31,32,33,34,35,35,36,37,38,39,38,39,40,41,42,43,44,45,46,
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[[[1,4],[2..4]],,,,,,,,,[[1,2,4],[3,4]],,,,,,,,,1,1,,,,,[[1,3,4],[2..4]],25,,,
,,,,,,10,,,25,25,,,,,,,,,10,,,25,25],
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[
(47,59)(48,60)(49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)
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(39,45)(40,46)(49,50)(53,54)(57,58)(61,62)(65,66)(69,70)
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(38,39)(43,46)(44,45)(49,57)(50,58)(51,55)(52,56)(61,69)(62,70)(63,67)(64,68)
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( 2, 7, 8)( 3, 4,10)( 6,11,12)(14,19,20)(15,16,22)(18,23,24)(26,27,28)
(29,35,41)(30,37,43)(31,39,45)(32,36,42)(33,38,44)(34,40,46)(48,53,54)
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0);
MBT("(2^2x3).L3(4)",7,
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21,22,23,24,25,26,21,22,27,27,28,29,27,30,31,32,31,32,33,34,35,36,31,32,37,37,
38,39,37,40,41,42,41,42,43,44,45,46,41,42],
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[[[1,2],[2,5],[3..5]],,,,,,[[1..3],[3,5],[4,5]],,,,[[1,4,5],[2,4,5],[3..5]],11
,,,,,,,,,[[1,3,4],[2,5],[3..5]],21,,,,,7,,,,21,21,,,,,7,,,,21,21],
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0,
[
(47,59)(48,60)(49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)
(58,70)
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(39,45)(40,46)(49,50)(53,54)(57,58)(61,62)(65,66)(69,70)
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(38,39)(43,46)(44,45)(49,57)(50,58)(51,55)(52,56)(61,69)(62,70)(63,67)(64,68)
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( 2, 7, 8)( 3, 4,10)( 6,11,12)(14,19,20)(15,16,22)(18,23,24)(26,27,28)
(29,35,41)(30,37,43)(31,39,45)(32,36,42)(33,38,44)(34,40,46)(48,53,54)
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MBT("(2^2x3).L3(4).2_2",5,
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[1,1,0,0,0,0,0,0],
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[[[1,3,4],[2,3,4]],1],
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[["L3(4).2_2",0],["2.L3(4).2_2",0],["2^2.L3(4).2_2",0],["3.L3(4).2_2",21],[
"6.L3(4).2_2",8]],
[(48,49),( 3, 4)(10,11)(24,27)(25,26)(30,31)(37,38),
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0);
MBT("(2^2x3).L3(4).2_2",7,
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[["L3(4).2_2",0],["2.L3(4).2_2",0],["2^2.L3(4).2_2",0],["3.L3(4).2_2",21],[
"6.L3(4).2_2",8]],
[(46,47),(30,39)(31,38)(32,36)(33,37)(34,35),
( 3, 4)(10,11)(24,27)(25,26)(30,31)(34,35)(38,39)],
0);
MBT("(2^2x3).L3(4).2_3",5,
[
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"6.L3(4).2_3",8]],
[(46,47),(44,45),( 3, 4)(10,11)(24,27)(25,26)(30,31)(34,35)(38,39),
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0);
MBT("(2^2x3).L3(4).2_3",7,
[
"constructed using `BrauerTableOfTypeMGA'"
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[["L3(4).2_3",0],["2.L3(4).2_3",0],["2^2.L3(4).2_3",0],["3.L3(4).2_3",21],[
"6.L3(4).2_3",8]],
[(46,47),( 3, 4)(10,11)(24,27)(25,26)(30,31)(37,38),
(28,35)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(50,52)(51,53)],
0);
MBT("(2^2x3).L3(4).3",5,
[
"constructed using `BrauerTableOfTypeMGA'"
],
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[1,1,0,0,0,0,0,0],
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[[[1,3,4],[2,3,4]],1],
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LIBTABLE.LOADSTATUS.ctbline3:="userloaded";
#############################################################################
##
#E
[ Dauer der Verarbeitung: 0.29 Sekunden
(vorverarbeitet)
]
|
2026-04-02
|