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|
#############################################################################
##
#W ctbunit4.tbl GAP table library Thomas Breuer
##
## This file contains the Brauer character tables related to the unitary
## group $U_6(2)$ of the ATLAS (see file 'ctounit4.tbl'),
## modulo all prime divisors of the group order.
##
#H ctbllib history
#H ---------------
#H $Log: ctbunit4.tbl,v $
#H Revision 4.11 2012/03/02 08:40:59 gap
#H added the Brauer tables of 3.U6(2).3.2 and 2^2.U6(2).3.2
#H TB
#H
#H Revision 4.10 2012/01/26 11:21:57 gap
#H added table automorphisms of U6(2).3.2 mod 2
#H TB
#H
#H Revision 4.9 2011/09/28 12:12:38 gap
#H removed Revision entries and SET_TABLEFILENAME calls
#H TB
#H
#H Revision 4.8 2010/09/15 08:23:19 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 4.7 2009/05/11 16:08:54 gap
#H more tables of non-bicyclic extensions of ATLAS groups
#H TB
#H
#H Revision 4.6 2005/08/10 14:44:02 gap
#H added modular tables of 2^2.U6(2) and (2^2x3).U6(2)
#H TB
#H
#H Revision 4.5 2004/08/31 11:51:20 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 4.4 2002/07/15 15:18:07 gap
#H added U6(2).3.2 mod 2
#H TB
#H
#H Revision 4.3 2001/05/04 16:46:53 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/ctbunit4.tbl,v
#H Working file: ctbunit4.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: 1999/07/14 11:39:37; author: gap; state: Exp; lines: +4 -3
#H cosmetic changes for the release ...
#H
#H TB
#H ----------------------------
#H revision 4.1
#H date: 1997/07/17 15:37:12; author: fceller; state: Exp; lines: +2 -2
#H for version 4
#H ----------------------------
#H revision 1.1
#H date: 1996/10/21 15:58:57; author: sam; state: Exp;
#H first proposal of the table library
#H ==========================================================================
##
TEXT1:= "origin: modular ATLAS of finite groups, tests: DEC, TENS";
MBT("2.U6(2).2",11,
TEXT1,
[56,56,57,58,59,60,61,62,63,64,65,66,67,68,56,56,69,70,71,72,73,56,56,74,75,
56,56,76,77,78,79,80,81,82,84,83,85,86,87,88,56,56,89,90,91,92,93,94,95],
[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],
[],
[[[1,4],[2,5],[3,7],[3,6],[4,8],[5,9],[7,11],[6,10],[8,11],[9,10]]],
[],
[["U6(2).2",0]],
[(104,105),( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)
( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 88, 89)( 90, 91)( 92, 93)( 94, 95)
( 96, 97)( 98, 99)(100,101)(102,103)(106,107)(108,109)(110,111)(112,113)],
0,
rec(version:=1,
date:="03.02.93"));
MBT("2.U6(2).2",3,
"origin: modular ATLAS of finite groups",
[7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,7,7,8,9],
[6,1,1],
[[66,67,68,69,70,71,74,75,76,77,80,90,91,94,97]],
[,[[1,3],[2,3]],2],
[[[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[-1,0,1,0,0,
0,0,0,0,0,0,0,0,0,0],[0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0],[0,-1,0,0,1,0,0,0,0,0,0,
0,0,0,0],[-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0],[0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0],[0,
0,0,-1,0,0,0,1,0,0,0,0,0,0,0],[1,-1,0,0,0,-1,0,0,1,0,0,0,0,0,0],[-1,1,0,0,-1,
0,0,0,0,1,0,0,0,0,0],[1,1,0,0,0,0,-1,-1,0,0,1,0,0,0,0],[0,1,0,1,0,0,0,0,0,1,0,
0,-1,0,1],[0,-1,-1,-2,-1,-1,2,2,0,-1,-2,0,1,1,-1],[0,-1,0,-1,0,0,0,0,0,-1,0,0,
1,0,0],[-1,0,-1,0,0,0,0,0,-1,0,0,1,0,0,0]]],
[["U6(2).2",0]],
[(49,50),(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(43,44)(45,46)(47,48)],
0,
rec(version:=1,
date:="23.07.92"));
MBT("2.U6(2).2",5,
TEXT1,
[42,43,42,43,44,45,46,47,46,47,42,43,48,49,50,42,43,51,52,53,44,45,44,45,44,
45,54,55,56,46,47,57,58,59,60,61,62,63,64,65,66,67,46,47],
[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],
[],
[[[1,3],[2,4],[3,5],[4,5]],1,1,1,[[1,4],[2,3],[3,5],[4,5]],5],
[],
[["U6(2).2",0]],
[(102,103),(96,97),( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)
( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 84, 85)( 86, 87)( 88, 89)
( 90, 91)( 92, 93)( 94, 95)( 98, 99)(100,101)],
0,
rec(version:=1,
date:="30.04.92"));
MBT("2.U6(2).2",7,
TEXT1,
[54,55,56,57,58,59,56,57,60,61,62,63,64,65,66,57,56,67,68,69,70,71,56,57,72,
73,57,56,74,75,76,77,78,80,79,56,57,81,82,83,84,85,86,87,88,89,90,91],
[0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[],
[,,[[1,6],[2,3],[4,5],[3,4],[5,7],[6,7]],3],
[],
[["U6(2).2",0]],
[(108,109),(102,103),( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)
( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 88, 89)( 90, 91)( 92, 93)
( 94, 95)( 96, 97)( 98, 99)(100,101)(104,105)(106,107)(110,111)],
0,
rec(version:=0,
date:="00.00.00"));
MBT("2.U6(2)",11,
TEXT1,
[41,42,43,44,45,46,47,41,48,49,50,51,41,52,41,53,54,55,56,57,58,59,60,41,61,
62,63,64,65],
[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],
[],
[[[1,4],[2,3,5],[4,6],[5,7],[6,7]]],
[],
[["U6(2)",0]],
[(25,27)(26,28)(48,50)(49,51)(56,57)(60,61)(70,72)(71,73),(18,19)(46,47)
(64,65)],
0,
rec(version:=0,
date:="00.00.00"));
MBT("2.U6(2)",3,
TEXT1,
[6,6,6,6,6,6,6,6,7,6,7],
[6,1],
[[47,48,49,51,52,54,55,62,64]],
[,[[1,3],[2,3]]],
[[[1,0,0,0,0,0,0,0,0],[-1,1,0,0,0,0,0,0,0],[-1,0,1,0,0,0,0,0,0],[0,-1,0,1,0,0,
0,0,0],[0,0,-1,0,1,0,0,0,0],[1,0,0,-1,0,1,0,0,0],[1,0,0,-1,0,0,1,0,0],[0,-1,
-1,2,0,-1,-1,0,1],[-1,-1,0,0,-1,0,0,1,0]]],
[["U6(2)",0]],
[(28,30)(29,31),(12,13)(24,25)],
0);
MBT("2.U6(2)",5,
TEXT1,
[35,35,36,37,37,35,38,39,40,35,41,42,43,36,36,36,44,45,46,37,47,48,49,50,51,
52,53,37],
[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[],
[[[1,3],[2,4],[3,5],[4,5]],1,[[1,4],[2,3],[3,5],[4,5]]],
[],
[["U6(2)",0]],
[(52,54)(53,55),(23,25)(24,26)(46,48)(47,49)(56,57)(60,61)(68,70)(69,71),
(18,19)(44,45)(64,65)],
0,
rec(version:=1,
date:="30.04.92"));
MBT("2.U6(2)",7,
TEXT1,
[41,42,43,42,44,45,46,47,48,42,49,50,51,52,42,53,42,54,55,56,57,58,42,59,60,
61,62,63,64,65],
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[],
[,[[1,6],[2,3],[4,5],[3,4],[5,7],[6,7]]],
[],
[["U6(2)",0]],
[(54,56)(55,57),(25,27)(26,28)(46,48)(47,49)(58,59)(62,63)(72,74)(73,75),
(18,19)(44,45)(66,67)],
0,
rec(version:=0,
date:="00.00.00"));
MBT("2^2.U6(2)",3,
"constructed using `PossibleCharacterTablesOfTypeV4G'",
[8,8,8,8,8,8,8,8,9,8,9,10,10,10,10,10,10,10,10,11,10,11],
[6,1,6,1],
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(302,305)(303,306)],
0,
rec(version:=1,
date:="03.02.93"));
MBT("3.U6(2).3",2,
TEXT1,
[5,5,5,6,6,6,5,5,5,6,6,6,5,5,5,6,6,6,5,5,5,6,6,6,5,5,5,6,6,6,5,5,5,6,6,6,5,5,
5,6,6,6,5,5,5,6,6,6,5,5,5,6,6,6,5,5,5,6,6,6],
[15,15],
[[115,116,117,121,122,123,133,134,135,139,140,141,145,146,147,151,152,153,157,
227,228,229,253,254,255,289,290,291,319,320],[118,119,120,124,125,126,136,137,
138,142,143,144,148,149,150,154,155,156,158,230,231,232,256,257,258,292,293,
294,322,323]],
[],
[[[-1,-2,0,1,-2,-2,0,0,1,-2,-1,-3,-1,0,0,-1,-2,-2,0,-1,-2,-1,0,-1,0,0,1,0,1,
0],[0,-1,-2,-2,1,-2,1,0,0,-3,-2,-1,0,-1,0,-2,-1,-2,0,-1,-1,-2,0,0,-1,0,0,1,0,
1],[-1,1,0,-1,-1,2,0,1,0,2,0,1,1,1,0,1,1,2,-1,0,1,1,0,1,1,1,0,0,-1,-1],[2,2,0,
-1,2,2,0,0,-1,2,1,3,1,0,0,1,2,2,0,1,2,1,0,1,0,0,-1,0,-1,0],[0,2,2,2,-1,2,-1,0,
0,3,2,1,0,1,0,2,1,2,0,1,1,2,0,0,1,0,0,-1,0,-1],[1,-1,1,1,1,-2,0,-1,0,-2,0,-1,
-1,-1,0,-1,-1,-2,1,0,-1,-1,0,-1,-1,-1,0,0,1,1],[-2,-2,-2,0,-2,-3,1,-1,1,-5,-3,
-4,-1,-2,0,-5,-3,-4,1,-2,-3,-3,0,-2,-1,0,1,0,2,1],[-1,-1,-1,-2,1,-1,1,1,-1,-1,
-2,0,1,0,-1,-1,-2,0,0,-1,0,-1,0,1,-1,0,0,1,-1,1],[0,0,0,0,-1,2,-1,1,1,3,2,1,0,
2,1,3,2,1,-1,1,1,2,0,1,2,1,0,0,-1,-2],[-2,-2,-1,1,-1,-3,1,-1,0,-5,-3,-4,-1,-2,
-1,-4,-4,-3,1,-2,-3,-3,0,-2,-2,-1,1,0,2,2],[1,0,0,-1,3,1,0,1,-1,2,1,3,1,1,0,3,
2,2,-1,1,2,1,0,2,0,0,-1,1,-2,0],[0,1,0,1,-1,3,-1,0,1,3,2,1,0,1,1,2,3,2,-1,1,1,
2,0,0,2,1,0,-1,0,-2],[2,1,-2,-5,5,2,1,0,-1,1,0,5,2,-1,0,0,3,2,0,1,3,0,0,2,-1,
0,-2,1,-2,1],[-1,3,2,3,-4,6,-1,1,0,8,4,3,1,3,0,5,3,6,-1,2,3,5,0,1,3,1,0,-2,-1,
-3],[-1,-4,0,3,0,-7,0,-1,1,-6,-1,-5,-3,-2,0,-3,-4,-6,2,-1,-4,-3,0,-3,-2,-2,1,
0,3,2],[-2,3,2,5,-6,3,-2,0,1,5,3,-1,-1,2,1,3,2,2,-1,1,0,3,0,-1,3,1,1,-2,1,
-3],[-1,-5,0,0,2,-9,1,-2,0,-10,-4,-6,-2,-4,-1,-7,-6,-7,2,-3,-5,-6,0,-3,-4,-2,
1,1,3,4],[4,3,-1,-5,4,6,0,1,-2,6,2,8,3,2,0,5,5,6,-2,2,5,3,0,4,1,1,-2,1,-4,
-1],[3,0,-1,-5,5,1,0,2,-1,4,2,6,3,2,1,5,5,3,-2,2,4,2,0,4,1,1,-2,2,-4,-1],[-2,
2,-1,0,-6,4,-1,0,2,3,1,-1,0,2,1,0,2,2,-1,0,0,2,0,-1,3,2,1,-2,1,-3],[-4,-5,-1,
1,-3,-9,2,-1,0,-10,-6,-8,-2,-3,-1,-7,-9,-7,2,-4,-6,-6,0,-3,-4,-2,2,1,3,4],[2,
-2,-4,-7,4,-2,1,0,0,-4,-3,1,1,-2,1,-3,1,-3,0,-1,0,-3,0,1,-1,1,-1,2,-1,1],[-3,
3,-1,-1,-6,5,0,1,0,4,-1,0,2,2,-1,0,0,4,-1,-1,1,2,0,1,2,2,1,-1,-1,-2],[-3,-5,1,
3,-3,-8,0,0,1,-6,-2,-7,-3,0,0,-2,-6,-6,1,-2,-5,-3,0,-2,-1,-1,2,1,2,1],[2,-1,2,
1,4,-5,0,-2,-1,-7,-2,-3,-3,-3,-1,-5,-4,-6,2,-1,-3,-3,0,-2,-3,-2,0,1,2,3],[5,5,
2,-2,4,7,-1,0,-2,6,2,7,2,0,0,3,4,5,-1,3,5,3,0,3,1,1,-2,0,-3,-1],[1,4,4,6,-3,3,
-2,-1,0,4,3,-1,-1,1,-1,2,0,1,0,1,1,3,0,-1,2,0,1,-2,1,-2],[-4,3,-4,0,-6,2,2,-2,
0,-7,-6,-6,-3,-4,-2,-11,-6,-3,2,-4,-4,-4,1,-4,-2,0,2,-2,4,2],[-2,-2,5,4,2,-4,
0,2,-2,0,-1,0,0,-1,-2,3,-5,0,0,0,0,0,0,3,-2,-2,0,2,-2,2],[7,0,0,-2,6,4,-2,0,2,
6,6,5,0,2,1,6,9,1,-2,4,4,4,0,2,5,2,-2,0,-2,-4]],[[0,-1,0,0,0,0,0,1,0,-1,-1,0,
-1,1,-1,-2,-1,1,0,0,-1,0,0,0,0,0,0,-1,1,0],[0,0,-1,0,0,0,0,0,1,0,-1,-1,-1,-1,
1,1,-2,-1,0,0,0,-1,0,0,0,-1,0,0,0,1],[0,1,1,1,1,1,1,0,0,2,3,2,2,0,0,2,4,1,-1,
1,2,2,1,1,1,0,-1,0,-1,-1],[1,1,0,0,0,0,0,-1,0,1,1,0,1,-1,1,2,1,-1,0,0,1,0,0,0,
0,0,0,1,-1,0],[0,1,1,0,0,0,0,0,-1,0,1,1,1,1,-1,-1,2,1,0,0,0,1,0,0,0,1,0,0,0,
-1],[0,-1,0,-1,-1,-1,-1,0,0,-2,-3,-2,-2,0,0,-2,-4,-1,1,-1,-2,-2,-1,-1,-1,0,1,
0,1,1],[0,-2,1,0,0,1,1,1,-1,-1,1,1,0,2,-2,-3,0,3,0,1,-1,1,1,0,0,0,0,-1,1,-1],[
0,-1,-3,0,-1,-1,-1,1,1,-2,-4,-2,-3,-1,1,0,-6,-3,1,-1,-1,-3,-1,0,-1,-1,0,0,1,
2],[-1,2,1,1,2,1,1,-1,1,4,4,2,3,-1,1,3,6,0,-1,1,3,3,1,1,2,0,-1,0,-2,-1],[-1,
-1,3,0,2,1,1,0,-1,1,3,2,2,2,-2,-2,5,4,-1,1,0,3,1,0,1,1,0,-1,0,-2],[1,-3,-3,-1,
-2,0,-1,1,0,-4,-5,-3,-4,0,0,-2,-8,-1,1,-1,-3,-4,-1,-1,-2,-1,1,0,2,2],[-1,3,-1,
2,1,0,0,-1,1,3,2,1,2,-2,2,5,4,-2,-1,0,3,1,0,1,1,0,-1,1,-2,0],[0,3,-1,0,1,1,1,
-1,0,4,5,2,4,-2,2,6,6,-1,-1,1,4,2,1,1,1,0,-1,2,-3,-1],[-2,-1,2,0,-1,0,0,1,-1,
-1,1,2,1,3,-3,-4,3,3,0,0,-1,2,0,0,0,2,0,-1,1,-2],[0,-4,-3,-2,-2,-3,-1,0,1,-4,
-7,-5,-5,-1,1,-3,-10,-3,2,-2,-4,-5,-2,-2,-2,-1,2,0,2,3],[0,-5,-1,-1,-3,-3,-2,
1,0,-6,-9,-5,-7,1,-1,-6,-13,-1,2,-2,-6,-6,-2,-2,-3,-1,2,-1,4,3],[2,3,-2,0,2,0,
0,-2,1,4,3,0,2,-4,4,8,3,-4,-1,0,4,0,0,1,1,-1,-1,2,-3,1],[-1,3,4,1,1,3,1,0,-2,
3,7,6,5,3,-3,-1,11,6,-2,2,2,6,2,1,2,2,-1,-1,-1,-4],[0,5,-4,2,-1,0,0,-1,2,4,2,
1,3,-4,4,9,3,-5,-1,0,5,0,0,2,1,-1,-2,2,-3,1],[-3,1,6,1,3,0,2,0,-1,4,7,5,5,4,
-3,-2,12,6,-2,2,2,7,2,1,3,2,-1,-2,-1,-4],[2,-7,-3,-4,-3,-1,-1,2,0,-7,-8,-5,-7,
1,0,-6,-14,0,2,-1,-6,-6,-1,-2,-3,-2,2,-1,4,3],[2,3,-2,1,0,3,1,0,0,3,5,3,3,-1,
1,6,4,0,-1,2,4,2,2,2,1,-1,-2,1,-2,-1],[-3,1,2,2,0,-1,0,1,0,0,0,2,0,2,-2,-3,3,
1,0,0,0,2,0,1,1,1,-1,-2,1,-1],[1,-4,0,-2,1,-1,0,0,1,-1,-3,-3,-3,-1,1,-2,-6,0,
1,0,-2,-2,0,-1,0,-2,1,-1,1,2],[0,5,5,2,2,2,0,-1,-2,2,5,4,3,1,-2,-1,8,2,-1,1,3,
4,1,1,1,2,-1,0,-1,-3],[2,-3,2,-1,-1,-1,-2,0,-1,-5,-7,-4,-5,0,-2,-7,-10,-1,2,
-2,-5,-3,-2,-2,-2,0,2,-1,3,2],[4,4,-1,1,1,1,-1,-2,0,2,1,-1,0,-3,2,5,-1,-4,0,1,
2,-1,0,0,0,-1,0,2,-2,1],[2,-8,7,-4,4,2,2,0,-2,-3,2,0,-3,4,-4,-9,-1,8,0,2,-4,2,
3,-2,0,0,2,-2,2,-2],[5,0,-10,0,-6,2,-2,2,0,-6,-9,-4,-6,-5,2,2,-15,-7,2,-2,-2,
-8,-2,1,-4,-2,0,2,2,4],[-6,9,4,6,4,-2,0,-2,2,8,6,3,6,-2,-1,5,14,-3,-2,0,6,6,0,
2,5,2,-2,0,-4,-2]]],
[["U6(2).3",0]],
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(56,57,58)(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),( 2, 3)( 5, 6)
( 8, 9)(12,13)(15,16)(17,20)(18,22)(19,21)(24,27)(25,29)(26,28)(31,32)(33,36)
(34,37)(35,38)(39,42)(40,43)(41,44)(45,48)(46,49)(47,50)(51,52)(53,56)(54,57)
(55,58)(59,60)(61,64)(62,65)(63,66)(67,70)(68,71)(69,72)(73,76)(74,77)(75,78)
(79,82)(80,83)(81,84)(85,94)(86,95)(87,96)(88,91)(89,92)(90,93)],
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0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
rec(version:=3,
date:="08.09.94"));
MBT("3.U6(2).3",5,
TEXT1,
[79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,
79,80,81,82,83,84,103,104,105,106,107,108,92,93,91,96,94,95,109,110,111,112,
113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,97,98,99,100,
101,102,129,130,131,132,133,134,135,136,79,80,81,82,83,84,137,138,139,140,141,
142,143,144,145,146,147,148,91,92,93,94,95,96,149,150,151,152,153,154,155,156,
157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,
176,177,178,97,98,99,100,101,102,179,180,92,93,91,96,94,95,79,80,81,82,83,84,
181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,
200,201,202,203,204,97,98,99,100,101,102,205,206,207,208,209,210,211,212,213,
215,216,214],
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[],
[[[1,2],[2,4],[3,5],[4,5]],1,1,1,1,1,,,,,,,[[1,3],[2,4],[3,5],[4,5]],13,13,13,
13,13,13,13,13,13,13,13],
[],
[["U6(2).3",0]],
[(268,269,270)(271,272,273),(106,107,108)(109,110,111)(112,113,114)
(115,116,117)(118,119,120)(121,122,123)(126,127,128)(129,130,131)(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)(159,160,161)(162,163,164)(165,166,167)(168,169,170)
(171,172,173)(174,175,176)(177,178,179)(180,181,182)(183,184,185)(188,189,190)
(191,192,193)(196,197,198)(199,200,201)(202,203,204)(205,206,207)(208,209,210)
(211,212,213)(214,215,216)(217,218,219)(220,221,222)(223,224,225)(226,227,228)
(229,230,231)(232,233,234)(235,236,237)(238,239,240)(241,242,243)(244,245,246)
(247,248,249)(250,251,252)(253,254,255)(256,257,258)(259,260,261)(262,263,264)
(265,266,267)(274,275,276)(277,278,279)(280,281,282)(283,284,285)(286,287,288)
(289,290,291)(292,293,294)(295,296,297),( 73, 76)( 74, 77)( 75, 78)(280,286)
(281,287)(282,288)(283,289)(284,290)(285,291),( 2, 3)( 5, 6)( 8, 9)
( 11, 12)( 14, 15)( 17, 18)( 21, 22)( 24, 25)( 27, 28)( 30, 31)( 33, 34)
( 35, 38)( 36, 40)( 37, 39)( 42, 43)( 45, 46)( 48, 49)( 51, 52)( 54, 55)
( 58, 59)( 61, 62)( 64, 65)( 66, 69)( 67, 71)( 68, 70)( 74, 75)( 77, 78)
( 79, 82)( 80, 84)( 81, 83)( 86, 87)( 88, 91)( 89, 93)( 90, 92)( 95, 96)
( 98, 99)(100,103)(101,105)(102,104)(106,109)(107,110)(108,111)(112,115)
(113,116)(114,117)(118,121)(119,122)(120,123)(124,125)(126,129)(127,130)
(128,131)(132,135)(133,136)(134,137)(138,141)(139,142)(140,143)(144,147)
(145,148)(146,149)(150,153)(151,154)(152,155)(156,159)(157,160)(158,161)
(162,165)(163,166)(164,167)(168,171)(169,172)(170,173)(174,177)(175,178)
(176,179)(180,183)(181,184)(182,185)(186,187)(188,191)(189,192)(190,193)
(194,195)(196,199)(197,200)(198,201)(202,205)(203,206)(204,207)(208,211)
(209,212)(210,213)(214,217)(215,218)(216,219)(220,223)(221,224)(222,225)
(226,229)(227,230)(228,231)(232,235)(233,236)(234,237)(238,241)(239,242)
(240,243)(244,247)(245,248)(246,249)(250,253)(251,254)(252,255)(256,259)
(257,260)(258,261)(262,265)(263,266)(264,267)(268,271)(269,272)(270,273)
(274,277)(275,278)(276,279)(280,283)(281,284)(282,285)(286,289)(287,290)
(288,291)(292,295)(293,296)(294,297)],
0,
rec(version:=1,
date:="30.04.92"));
MBT("3.U6(2).3",7,
"origin: modular ATLAS of finite groups",
[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,
136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,
155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,
174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,
193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,
212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,
231,232,139,140,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,
248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,
267,268,269,270,271,278,279,280,275,276,277,272,273,274,281,282,283,284,285,
286,287,288,289,290,291,292,293,294,295,296,297,298],
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[],
[["U6(2).3",0]],
[(112,113,114)(115,116,117)(118,119,120)(121,122,123)(124,125,126)
(127,128,129)(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)(159,160,161)(162,163,164)
(165,166,167)(168,169,170)(171,172,173)(174,175,176)(177,178,179)(180,181,182)
(183,184,185)(186,187,188)(189,190,191)(194,195,196)(197,198,199)(202,203,204)
(205,206,207)(208,209,210)(211,212,213)(214,215,216)(217,218,219)(220,221,222)
(223,224,225)(226,227,228)(229,230,231)(232,233,234)(235,236,237)(238,239,240)
(241,242,243)(244,245,246)(247,248,249)(250,251,252)(253,254,255)(256,257,258)
(259,260,261)(262,263,264)(265,266,267)(268,269,270)(271,272,273)(274,275,276)
(277,278,279)(280,281,282)(283,284,285)(286,287,288)(289,290,291)(292,293,294)
(295,296,297)(298,299,300)(301,302,303)(304,305,306)(307,308,309)(310,311,312)
(313,314,315),( 76, 79)( 77, 80)( 78, 81)(298,304)(299,305)(300,306)(301,307)
(302,308)(303,309),( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)
( 21, 22)( 24, 25)( 27, 28)( 30, 31)( 33, 34)( 36, 37)( 38, 41)( 39, 43)
( 40, 42)( 45, 46)( 48, 49)( 51, 52)( 54, 55)( 57, 58)( 61, 62)( 64, 65)
( 66, 69)( 67, 71)( 68, 70)( 74, 75)( 77, 78)( 80, 81)( 82, 85)( 83, 87)
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(106,109)(107,111)(108,110)(112,115)(113,116)(114,117)(118,121)(119,122)
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(113,129)(114,130)(115,127)(116,128)(117,125)(118,126)(133,135)(134,136)
(137,141)(138,142)(145,147)(146,148)(149,153)(150,154)(157,159)(158,160)
(161,165)(162,166)(169,171)(170,172)(173,177)(174,178)(181,183)(182,184)
(185,189)(186,190)(197,199)(198,200)(201,205)(202,206)(208,209)(211,212)
(213,215)(218,220)(219,221)(224,226)(225,227)(228,240)(229,241)(230,244)
(231,245)(232,242)(233,243)(234,250)(235,251)(236,248)(237,249)(238,246)
(239,247)(258,260)(259,261)(262,266)(263,267)(270,272)(271,273)(274,278)
(275,279)(280,283)(281,285)(282,284)(288,290)(289,291)(292,296)(293,297)
(298,301)(299,303)(300,302)(305,306)(307,309)(312,314)(313,315)(318,320)
(319,321)(324,326)(325,327)(328,332)(329,333)(334,346)(335,347)(336,350)
(337,351)(338,348)(339,349)(340,356)(341,357)(342,354)(343,355)(344,352)
(345,353)
,
( 2, 9)( 4, 11)( 6, 7)( 14, 21)( 16, 23)( 18, 19)( 26, 33)( 28, 35)
( 30, 31)( 41, 48)( 43, 50)( 45, 46)( 53, 60)( 55, 62)( 57, 58)( 65, 66)
( 74, 80)( 75, 84)( 76, 82)( 77, 83)( 78, 81)( 79, 85)( 93,100)( 95,102)
( 97, 98)(108,115)(110,117)(112,113)(120,127)(122,129)(124,125)(132,139)
(134,141)(136,137)(144,151)(146,153)(148,149)(156,163)(158,165)(160,161)
(168,175)(170,177)(172,173)(180,187)(182,189)(184,185)(192,193)(196,203)
(198,205)(200,201)(210,216)(211,220)(212,218)(213,219)(214,217)(215,221)
(229,236)(231,238)(233,234)(241,248)(243,250)(245,246)(253,254)(257,264)
(259,266)(261,262)(269,276)(271,278)(273,274)(287,294)(289,296)(291,292)
(304,310)(305,314)(306,312)(307,313)(308,311)(309,315)(323,330)(325,332)
(327,328)(335,342)(337,344)(339,340)(347,354)(349,356)(351,352)
],
0);
MBT("(2^2x3).U6(2)",7,
[
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
[1,1,2,3,4,1,5,6,7,8,9,10,11,12,13,14,15,1,16,17,18,19,20,21,22,23,24,25,26,27
,28,29,30,1,31,32,33,34,35,36,37,38,39,1,40,41,42,43,42,44,45,46,47,48,42,49,
50,51,52,42,53,42,54,55,56,57,58,42,59,60,61,62,63,64,65,66,67,68,69,70,71,72,
73,74,75,76,77,78,79,80,81,80,81,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,
95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115
,116,117,80,81,80,81,80,81,118,119,120,121,122,123,124,125,126,127,128,129,130
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146,147,140,141,140,141,148,149,150,151,152,153,154,155,156,157,158,159,160,
161,162,163,164,165,140,141,166,167,168,169,170,171,172,173,174,175,176,177,
178,179,180,181,182,183,184,185,186,185,187,188,189,190,191,185,192,193,194,
195,185,196,185,197,198,199,200,201,185,202,203,204,205,206,207,208,209,210,
211,212,209,210,213,214,209,210,215,216,209,210,209,210,217,218,219,220,221,
222,223,224,225,226,227,228,229,230,231,232,233,234,209,210,235,236,237,238,
239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,254,256,
257,258,259,260,254,261,262,263,264,254,265,254,266,267,268,269,270,254,271,
272,273,274,275,276,277,278,279,280,281,278,279,282,283,278,279,284,285,278,
279,278,279,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,
302,303,278,279,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,
319,320,321],
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,,,,,,,,,,,,,,,,,,,,,,,,,,42,,,,,,,,,,,,,,,,,,,,,,,,140,140,,,,,,,,,,,,,,,,,,,
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(276,288)(277,289)(278,290)(279,291)
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( 35, 36)( 46, 47)( 48, 49)( 50, 51)( 58, 59)( 60, 61)( 62, 63)( 66, 67)
( 80, 86)( 81, 87)( 82, 88)( 83, 89)( 84, 90)( 85, 91)( 98, 99)(100,101)
(102,103)(113,114)(115,116)(117,118)(125,126)(127,128)(129,130)(137,138)
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( 47, 51)( 54, 56)( 55, 57)( 58, 62)( 59, 63)( 69, 70)( 72, 73)( 75, 76)
( 77, 79)( 82, 84)( 83, 85)( 88, 90)( 89, 91)( 94, 96)( 95, 97)( 98,102)
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(275,279)(282,284)(283,285)(286,290)(287,291)(292,295)(293,297)(294,296)
(300,302)(301,303)(304,308)(305,309)(310,313)(311,315)(312,314)(317,318)
(319,321)(324,326)(325,327)(330,332)(331,333)(336,338)(337,339)(340,344)
(341,345)(348,350)(349,351)(352,356)(353,357)(358,370)(359,371)(360,374)
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( 30, 31)( 41, 48)( 43, 50)( 45, 46)( 53, 60)( 55, 62)( 57, 58)( 65, 66)
( 74, 80)( 75, 84)( 76, 82)( 77, 83)( 78, 81)( 79, 85)( 93,100)( 95,102)
( 97, 98)(108,115)(110,117)(112,113)(120,127)(122,129)(124,125)(132,139)
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(321,327)(335,342)(337,344)(339,340)(347,354)(349,356)(351,352)(359,366)
(361,368)(363,364)(371,378)(373,380)(375,376)
],
0);
MBT("(2^2x3).U6(2)",11,
[
"constructed using `PossibleCharacterTablesOfTypeV4G'"
],
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41,52,41,53,54,55,56,57,58,59,60,41,61,62,63,64,65,66,67,66,67,68,69,70,71,72,
73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,66,67,88,89,90,91,92,93,94,95,96,
97,98,99,100,101,102,103,104,105,66,67,106,107,108,109,110,111,112,113,114,115
,116,117,118,119,120,121,122,123,124,125,126,127,128,129,66,67,130,131,132,133
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151,152,153,140,141,154,155,156,157,140,141,158,159,160,161,140,141,162,163,
164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,
183,184,185,186,187,188,189,190,184,191,192,193,194,184,195,184,196,197,198,
199,200,201,202,203,184,204,205,206,207,208,209,210,209,210,211,212,213,214,
215,216,217,218,219,220,221,222,209,210,223,224,225,226,209,210,227,228,229,
230,209,210,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,
247,248,249,250,251,252,253,254,255,256,257,258,259,253,260,261,262,263,253,
264,253,265,266,267,268,269,270,271,272,253,273,274,275,276,277,278,279,278,
279,280,281,282,283,284,285,286,287,288,289,290,291,278,279,292,293,294,295,
278,279,296,297,298,299,278,279,300,301,302,303,304,305,306,307,308,309,310,
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( 35, 36)( 46, 47)( 48, 49)( 50, 51)( 58, 59)( 60, 61)( 62, 63)( 66, 67)
( 80, 86)( 81, 87)( 82, 88)( 83, 89)( 84, 90)( 85, 91)( 98, 99)(100,101)
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(310,316)(311,317)(312,318)(313,319)(314,320)(315,321)(328,329)(330,331)
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MBT("(2^2x3).U6(2).2",5,
[
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],
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MBT("(2^2x3).U6(2).2",7,
[
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],
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(115,116)(129,131)(130,132)(139,140)(141,142)(143,144)(152,153)(161,162)
(163,164)(165,166)(174,175)(186,188)(187,189)(194,195)(201,202)(210,211)
(212,213)(214,215)
],
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MBT("(2^2x3).U6(2).2",11,
[
"constructed using `BrauerTableOfTypeMGA'"
],
[180,181,180,181,182,183,184,185,186,187,188,189,190,191,192,193,180,181,194,
195,196,197,180,181,198,199,200,201,180,181,202,203,204,205,206,207,208,209,
210,211,212,213,214,215,216,217,218,219,220,221,222,223],
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[],
[["U6(2).2",0],["2.U6(2).2",0],["2^2.U6(2).2",0],["3.U6(2).2",81],["6.U6(2).2"
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(115,116)(125,126)(136,138)(137,139)(146,147)(148,149)(150,151)(159,160)
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MBT("(2^2x3).U6(2).3",5,
[
"constructed using `BrauerTableOfTypeMGA'"
],
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245,238,239,244,245,246,247,248,249,250,251,252,253,244,245,240,241,254,255,
256,257,258,259,260,261,262,263,264,265,266,267],
[0,0,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
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[,,[[1,2],[2,3],[3,5],[4,5]],3,[[1,3],[2,4],[3,5],[4,5]],5,,,[[1,4],[3,5],[2,3
],[4,5]],9],
[],
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,
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(224,227)(228,231)(229,232)(230,233)(234,237)(235,238)(236,239)(240,243)
(241,244)(242,245)(246,249)(247,250)(248,251)(252,255)(253,256)(254,257)
(258,261)(259,262)(260,263)(264,265)(266,269)(267,270)(268,271)(272,273)
(274,277)(275,278)(276,279)(280,283)(281,284)(282,285)(286,289)(287,290)
(288,291)(292,295)(293,296)(294,297)(298,301)(299,302)(300,303)(304,307)
(305,308)(306,309)(310,313)(311,314)(312,315)(316,319)(317,320)(318,321)
(322,325)(323,326)(324,327)(328,331)(329,332)(330,333)(334,337)(335,338)
(336,339)(340,343)(341,344)(342,345)(346,349)(347,350)(348,351)(352,355)
(353,356)(354,357)(358,361)(359,362)(360,363)(364,367)(365,368)(366,369)
(370,373)(371,374)(372,375)
],
0);
MBT("(2^2x3).U6(2).3",7,
[
"constructed using `BrauerTableOfTypeMGA'"
],
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335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,324,325,350,351,
352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367],
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,0,0,0,0,0],
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[[[1,2],[2,4],[3,5],[5,6],[4,7],[6,7]],1],
[],
[["U6(2).3",0],["2^2.U6(2).3",0],["3.U6(2).3",31]],
[
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(216,217,218)(219,220,221)(222,223,224)(225,226,227)(228,229,230)(231,232,233)
(234,235,236)(237,238,239)(240,241,242)(243,244,245)(246,247,248)(249,250,251)
(252,253,254)(255,256,257)(258,259,260)(261,262,263)(264,265,266)(267,268,269)
(270,271,272)(273,274,275)(278,279,280)(281,282,283)(286,287,288)(289,290,291)
(292,293,294)(295,296,297)(298,299,300)(301,302,303)(304,305,306)(307,308,309)
(310,311,312)(313,314,315)(316,317,318)(319,320,321)(322,323,324)(325,326,327)
(328,329,330)(331,332,333)(334,335,336)(337,338,339)(340,341,342)(343,344,345)
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(364,365,366)(367,368,369)(370,371,372)(373,374,375)(376,377,378)(379,380,381)
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,
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(384,390)(385,391)(386,392)(387,393)
,
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(310,313)(311,314)(312,315)(316,319)(317,320)(318,321)(322,325)(323,326)
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(372,375)(376,379)(377,380)(378,381)(382,385)(383,386)(384,387)(388,391)
(389,392)(390,393)(394,397)(395,398)(396,399)
],
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MBT("(2^2x3).U6(2).3",11,
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"constructed using `BrauerTableOfTypeMGA'"
],
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311,312,313,296,297,314,315,316,317,296,297,318,319,320,321,322,323,324,325,
326,327,328,329,330,331,332,333,334,335,336,337,338,339],
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[],
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(286,287,288)(289,290,291)(292,293,294)(295,296,297)(298,299,300)(301,302,303)
(304,305,306)(307,308,309)(310,311,312)(313,314,315)(316,317,318)(319,320,321)
(322,323,324)(325,326,327)(328,329,330)(331,332,333)(334,335,336)(337,338,339)
(340,341,342)(343,344,345)(346,347,348)(349,350,351)(352,353,354)(355,356,357)
(358,359,360)(361,362,363)(370,371,372)(373,374,375)(376,377,378)(379,380,381)
(382,383,384)(385,386,387)
,
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( 25, 27)( 30, 32)( 31, 33)( 37, 38)( 40, 41)( 43, 44)( 45, 47)( 50, 52)
( 51, 53)( 55, 56)( 59, 61)( 60, 62)( 63, 69)( 64, 70)( 65, 73)( 66, 74)
( 67, 71)( 68, 72)( 77, 79)( 78, 80)( 83, 85)( 84, 86)( 89, 91)( 90, 92)
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(196,199)(197,200)(198,201)(202,205)(203,206)(204,207)(208,209)(210,213)
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(306,309)(310,313)(311,314)(312,315)(316,319)(317,320)(318,321)(322,325)
(323,326)(324,327)(328,331)(329,332)(330,333)(334,337)(335,338)(336,339)
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(354,357)(358,361)(359,362)(360,363)(364,367)(365,368)(366,369)(370,373)
(371,374)(372,375)(376,379)(377,380)(378,381)(382,385)(383,386)(384,387)
],
0);
LIBTABLE.LOADSTATUS.ctbunit4:="userloaded";
#############################################################################
##
#E
|