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products/sources/formale Sprachen/GAP/pkg/ctbllib/data/ (Algebra von RWTH Aachen Version 4.15.1^©) Datei vom 1.2.2023 mit Größe 99 kB

Quelle ctbunit4.tbl Sprache: unbekannt

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

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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,
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[["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],
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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[],
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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)
( 84, 86)( 89, 90)( 91, 94)( 92, 96)( 93, 95)( 98, 99)(101,102)(104,105)
(106,109)(107,111)(108,110)(112,115)(113,116)(114,117)(118,121)(119,122)
(120,123)(124,127)(125,128)(126,129)(130,131)(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)
(186,189)(187,190)(188,191)(192,193)(194,197)(195,198)(196,199)(200,201)
(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)
(298,301)(299,302)(300,303)(304,307)(305,308)(306,309)(310,313)(311,314)
(312,315)],
0,
rec(version:=0,
date:="00.00.00"));

MBT("3.U6(2)",11,
TEXT1,
[41,42,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,41,
42,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,41,42,81,82,83,84,85,
86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,41,42,105,106,
107,108,109,110,111,112,113,114],
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[],
[[[1,3],[2,4],[3,5],[4,6,7],[5,6,7]],1],
[],
[["U6(2)",0]],
[( 29, 32)( 30, 33)( 31, 34)( 75, 78)( 76, 79)( 77, 80)(109,112)(110,113)
(111,114),( 26, 29)( 27, 30)( 28, 31)( 72, 75)( 73, 76)( 74, 77)(106,109)
(107,110)(108,111),(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)
( 21, 22)( 24, 25)( 27, 28)( 30, 31)( 33, 34)( 36, 37)( 39, 40)( 42, 43)
( 44, 47)( 45, 49)( 46, 48)( 51, 52)( 54, 55)( 57, 58)( 60, 61)( 63, 64)
( 67, 68)( 70, 71)( 73, 74)( 76, 77)( 79, 80)( 81, 84)( 82, 86)( 83, 85)
( 89, 90)( 91, 94)( 92, 96)( 93, 95)( 98, 99)(100,103)(101,105)(102,104)
(107,108)(110,111)(113,114)(116,117)(119,120)(121,124)(122,126)(123,125)],
0,
rec(version:=0,
date:="00.00.00"));

MBT("3.U6(2)",2,
TEXT1,
[3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4],
[15,15],
[[47,49,53,55,57,59,61,95,109,121],[48,50,54,56,58,60,62,96,110,122]],
[],
[[[-2,-2,1,-3,0,-2,-1,-2,0,1],[3,2,-1,3,0,2,1,2,0,-1],[-3,-2,1,-3,0,-3,0,-2,0,
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-4,1,-3,1,-2,-1,-2,0,1],[-4,-5,1,-6,0,-5,0,-4,0,2],[8,5,-3,3,-2,0,1,3,0,-1],[
1,2,0,-1,-3,-2,0,0,1,0]],[[0,1,1,1,0,1,-1,1,1,-1],[1,-1,-1,-1,0,-1,1,-1,-1,
1],[-1,1,1,1,0,0,0,1,1,-1],[-1,1,0,0,0,1,-1,0,0,0],[-2,-2,0,-1,0,-1,1,-1,-1,
1],[1,0,-1,1,0,1,-1,0,0,0],[-1,-1,1,1,1,1,-1,1,1,-1],[0,1,1,2,0,1,0,2,2,-2],[
6,2,-3,-1,-2,-3,1,0,-1,1],[1,2,0,-1,-3,-2,0,0,1,0]]],
[["U6(2)",0]],
[( 2, 3)( 5, 6)( 8, 9)(12,13)(15,16)(17,20)(18,22)(19,21)(24,27)(25,29)(26,28)
(31,32)],
[1,1,-1,0,0,-1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
rec(version:=3,
date:="08.09.94"));

MBT("3.U6(2)",5,
TEXT1,
[35,36,37,38,39,40,41,42,35,36,43,44,39,40,45,46,47,48,49,50,51,52,53,54,55,
56,41,42,57,58,59,60,61,62,63,64,35,36,65,66,67,68,39,40,69,70,71,72,73,74,75,
76,77,78,41,42,79,80,81,82,83,84,39,40,35,36,85,86,87,88,89,90,91,92,41,42,93,
94,95,96],
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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],
[],
[[[1,2],[2,4],[3,5],[4,5]],1,,,[[1,3],[2,4],[3,5],[4,5]],5,5,5],
[],
[["U6(2)",0]],
[(85,88)(86,89)(87,90),( 29, 32)( 30, 33)( 31, 34)( 72, 75)( 73, 76)( 74, 77)
(109,112)(110,113)(111,114),( 26, 29)( 27, 30)( 28, 31)( 69, 72)( 70, 73)
( 71, 74)(106,109)(107,110)(108,111),(  2,  3)(  5,  6)(  8,  9)( 11, 12)
( 14, 15)( 17, 18)( 21, 22)( 24, 25)( 27, 28)( 30, 31)( 33, 34)( 36, 37)
( 39, 40)( 41, 44)( 42, 46)( 43, 45)( 48, 49)( 51, 52)( 54, 55)( 57, 58)
( 60, 61)( 64, 65)( 67, 68)( 70, 71)( 73, 74)( 76, 77)( 78, 81)( 79, 83)
( 80, 82)( 86, 87)( 89, 90)( 91, 94)( 92, 96)( 93, 95)( 98, 99)(100,103)
(101,105)(102,104)(107,108)(110,111)(113,114)(116,117)(118,121)(119,123)
(120,122)],
0,
rec(version:=1,
date:="30.04.92"));

MBT("3.U6(2)",7,
TEXT1,
[41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,55,56,55,56,57,58,59,60,61,
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,
88,89,90,91,92,55,56,55,56,55,56,93,94,95,96,97,98,99,100,101,102,103,104,105,
106,107,108,109,110,111,112,113,114],
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[],
[,,,,,,,,,,,,,,[[1,7],[2,7],[3,7],[4,7],[5,7],[6,7]],15],
[],
[["U6(2)",0]],
[(88,91)(89,92)(90,93),( 29, 32)( 30, 33)( 31, 34)( 72, 75)( 73, 76)( 74, 77)
(112,115)(113,116)(114,117),( 26, 29)( 27, 30)( 28, 31)( 69, 72)( 70, 73)
( 71, 74)(109,112)(110,113)(111,114),(  2,  3)(  5,  6)(  8,  9)( 11, 12)
( 14, 15)( 17, 18)( 21, 22)( 24, 25)( 27, 28)( 30, 31)( 33, 34)( 36, 37)
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MBT("3.U6(2).3.2",7,
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--> --------------------

--> maximum size reached

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