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#############################################################################
##
#W ctounit3.tbl GAP table library Thomas Breuer
##
#H @(#)$Id: ctounit3.tbl,v 4.16 2004/02/17 17:33:14 gap Exp $
##
#Y Copyright (C) 1996, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
##
## This file contains the ordinary character tables related to the unitary
## groups $U_3(11)$, $U_4(2)$ and $U_5(2)$ of the ATLAS.
##
Revision.ctounit3_tbl :=
"@(#)$Id: ctounit3.tbl,v 4.16 2004/02/17 17:33:14 gap Exp $";
SET_TABLEFILENAME("ctounit3");
ALN:= Ignore;
MOT("2.U4(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[51840,51840,576,96,1296,1296,1296,1296,216,216,108,108,96,96,8,10,10,144,144,
144,144,36,36,36,36,12,18,18,18,18,24,24,24,24],
[,[1,1,1,2,7,7,5,5,9,9,11,11,3,3,4,16,16,7,7,5,5,9,9,11,11,10,29,29,27,27,21,
21,19,19],[1,2,3,4,1,2,1,2,1,2,1,2,13,14,15,16,17,3,3,3,3,3,3,3,3,4,5,6,7,8,
13,14,13,14],,[1,2,3,4,7,8,5,6,9,10,11,12,13,14,15,1,2,20,21,18,19,23,22,25,
24,26,29,30,27,28,33,34,31,32]],
0,
[( 5, 7)( 6, 8)(18,20)(19,21)(22,23)(24,25)(27,29)(28,30)(31,33)(32,34)],
["ConstructProj",[["U4(2)",[]],["2.U4(2)",[]]]]);
ARC("2.U4(2)","tomfusion",rec(name:="2.U4(2)",map:=[1,2,3,10,4,12,4,12,5,13,6,
14,8,9,27,11,32,15,16,15,16,18,18,19,19,41,31,58,31,58,39,40,39,40],text:=[
"fusion map is unique"
]));
ALF("2.U4(2)","U4(2)",[1,1,2,3,4,4,5,5,6,6,7,7,8,8,9,10,10,11,11,12,12,13,
14,15,15,16,17,17,18,18,19,19,20,20]);
ALF("2.U4(2)","2.U4(2).2",[1,2,3,4,5,6,5,6,7,8,9,10,11,12,13,14,15,16,17,
16,17,18,18,19,19,20,21,22,21,22,23,24,23,24]);
MOT("2.U4(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[103680,103680,1152,192,1296,1296,432,432,216,216,192,192,16,20,20,144,144,36,
36,24,18,18,24,24,1440,96,192,192,32,36,36,12,16,16,20,20,24,24],
[,[1,1,1,2,5,5,7,7,9,9,3,3,4,14,14,5,5,7,9,8,21,21,17,17,2,1,4,4,4,8,10,9,11,
11,15,15,20,20],[1,2,3,4,1,2,1,2,1,2,11,12,13,14,15,3,3,3,3,4,5,6,11,12,25,26,
27,28,29,25,25,26,33,34,35,36,27,28],,[1,2,3,4,5,6,7,8,9,10,11,12,13,1,2,16,
17,18,19,20,21,22,23,24,25,26,28,27,29,30,31,32,34,33,25,25,38,37]],
0,
[(35,36),(27,28)(33,34)(35,36)(37,38),(27,28)(33,34)(37,38)],
["ConstructProj",[["U4(2).2",[]],["2.U4(2).2",[]]]]);
ARC("2.U4(2).2","tomfusion",rec(name:="2.U4(2).2",map:=[1,2,3,9,5,16,6,17,7,
18,11,10,46,15,56,20,19,21,22,82,55,138,84,83,8,4,44,44,45,81,80,23,47,47,140,
140,169,169],text:=[
"fusion map is unique"
]));
ALF("2.U4(2).2","U4(2).2",[1,1,2,3,4,4,5,5,6,6,7,7,8,9,9,10,10,11,12,13,
14,14,15,15,16,17,18,18,19,20,21,22,23,23,24,24,25,25]);
ALF("2.U4(2).2","2.S6(2)",[1,2,4,5,9,10,7,8,11,12,13,14,18,19,20,24,23,22,
27,25,34,35,40,41,3,6,15,15,16,21,26,28,31,31,36,37,38,38],[
"fusion map is unique up to table autom."
]);
MOT("3.U3(11)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,37]"
],
[212747040,212747040,212747040,15840,15840,15840,144,15840,15840,15840,15840,
15840,15840,144,144,144,120,120,120,120,120,120,144,144,144,120,120,120,120,
120,120,120,120,120,120,120,120,15972,15972,15972,363,363,363,363,363,363,363,
363,363,144,144,144,144,144,144,144,144,144,144,144,144,120,120,120,120,120,
120,120,120,120,120,120,120,132,132,132,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,120,120,120,120,120,120,120,120,120,120,120,
120,120,120,120,120,120,120,120,120,120,120,120,120,132,132,132,132,132,132],
[,[1,3,2,1,3,2,7,4,6,5,4,6,5,4,6,5,20,22,21,17,19,18,7,7,7,8,10,9,11,13,12,20,
22,21,17,19,18,38,40,39,41,43,42,44,46,45,47,49,48,23,25,24,23,25,24,23,25,24,
23,25,24,35,37,36,35,37,36,32,34,33,32,34,33,38,40,39,83,85,84,86,88,87,89,91,
90,92,94,93,95,97,96,98,100,99,101,103,102,104,106,105,107,109,108,110,112,
111,80,82,81,77,79,78,68,70,69,71,73,72,62,64,63,65,67,66,68,70,69,71,73,72,
62,64,63,65,67,66,74,76,75,74,76,75],[1,1,1,4,4,4,1,11,11,11,8,8,8,14,14,14,
20,20,20,17,17,17,4,4,4,29,29,29,26,26,26,35,35,35,32,32,32,38,38,38,41,41,41,
44,44,44,47,47,47,11,11,11,8,8,8,14,14,14,14,14,14,71,71,71,68,68,68,65,65,65,
62,62,62,74,74,74,89,89,89,92,92,92,95,95,95,98,98,98,101,101,101,104,104,104,
107,107,107,110,110,110,80,80,80,77,77,77,86,86,86,83,83,83,122,122,122,119,
119,119,128,128,128,125,125,125,134,134,134,131,131,131,116,116,116,113,113,
113,140,140,140,137,137,137],,[1,3,2,4,6,5,7,8,10,9,11,13,12,14,16,15,1,3,2,1,
3,2,23,25,24,26,28,27,29,31,30,4,6,5,4,6,5,38,40,39,41,43,42,44,46,45,47,49,
48,50,52,51,53,55,54,59,61,60,56,58,57,8,10,9,11,13,12,8,10,9,11,13,12,74,76,
75,110,112,111,107,109,108,77,79,78,80,82,81,83,85,84,86,88,87,89,91,90,92,94,
93,95,97,96,98,100,99,101,103,102,104,106,105,26,28,27,29,31,30,26,28,27,29,
31,30,26,28,27,29,31,30,26,28,27,29,31,30,137,139,138,140,142,141],,,,,,[1,3,
2,4,6,5,7,11,13,12,8,10,9,14,16,15,17,19,18,20,22,21,23,25,24,29,31,30,26,28,
27,32,34,33,35,37,36,1,3,2,1,3,2,1,3,2,1,3,2,53,55,54,50,52,51,56,58,57,59,61,
60,65,67,66,62,64,63,71,73,72,68,70,69,4,6,5,80,82,81,77,79,78,86,88,87,83,85,
84,92,94,93,89,91,90,98,100,99,95,97,96,104,106,105,101,103,102,110,112,111,
107,109,108,116,118,117,113,115,114,122,124,123,119,121,120,128,130,129,125,
127,126,134,136,135,131,133,132,11,13,12,8,10,9],,,,,,,,,,,,,,,,,,,,,,,,,,[1,
2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,20,21,22,17,18,19,23,24,25,26,27,28,29,
30,31,35,36,37,32,33,34,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
56,57,58,59,60,61,68,69,70,71,72,73,62,63,64,65,66,67,74,75,76,1,2,3,1,2,3,1,
2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,119,120,121,122,123,
124,125,126,127,128,129,130,131,132,133,134,135,136,113,114,115,116,117,118,
137,138,139,140,141,142]],
0,
[(113,125)(114,126)(115,127)(116,128)(117,129)(118,130)(119,131)(120,132)
(121,133)(122,134)(123,135)(124,136),( 77, 83, 89, 95,101,107, 80, 86, 92, 98,
104,110)( 78, 84, 90, 96,102,108, 81, 87, 93, 99,105,111)( 79, 85, 91, 97,
103,109, 82, 88, 94,100,106,112),(44,47)(45,48)(46,49),(41,44)(42,45)(43,46),
( 17, 20)( 18, 21)( 19, 22)( 32, 35)( 33, 36)( 34, 37)( 62, 68)( 63, 69)
( 64, 70)( 65, 71)( 66, 72)( 67, 73)(113,131,125,119)(114,132,126,120)
(115,133,127,121)(116,134,128,122)(117,135,129,123)(118,136,130,124),( 8, 11)
( 9, 12)( 10, 13)( 26, 29)( 27, 30)( 28, 31)( 50, 53)( 51, 54)( 52, 55)
( 56, 59)( 57, 60)( 58, 61)( 62, 65)( 63, 66)( 64, 67)( 68, 71)( 69, 72)
( 70, 73)(113,128)(114,129)(115,130)(116,125)(117,126)(118,127)(119,134)
(120,135)(121,136)(122,131)(123,132)(124,133)(137,140)(138,141)(139,142),
( 2, 3)( 5, 6)( 9, 10)( 12, 13)( 15, 16)( 18, 19)( 21, 22)( 24, 25)
( 27, 28)( 30, 31)( 33, 34)( 36, 37)( 39, 40)( 42, 43)( 45, 46)( 48, 49)
( 51, 52)( 54, 55)( 56, 59)( 57, 61)( 58, 60)( 63, 64)( 66, 67)( 69, 70)
( 72, 73)( 75, 76)( 78, 79)( 81, 82)( 84, 85)( 87, 88)( 90, 91)( 93, 94)
( 96, 97)( 99,100)(102,103)(105,106)(108,109)(111,112)(114,115)(117,118)
(120,121)(123,124)(126,127)(129,130)(132,133)(135,136)(138,139)(141,142)],
["ConstructProj",[["U3(11)",[]],,["3.U3(11)",[-1,-1,-7,-7,-1,-1,-1,-1,-1,-7,
-7,-7,-7,-1,-1,-7,-7,-7,-7,11,11,11,11,41,41,41,41,-79,-79,-79,-79,-79,-79,
-79,-79,-73,-73,-73,-73,-73,-73,-73,-73,-73,-73,-73,-73]]]]);
ALF("3.U3(11)","U3(11)",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,
9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,
18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,25,25,
26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,33,33,
34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,
42,42,42,43,43,43,44,44,44,45,45,45,46,46,46,47,47,47,48,48,48]);
ALF("3.U3(11)","3.U3(11).2",[1,2,2,3,4,4,5,6,7,8,6,8,7,9,10,10,11,12,12,
13,14,14,15,16,16,17,18,19,17,19,18,20,21,21,22,23,23,24,25,25,26,27,27,
28,29,30,28,30,29,31,32,33,31,33,32,34,35,35,36,37,37,38,39,40,38,40,39,
41,42,43,41,43,42,44,45,45,46,47,48,46,48,47,49,50,51,49,51,50,52,53,54,
52,54,53,55,56,57,55,57,56,58,59,60,58,60,59,61,62,63,61,63,62,64,65,66,
64,66,65,67,68,69,67,69,68,70,71,72,70,72,71,73,74,75,73,75,74,76,77,78,
76,78,77]);
ALF("3.U3(11)","3.U3(11).3",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,
43,41,42,43,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,
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MOT("3.U3(11).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,37]"
],
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["ConstructMixed","3.U3(11)","U3(11).2",
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[ 128, 129 ], [ 131, 134 ], [ 132, 133 ], [ 135, 138 ], [ 136, 137 ],
[ 139, 142 ], [ 140, 141 ] ], ()]);
ALF("3.U3(11).2","U3(11).2",[1,1,2,2,3,4,4,4,5,5,6,6,7,7,8,8,9,9,9,10,10,
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ALF("3.U3(11).2","3.U3(11).S3",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
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MOT("3.U3(11).3",
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"origin: ATLAS of finite groups"
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(116,128)(117,129)(118,130)(343,367)(344,368)(345,369)(346,370)(347,371)
(348,372)(349,373)(350,374)(351,375)(352,376)(353,377)(354,378)(355,379)
(356,380)(357,381)(358,382)(359,383)(360,384)(361,385)(362,386)(363,387)
(364,388)(365,389)(366,390),( 71, 77, 83, 89, 95,101, 74, 80, 86, 92, 98,104)
( 72, 78, 84, 90, 96,102, 75, 81, 87, 93, 99,105)( 73, 79, 85, 91, 97,103, 76,
82, 88, 94,100,106)(271,283,295,307,319,331,279,291,303,315,327,339,272,284,
296,308,320,332,277,289,301,313,325,337,273,285,297,309,321,333,278,290,302,
314,326,338)(274,286,298,310,322,334,282,294,306,318,330,342,275,287,299,311,
323,335,280,292,304,316,328,340,276,288,300,312,324,336,281,293,305,317,329,
341),( 17, 20)( 18, 21)( 19, 22)( 32, 35)( 33, 36)( 34, 37)( 56, 62)( 57, 63)
( 58, 64)( 59, 65)( 60, 66)( 61, 67)(107,125,119,113)(108,126,120,114)
(109,127,121,115)(110,128,122,116)(111,129,123,117)(112,130,124,118)(199,205)
(200,206)(201,207)(202,208)(203,209)(204,210)(223,229)(224,230)(225,231)
(226,232)(227,233)(228,234)(241,253)(242,254)(243,255)(244,256)(245,257)
(246,258)(247,259)(248,260)(249,261)(250,262)(251,263)(252,264)
(343,379,367,355)(344,380,368,356)(345,381,369,357)(346,382,370,358)
(347,383,371,359)(348,384,372,360)(349,385,373,361)(350,386,374,362)
(351,387,375,363)(352,388,376,364)(353,389,377,365)(354,390,378,366),( 8, 11)
( 9, 12)( 10, 13)( 26, 29)( 27, 30)( 28, 31)( 44, 47)( 45, 48)( 46, 49)
( 50, 53)( 51, 54)( 52, 55)( 56, 59)( 57, 60)( 58, 61)( 62, 65)( 63, 66)
( 64, 67)(107,122)(108,123)(109,124)(110,119)(111,120)(112,121)(113,128)
(114,129)(115,130)(116,125)(117,126)(118,127)(131,134)(132,135)(133,136)
(157,163)(158,164)(159,165)(160,166)(161,167)(162,168)(175,181)(176,182)
(177,183)(178,184)(179,185)(180,186)(187,193)(188,194)(189,195)(190,196)
(191,197)(192,198)(211,217)(212,218)(213,219)(214,220)(215,221)(216,222)
(241,247)(242,248)(243,249)(244,250)(245,251)(246,252)(253,259)(254,260)
(255,261)(256,262)(257,263)(258,264)(343,373)(344,374)(345,375)(346,376)
(347,377)(348,378)(349,367)(350,368)(351,369)(352,370)(353,371)(354,372)
(355,385)(356,386)(357,387)(358,388)(359,389)(360,390)(361,379)(362,380)
(363,381)(364,382)(365,383)(366,384)(391,397)(392,398)(393,399)(394,400)
(395,401)(396,402),( 2, 3)( 5, 6)( 9, 10)( 12, 13)( 15, 16)( 18, 19)
( 21, 22)( 24, 25)( 27, 28)( 30, 31)( 33, 34)( 36, 37)( 39, 40)( 42, 43)
( 45, 46)( 48, 49)( 50, 53)( 51, 55)( 52, 54)( 57, 58)( 60, 61)( 63, 64)
( 66, 67)( 69, 70)( 72, 73)( 75, 76)( 78, 79)( 81, 82)( 84, 85)( 87, 88)
( 90, 91)( 93, 94)( 96, 97)( 99,100)(102,103)(105,106)(108,109)(111,112)
(114,115)(117,118)(120,121)(123,124)(126,127)(129,130)(132,133)(135,136)
(137,140)(138,141)(139,142)(143,144)(145,148)(146,149)(147,150)(151,154)
(152,155)(153,156)(157,160)(158,161)(159,162)(163,166)(164,167)(165,168)
(169,172)(170,173)(171,174)(175,178)(176,179)(177,180)(181,184)(182,185)
(183,186)(187,190)(188,191)(189,192)(193,196)(194,197)(195,198)(199,202)
(200,203)(201,204)(205,208)(206,209)(207,210)(211,214)(212,215)(213,216)
(217,220)(218,221)(219,222)(223,226)(224,227)(225,228)(229,232)(230,233)
(231,234)(235,238)(236,239)(237,240)(241,244)(242,245)(243,246)(247,250)
(248,251)(249,252)(253,256)(254,257)(255,258)(259,262)(260,263)(261,264)
(265,268)(266,269)(267,270)(271,276,272,274,273,275)(277,282,278,280,279,281)
(283,288,284,286,285,287)(289,294,290,292,291,293)(295,300,296,298,297,299)
(301,306,302,304,303,305)(307,312,308,310,309,311)(313,318,314,316,315,317)
(319,324,320,322,321,323)(325,330,326,328,327,329)(331,336,332,334,333,335)
(337,342,338,340,339,341)(343,346)(344,347)(345,348)(349,352)(350,353)
(351,354)(355,358)(356,359)(357,360)(361,364)(362,365)(363,366)(367,370)
(368,371)(369,372)(373,376)(374,377)(375,378)(379,382)(380,383)(381,384)
(385,388)(386,389)(387,390)(391,394)(392,395)(393,396)(397,400)(398,401)
(399,402),(271,273,272)(274,276,275)(277,279,278)(280,282,281)(283,285,284)
(286,288,287)(289,291,290)(292,294,293)(295,297,296)(298,300,299)(301,303,302)
(304,306,305)(307,309,308)(310,312,311)(313,315,314)(316,318,317)(319,321,320)
(322,324,323)(325,327,326)(328,330,329)(331,333,332)(334,336,335)(337,339,338)
(340,342,341)],
["ConstructProj",[["U3(11).3",[]],,["3.U3(11).3",[2,2,5,5,2,2,2,5,5,5,5,2,2,5,
5,5,5,11,11,11,11,29,29,29,29,29,29,29,29,29,29,29,29,137,137,137,137,137,137,
137,137,137,137,137,137]]]]);
ALF("3.U3(11).3","U3(11).3",[1,1,1,2,2,2,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,
9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,
17,17,18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25,
25,25,26,26,26,27,27,27,28,28,28,29,29,29,30,30,30,31,31,31,32,32,32,33,
33,33,34,34,34,35,35,35,36,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,
41,41,42,42,42,43,43,43,44,44,44,45,45,45,46,46,46,47,47,47,48,48,48,49,
50,51,51,51,52,52,52,53,53,53,54,54,54,55,55,55,56,56,56,57,57,57,58,58,
58,59,59,59,60,60,60,61,61,61,62,62,62,63,63,63,64,64,64,65,65,65,66,66,
66,67,67,67,68,68,68,69,69,69,70,70,70,71,71,71,72,72,72,73,73,73,74,74,
74,75,75,75,76,76,76,77,77,77,78,78,78,79,79,79,80,80,80,81,81,81,82,82,
82,83,83,83,84,84,84,85,85,85,86,86,86,87,87,87,88,88,88,89,89,89,90,90,
90,91,91,91,92,92,92,93,93,93,94,94,94,95,95,95,96,96,96,97,97,97,98,98,
98,99,99,99,100,100,100,101,101,101,102,102,102,103,103,103,104,104,104,
105,105,105,106,106,106,107,107,107,108,108,108,109,109,109,110,110,110,
111,111,111,112,112,112,113,113,113,114,114,114,115,115,115,116,116,116,
117,117,117,118,118,118,119,119,119,120,120,120,121,121,121,122,122,122,
123,123,123,124,124,124,125,125,125,126,126,126,127,127,127,128,128,128,
129,129,129,130,130,130,131,131,131,132,132,132,133,133,133,134,134,134,
135,135,135,136,136,136]);
ALF("3.U3(11).3","3.U3(11).S3",[1,2,2,3,4,4,5,6,7,8,6,8,7,9,10,10,11,12,12,13,
14,14,15,16,16,17,18,19,17,19,18,20,21,21,22,23,23,24,25,25,26,27,27,28,29,30,
28,30,29,31,32,32,33,34,34,35,36,37,35,37,36,38,39,40,38,40,39,41,42,42,43,44,
45,43,45,44,46,47,48,46,48,47,49,50,51,49,51,50,52,53,54,52,54,53,55,56,57,55,
57,56,58,59,60,58,60,59,61,62,63,61,63,62,64,65,66,64,66,65,67,68,69,67,69,68,
70,71,72,70,72,71,73,74,75,73,75,74,76,77,78,76,77,78,79,79,80,81,82,80,81,82,
83,84,85,83,84,85,86,87,88,89,90,91,89,90,91,86,87,88,92,93,94,92,93,94,95,96,
97,98,99,100,98,99,100,95,96,97,101,102,103,104,105,106,104,105,106,101,102,
103,107,108,109,107,108,109,110,111,112,110,111,112,113,114,115,116,117,118,
116,117,118,113,114,115,119,120,121,119,120,121,122,123,124,122,123,124,125,
126,127,125,126,127,128,129,130,131,132,133,131,132,133,128,129,130,134,135,
136,137,138,139,137,138,139,134,135,136,140,141,142,140,141,142,143,144,145,
146,147,148,146,147,148,143,144,145,149,150,151,152,153,154,152,153,154,149,
150,151,155,156,157,158,159,160,158,159,160,155,156,157,161,162,163,164,165,
166,164,165,166,161,162,163,167,168,169,170,171,172,170,171,172,167,168,169,
173,174,175,176,177,178,176,177,178,173,174,175,179,180,181,182,183,184,182,
183,184,179,180,181,185,186,187,188,189,190,188,189,190,185,186,187,191,192,
193,194,195,196,194,195,196,191,192,193,197,198,199,200,201,202,200,201,202,
197,198,199,203,204,205,206,207,208,206,207,208,203,204,205]);
MOT("3.U3(11).S3",
[
"origin: ATLAS of finite groups"
],
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432,864,432,360,360,360,360,360,360,792,396,333,333,333,333,333,333,333,333,
333,333,333,333,333,333,333,333,333,333,360,360,360,360,360,360,360,360,360,
360,360,360,396,396,396,47520,47520,47520,333,47520,47520,47520,432,432,432,
47520,47520,47520,47520,47520,47520,432,432,432,432,432,432,432,432,432,432,
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396,396,396,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,
333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,333,
333,360,360,360,360,360,360,360,360,360,360,360,360,360,360,360,360,360,360,
360,360,360,360,360,360,396,396,396,396,396,396,2640,2640,24,24,20,20,24,20,20
,22,24,24,44,44],
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59,43,44,45,38,40,39,35,37,36,38,40,39,35,37,36,41,42,42,76,77,78,79,76,77,78,
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38,38,38,38,38,35,35,35,35,35,35,41,41,41,50,50,50,51,51,51,53,53,53,54,54,54,
56,56,56,57,57,57,59,59,59,60,60,60,45,45,45,44,44,44,48,48,48,47,47,47,64,64,
64,64,64,64,67,67,67,67,67,67,70,70,70,70,70,70,61,61,61,61,61,61,73,73,73,73,
73,73,209,210,209,212,214,213,210,217,216,218,212,212,221,222],,[1,2,3,4,5,6,8
,7,9,10,1,2,1,2,15,16,17,19,18,3,4,3,4,24,25,26,27,28,30,29,33,34,31,32,6,8,7,
6,8,7,41,42,58,59,60,43,45,44,46,48,47,49,51,50,52,54,53,55,57,56,17,19,18,17,
19,18,17,19,18,17,19,18,73,75,74,76,77,78,79,80,81,82,83,84,85,89,90,91,86,87,
88,92,93,94,98,99,100,95,96,97,104,105,106,101,102,103,76,77,78,76,77,78,116,
117,118,113,114,115,80,81,82,80,81,82,125,126,127,89,90,91,86,87,88,89,90,91,
86,87,88,140,141,142,174,175,173,177,178,176,146,147,148,143,144,145,152,153,
154,149,150,151,158,159,160,155,156,157,164,165,166,161,162,163,170,171,172,
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114,115,116,117,118,113,114,115,206,207,208,203,204,205,209,210,211,212,209,
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,16,17,18,19,20,21,22,23,1,2,1,2,28,29,30,31,32,33,34,35,36,37,38,39,40,3,4,43
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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,
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221,222]],
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187)(188,189,190)(191,192,193)(194,195,196)(197,198,199)(200,201,202)(203,204,
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(62,65,68,71)(63,66,69,72)(107,110)(108,111)(109,112)(119,122)(120,123)(121,
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(180,186,192,198)(181,187,193,199)(182,188,194,200)(183,189,195,201)(184,190,
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63)(65,66)(68,69)(71,72)(74,75)(86,89)(87,90)(88,91)(95,98)(96,99)(97,100)
(101,104)(102,105)(103,106)(113,116)(114,117)(115,118)(128,131)(129,132)(130,
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(187,190)(191,194)(192,195)(193,196)(197,200)(198,201)(199,202)(203,206)(204,
207)(205,208)(219,220),(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),(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(143,146)
(144,147)(145,148)(149,152)(150,153)(151,154)(155,158)(156,159)(157,160)(161,
164)(162,165)(163,166)(167,170)(168,171)(169,172)(173,176)(174,177)(175,178),
(43,46,49,52,55,58)(44,47,50,53,56,59,45,48,51,54,57,60)(143,149,155,161,167,
173,148,154,160,166,172,178,144,150,156,162,168,174,146,152,158,164,170,176,
145,151,157,163,169,175,147,153,159,165,171,177)],
["ConstructGS3","3.U3(11).2","3.U3(11).3",[8,9,50],[[2,3],[5,6],[8,9],[10,13],
[12,14],[11,15],[18,19],[21,22],[24,25],[27,28],[29,32],[31,33],[30,34],[36,
37],[38,41],[40,42],[39,43],[45,46],[47,50],[49,51],[48,52],[54,55],[57,58],
[60,61],[63,64],[65,68],[67,69],[66,70],[71,74],[73,75],[72,76],[77,80],[79,
81],[78,82],[83,86],[85,87],[84,88],[89,92],[91,93],[90,94],[95,98],[97,99],
[96,100],[101,104],[103,105],[102,106],[107,110],[109,111],[108,112],[113,
116],[115,117],[114,118],[119,122],[121,123],[120,124],[125,128],[127,129],
[126,130],[131,134],[133,135],[132,136],[137,140],[139,141],[138,142],[143,
146],[145,147],[144,148],[152,155],[154,156],[153,157],[149,158],[151,159],
[150,160],[163,166],[165,167],[164,168],[169,172],[171,173],[170,174],[178,
181],[180,182],[179,183],[175,184],[177,185],[176,186],[190,193],[192,194],
[191,195],[187,196],[189,197],[188,198],[199,202],[201,203],[200,204],[205,
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[248,252],[253,256],[255,257],[254,258],[262,265],[264,266],[263,267],[259,
268],[261,269],[260,270],[274,277],[276,278],[275,279],[271,280],[273,281],
[272,282],[286,289],[288,290],[287,291],[283,292],[285,293],[284,294],[298,
301],[300,302],[299,303],[295,304],[297,305],[296,306],[310,313],[312,314],
[311,315],[307,316],[309,317],[308,318],[322,325],[324,326],[323,327],[319,
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[332,342],[346,349],[348,350],[347,351],[343,352],[345,353],[344,354],[358,
361],[360,362],[359,363],[355,364],[357,365],[356,366],[370,373],[372,374],
[371,375],[367,376],[369,377],[368,378],[382,385],[384,386],[383,387],[379,
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[53,26],[56,28],[59,30],[62,32]],(1,13,26,47,72,101,130,152,175,203,15,29,54,
80,106,128,151,179,208,22,39,65,90,120,147,171,195,219,48,74,96,123,150,180,
210,25,44,69,95,121,146,169,197)(2,14,27,50,75,98,124,149,178,200,5,6,9,11,20,
34,58,82,107,136,158,181,209,24,40,64,88,110,133,161,190,212,31,55,79,104,127,
155,184,206,19,35,60,86,109,137,166,188,211,30,56,81,108,138,168,198)(3,102,
132,162,192,222,52,76,97,122,148,170,193,221,51,77,103,131,160,182,205,18,33,
59,84,114,141,165,189,213,36,62,87,111,135,159,183,207,21,38,63,89,118,143,
172,194,217,45,71,99,126,156,186,216,43,67,91,119,145,173,202,8,12,23,41,66,
92,115,140,163,191,220,49,73,100,125,154,176,199,4)(7,10,17,32,57,83,112,134,
157,185,214,37,61,85,113,139,167,196,218,46,70,94,116,142,164,187,215,42,68,
93,117,144,174,204,16,28,53,78,105,129,153,177,201)]);
ALF("3.U3(11).S3","U3(11).S3",[1,1,2,2,3,4,4,4,5,5,6,6,7,7,8,8,9,9,9,10,10,
11,11,12,12,13,13,14,14,14,15,15,16,16,17,17,17,18,18,18,19,19,20,20,20,
21,21,21,22,22,22,23,23,23,24,24,24,25,25,25,26,26,26,27,27,27,28,28,28,
29,29,29,30,30,30,31,31,31,32,33,33,33,34,34,34,35,35,35,36,36,36,37,37,
37,38,38,38,39,39,39,40,40,40,41,41,41,42,42,42,43,43,43,44,44,44,45,45,
45,46,46,46,47,47,47,48,48,48,49,49,49,50,50,50,51,51,51,52,52,52,53,53,
53,54,54,54,55,55,55,56,56,56,57,57,57,58,58,58,59,59,59,60,60,60,61,61,
61,62,62,62,63,63,63,64,64,64,65,65,65,66,66,66,67,67,67,68,68,68,69,69,
69,70,70,70,71,71,71,72,72,72,73,73,73,74,74,74,75,75,75,76,77,78,79,80,
81,82,83,84,85,86,87,88,89]);
MOT("U3(11)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,37]"
],
[70915680,5280,144,5280,5280,48,40,40,48,40,40,40,40,5324,121,121,121,48,48,
48,48,40,40,40,40,44,37,37,37,37,37,37,37,37,37,37,37,37,40,40,40,40,40,40,40,
40,44,44],
[,[1,1,3,2,2,2,8,7,3,4,5,8,7,14,15,16,17,9,9,9,9,13,13,12,12,14,29,30,31,32,
33,34,35,36,37,38,28,27,24,25,22,23,24,25,22,23,26,26],[1,2,1,5,4,6,8,7,2,11,
10,13,12,14,15,16,17,5,4,6,6,25,24,23,22,26,31,32,33,34,35,36,37,38,28,27,30,
29,42,41,44,43,46,45,40,39,48,47],,[1,2,3,4,5,6,1,1,9,10,11,2,2,14,15,16,17,
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[GALOIS,[4,3]],[370,10,1,10,10,-2,0,0,1,0,0,0,0,7,7,-4,-4,1,1,1,1,0,0,0,0,-1,
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[GALOIS,[29,11]],
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[GALOIS,[37,21]],
[GALOIS,[37,9]],
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[(39,43)(40,44)(41,45)(42,46),(27,29,31,33,35,37,28,30,32,34,36,38),(20,21),
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(40,46,44,42),( 4, 5)(10,11)(18,19)(22,23)(24,25)(39,40)(41,42)(43,44)(45,46)
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(47,48),(27,28)(29,30)(31,32)(33,34)(35,36)(37,38),(27,38,36,34,32,30,28,37,
35,33,31,29)]);
ARC("U3(11)","CAS",[rec(name:="u3q11",
permchars:=(10,14,13,12)(19,27,26,23,21)(20,28,25,24,22)(31,33)(32,34)
(37,47,42,38,48,41)(39,43,40,44)(45,46),
permclasses:=(10,11)(18,21,19,20)(23,24,25)(29,30)(31,36,37,34)(32,35,38,33)
(39,40)(41,44)(42,43)(45,46),
text:=Concatenation(
" test: 1. o.r., sym 2 decompose correctly \n",
""))]);
ARC("U3(11)","projectives",["3.U3(11)",[[111,-9,0,-9,-9,3,1,1,0,1,1,1,1,-10,1,
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[GALOIS,[20,2]],[1332,12,0,12,12,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,-2,-2,
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[GALOIS,[22,2]],[1332,12,0,-12,-12,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,2*E(4),
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[GALOIS,[24,11]],
[GALOIS,[24,13]],
[GALOIS,[24,3]],[1332,-12,0,12*E(4),-12*E(4),0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,0,
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E(4),-E(4)],
[GALOIS,[28,11]],
[GALOIS,[28,13]],
[GALOIS,[28,23]],
[GALOIS,[28,9]],
[GALOIS,[28,19]],
[GALOIS,[28,33]],
[GALOIS,[28,3]],[1440,0,0,0,0,0,0,0,0,0,0,0,0,-12,-1,-1,-1,0,0,0,0,0,0,0,0,0,
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[GALOIS,[36,11]],
[GALOIS,[36,5]],
[GALOIS,[36,18]],
[GALOIS,[36,21]],
[GALOIS,[36,9]],
[GALOIS,[36,14]],
[GALOIS,[36,6]],
[GALOIS,[36,7]],
[GALOIS,[36,3]],
[GALOIS,[36,17]],
[GALOIS,[36,2]]],]);
ARC("U3(11)","isSimple",true);
ARC("U3(11)","extInfo",["3","3.2"]);
ARC("U3(11)","tomfusion",rec(name:="U3(11)",map:=[1,2,3,4,4,5,7,7,8,12,12,15,
15,17,18,19,20,23,23,22,22,34,34,34,34,39,55,55,55,55,55,55,55,55,55,55,55,55,
58,58,58,58,58,58,58,58,59,59],text:=[
"fusion map is unique up to table automorphisms"
]));
ALF("U3(11)","U3(11).2",[1,2,3,4,4,5,6,7,8,9,9,10,11,12,13,14,14,15,15,16,
17,18,18,19,19,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,
30,30,31,31]);
ALF("U3(11)","U3(11).3",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,15,15,16,17,
18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
42,43,44,45,46]);
ALN("U3(11)",["u3q11"]);
MOT("U3(11).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,37]"
],
[141831360,10560,288,5280,96,80,80,96,40,80,80,10648,242,121,48,96,96,40,40,
88,37,37,37,37,37,37,40,40,40,40,44,2640,2640,24,24,20,20,24,20,20,22,24,24,
44,44],
[,[1,1,3,2,2,7,6,3,4,7,6,12,13,14,8,8,8,11,10,12,22,23,24,25,26,21,19,18,19,
18,20,1,2,3,5,7,6,8,11,10,13,17,16,20,20],[1,2,1,4,5,7,6,2,9,11,10,12,13,14,4,
5,5,19,18,20,23,24,25,26,21,22,28,29,30,27,31,32,33,32,35,37,36,33,40,39,41,
35,35,44,45],,[1,2,3,4,5,1,1,8,9,2,2,12,13,14,15,17,16,4,4,20,26,21,22,23,24,
25,9,9,9,9,31,32,33,34,35,32,32,38,33,33,41,43,42,44,45],,,,,,[1,2,3,4,5,6,7,
8,9,10,11,1,1,1,15,16,17,18,19,2,21,22,23,24,25,26,27,28,29,30,4,32,33,34,35,
36,37,38,39,40,32,42,43,33,33],,,,,,,,,,,,,,,,,,,,,,,,,,[1,2,3,4,5,7,6,8,9,11,
10,12,13,14,15,16,17,19,18,20,1,1,1,1,1,1,28,29,30,27,31,32,33,34,35,37,36,38,
40,39,41,42,43,44,45]],
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1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[110,-10,2,-10,2,0,0,2,0,0,0,-11,0,
0,2,2,2,0,0,1,-1,-1,-1,-1,-1,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
E(11)-E(11)^2+E(11)^3+E(11)^4+E(11)^5-E(11)^6-E(11)^7-E(11)^8+E(11)^9-E(11)^10
,-E(11)+E(11)^2-E(11)^3-E(11)^4-E(11)^5+E(11)^6+E(11)^7+E(11)^8-E(11)^9
+E(11)^10],
[TENSOR,[3,2]],[111,-9,3,11,-1,1,1,3,-1,1,1,-10,1,1,-1,-1,-1,1,1,2,0,0,0,0,0,
0,-1,-1,-1,-1,0,-1,11,-1,1,-1,-1,-1,1,1,-1,1,1,0,0],
[TENSOR,[5,2]],[222,22,6,-2,2,2,2,-2,0,2,2,-20,2,2,-2,2,2,-2,-2,0,0,0,0,0,0,0,
0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[370,10,1,10,-2,0,0,1,0,0,0,7,7,-4,1,
1,1,0,0,-1,0,0,0,0,0,0,0,0,0,0,-1,10,10,1,-2,0,0,1,0,0,-1,1,1,-1,-1],
[TENSOR,[8,2]],[740,20,2,20,-4,0,0,2,0,0,0,14,-8,3,2,2,2,0,0,-2,0,0,0,0,0,0,0,
0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1110,30,3,-10,2,0,0,3,0,0,0,21,-1,-1,
-1,-1,-1,0,0,-3,0,0,0,0,0,0,0,0,0,0,1,10,10,1,2,0,0,1,0,0,-1,-1,-1,-1,-1],
[TENSOR,[11,2]],[1110,-10,-6,10,2,0,0,2,0,0,0,21,-1,-1,-2,2,2,0,0,1,0,0,0,0,0,
0,0,0,0,0,-1,10,-10,-2,0,0,0,2,0,0,-1,0,0,1,1],
[TENSOR,[13,2]],[1110,-10,3,10,2,0,0,-1,0,0,0,21,-1,-1,1,E(12)^4-2*E(12)^7
+E(12)^8+2*E(12)^11,E(12)^4+2*E(12)^7+E(12)^8-2*E(12)^11,0,0,1,0,0,0,0,0,0,0,
0,0,0,-1,10,-10,1,0,0,0,-1,0,0,-1,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,1,1],
[TENSOR,[15,2]],
[GALOIS,[15,5]],
[TENSOR,[17,2]],[2220,-20,6,-20,-4,0,0,-2,0,0,0,42,-2,-2,-2,2,2,0,0,2,0,0,0,0,
0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1221,21,-3,1,1,1,1,-3,-1,1,1,11,0,
0,1,1,1,1,1,-1,0,0,0,0,0,0,-1,-1,-1,-1,1,11,-1,-1,1,1,1,-1,-1,-1,0,1,1,-1,-1],
[TENSOR,[20,2]],[2442,2,-6,-22,-2,2,2,2,0,2,2,22,0,0,2,-2,-2,-2,-2,2,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1331,11,-1,11,-1,1,1,-1,1,1,1,0,0,
0,-1,-1,-1,1,1,0,-1,-1,-1,-1,-1,-1,1,1,1,1,0,11,11,-1,-1,1,1,-1,1,1,0,-1,-1,0,
0],
[TENSOR,[23,2]],[2664,-24,0,0,0,4,4,0,0,-4,-4,2,2,2,0,0,0,0,0,-2,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1332,12,0,12,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,0,2,E(5)+E(5)^4,E(5)^2+E(5)^3,1,1,1,0,0,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,1,0,0,0,0,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,E(5)+E(5)^4,
E(5)^2+E(5)^3,1,12,12,0,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,E(5)+E(5)^4,
E(5)^2+E(5)^3,1,0,0,1,1],
[TENSOR,[26,2]],
[GALOIS,[26,2]],
[TENSOR,[28,2]],[1332,12,0,12,0,E(5)+E(5)^4,E(5)^2+E(5)^3,0,-2,E(5)+E(5)^4,
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E(5)+E(5)^4,E(5)^2+E(5)^3,0,-E(5)-E(5)^4,-E(5)^2-E(5)^3,1,0,0,-1,-1],
[TENSOR,[30,2]],
[GALOIS,[30,2]],
[TENSOR,[32,2]],[2664,24,0,-24,0,2*E(5)+2*E(5)^4,2*E(5)^2+2*E(5)^3,0,0,
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-2*E(5)^2-2*E(5)^3,2,0,0,0,0,0,0,0,0,0,0,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[34,2]],[2664,-24,0,0,0,2*E(5)+2*E(5)^4,2*E(5)^2+2*E(5)^3,0,0,
-2*E(5)-2*E(5)^4,-2*E(5)^2-2*E(5)^3,2,2,2,0,0,0,0,0,-2,0,0,0,0,0,0,
E(40)^7-E(40)^13-E(40)^23+E(40)^37,E(40)^21-E(40)^29+E(40)^31-E(40)^39,
-E(40)^7+E(40)^13+E(40)^23-E(40)^37,-E(40)^21+E(40)^29-E(40)^31+E(40)^39,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[36,13]],
[GALOIS,[36,9]],
[GALOIS,[36,3]],[2880,0,0,0,0,0,0,0,0,0,0,-24,-2,-2,0,0,0,0,0,0,
-E(37)-E(37)^10-E(37)^11-E(37)^26-E(37)^27-E(37)^36,-E(37)^2-E(37)^15-E(37)^17
-E(37)^20-E(37)^22-E(37)^35,-E(37)^3-E(37)^4-E(37)^7-E(37)^30-E(37)^33
-E(37)^34,-E(37)^6-E(37)^8-E(37)^14-E(37)^23-E(37)^29-E(37)^31,
-E(37)^9-E(37)^12-E(37)^16-E(37)^21-E(37)^25-E(37)^28,-E(37)^5-E(37)^13
-E(37)^18-E(37)^19-E(37)^24-E(37)^32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[40,5]],
[GALOIS,[40,9]],
[GALOIS,[40,6]],
[GALOIS,[40,3]],
[GALOIS,[40,2]]],
[(44,45),(27,29)(28,30),(21,22,23,24,25,26),(16,17)(42,43),(16,17)(27,29)
(28,30)(42,43),( 6, 7)(10,11)(18,19)(27,30,29,28)(36,37)(39,40),
(21,26,25,24,23,22)]);
ARC("U3(11).2","CAS",[rec(name:="psu(3,11):2",
permchars:=( 8, 9)(11,12)(13,14)(19,31,26,23,21)(22,32,29,28,30,25,36,35,37,
33,27,24)(38,39)(41,43,44,42,45),
permclasses:=( 6, 7)(18,19)(36,37),
text:=Concatenation(
"Maximal subgroup of sporadic Janko group j4.\n",
"Test: 1.OR, JAMES, JAMES,n=3,\n",
"and restricted characters decompose properly."))]);
ALF("U3(11).2","U3(11).S3",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,76,77,78,79,80,81,82,83,84,85,86,87,88,
89]);
ALF("U3(11).2","J4",[1,2,4,5,6,8,8,10,14,17,17,19,20,20,21,22,22,30,31,34,
50,51,52,50,51,52,53,54,53,54,60,3,5,11,15,18,18,21,30,31,35,37,38,60,60],[
"fusion determined using subgroup 5x8:2 in the intersection of\n",
"U3(11).2 and J4N11, the fusion on the CAS table is wrong"
]);
ALN("U3(11).2",["psu(3,11):2"]);
MOT("U3(11).3",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11,37]"
],
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144,144,144,144,120,120,120,120,132,111,111,111,111,111,111,111,111,111,111,
111,111,120,120,120,120,120,120,120,120,132,132,15840,15840,333,333,15840,
15840,144,144,15840,15840,15840,15840,144,144,144,144,144,144,144,144,144,144,
120,120,120,120,120,120,120,120,120,120,120,120,132,132,120,120,120,120,120,
120,120,120,132,132,111,111,111,111,111,111,111,111,111,111,111,111,111,111,
111,111,111,111,111,111,111,111,111,111,120,120,120,120,120,120,120,120,120,
120,120,120,120,120,120,120,132,132,132,132],
[,[1,1,3,2,2,2,8,7,3,4,5,8,7,14,15,9,9,9,9,13,13,12,12,14,27,28,29,30,31,32,
33,34,35,36,26,25,22,23,20,21,22,23,20,21,24,24,48,47,50,49,48,47,48,47,52,51,
52,51,52,51,54,53,54,53,54,53,54,53,72,71,70,69,56,55,58,57,72,71,70,69,82,81,
80,79,80,79,78,77,78,77,82,81,98,97,100,99,102,101,104,103,106,105,108,107,
110,109,112,111,114,113,116,115,96,95,94,93,88,87,90,89,84,83,86,85,88,87,90,
89,84,83,86,85,92,91,92,91],[1,2,1,5,4,6,8,7,2,11,10,13,12,14,15,5,4,6,6,23,
22,21,20,24,29,30,31,32,33,34,35,36,26,25,28,27,40,39,42,41,44,43,38,37,46,45,
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36,36,26,26,25,25,28,28,27,27,40,40,39,39,42,42,41,41,44,44,43,43,38,38,37,37,
46,46,45,45],,[1,2,3,4,5,6,1,1,9,10,11,2,2,14,15,16,17,19,18,4,5,4,5,24,36,35,
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75,74,73,76,75,74,73,76,75,134,133,136,135],,,,,,[1,2,3,5,4,6,7,8,9,11,10,12,
13,1,1,17,16,18,19,21,20,23,22,2,26,25,28,27,30,29,32,31,34,33,36,35,38,37,40,
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125,126,127,128,129,130,131,132,117,118,119,120,133,134,135,136]],
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MOT("U3(11).S3",
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MOT("U4(2)",
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-E(3)+E(3)^2,0,1,-E(3),-E(3)^2,E(3),E(3)^2],
[GALOIS,[2,2]],[6,-2,2,-3,-3,3,0,2,0,1,1,1,1,1,-2,-1,0,0,-1,-1],[10,2,-2,
5*E(3)+2*E(3)^2,2*E(3)+5*E(3)^2,1,1,2,0,0,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,-1,-1,
-1,1,E(3)^2,E(3),-E(3),-E(3)^2],
[GALOIS,[5,2]],[15,-1,-1,6,6,3,0,3,-1,0,2,2,-1,-1,2,-1,0,0,0,0],[15,7,3,-3,-3,
0,3,-1,1,0,1,1,-2,-2,1,0,0,0,-1,-1],[20,4,4,2,2,5,-1,0,0,0,-2,-2,1,1,1,1,-1,
-1,0,0],[24,8,0,6,6,0,3,0,0,-1,2,2,2,2,-1,0,0,0,0,0],[30,-10,2,3,3,3,3,-2,0,0,
-1,-1,-1,-1,-1,-1,0,0,1,1],[30,6,2,6*E(3)-3*E(3)^2,-3*E(3)+6*E(3)^2,-3,0,2,0,
0,2*E(3)+E(3)^2,E(3)+2*E(3)^2,-E(3)+E(3)^2,E(3)-E(3)^2,0,-1,0,0,-E(3)^2,
-E(3)],
[GALOIS,[12,2]],[40,-8,0,2*E(3)+8*E(3)^2,8*E(3)+2*E(3)^2,-2,1,0,0,0,-2*E(3),
-2*E(3)^2,-2*E(3),-2*E(3)^2,1,0,E(3)^2,E(3),0,0],
[GALOIS,[14,2]],[45,-3,-3,-9*E(3),-9*E(3)^2,0,0,1,1,0,3*E(3),3*E(3)^2,0,0,0,0,
0,0,E(3),E(3)^2],
[GALOIS,[16,2]],[60,-4,4,6,6,-3,-3,0,0,0,2,2,-1,-1,-1,1,0,0,0,0],[64,0,0,-8,
-8,4,-2,0,0,-1,0,0,0,0,0,0,1,1,0,0],[81,9,-3,0,0,0,0,-3,-1,1,0,0,0,0,0,0,0,0,
0,0]],
[( 4, 5)(11,12)(13,14)(17,18)(19,20)]);
ARC("U4(2)","CAS",[rec(name:="u4q2",
permchars:=(),
permclasses:=(13,14)(17,18),
text:=Concatenation(
"names:=u4q2; psu4[2], su4(2)\n",
" 2a3(2) (lie-not.)\n",
" order: 2^6.3^4.5 = 25,920\n",
" number of classes: 20\n",
" source:mckay, john\n",
" the non-abelian simple groups g,\n",
" ord(g)<10^6 - character tables\n",
" comm.algebra 7\n",
" (1979),1407-1445\n",
" test: 1. o.r., sym 2 decompose correctly\n",
" comments: - \n",
""))]);
ARC("U4(2)","projectives",["2.U4(2)",[[4,0,0,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,-2,
1,2,0,-1,2*E(3)+E(3)^2,E(3)+2*E(3)^2,0,0,E(3)-E(3)^2,0,E(3)^2,E(3),-E(3)^2,
-E(3)],
[GALOIS,[1,2]],[20,0,0,-7,-7,2,2,2,0,0,3,3,0,0,0,0,-1,-1,-1,-1],[20,0,0,
-5*E(3)-8*E(3)^2,-8*E(3)-5*E(3)^2,2,2,2,0,0,-3*E(3),-3*E(3)^2,0,0,0,0,-E(3),
-E(3)^2,-E(3),-E(3)^2],
[GALOIS,[4,2]],[20,0,0,E(3)-5*E(3)^2,-5*E(3)+E(3)^2,-4,-1,2,0,0,-E(3)+E(3)^2,
E(3)-E(3)^2,0,0,E(3)-E(3)^2,0,-E(3)^2,-E(3),-1,-1],
[GALOIS,[6,2]],[36,0,0,9*E(3),9*E(3)^2,0,0,2,0,1,3*E(3),3*E(3)^2,0,0,0,0,0,0,
-E(3),-E(3)^2],
[GALOIS,[8,2]],[60,0,0,-3,-3,-6,0,-2,0,0,3,3,0,0,0,0,0,0,1,1],[60,0,0,
3*E(3)-6*E(3)^2,-6*E(3)+3*E(3)^2,0,3,-2,0,0,E(3)+2*E(3)^2,2*E(3)+E(3)^2,0,0,
-E(3)+E(3)^2,0,0,0,E(3),E(3)^2],
[GALOIS,[11,2]],[64,0,0,-8,-8,4,-2,0,0,-1,0,0,0,0,0,0,1,1,0,0],[80,0,0,8,8,2,
-4,0,0,0,0,0,0,0,0,0,-1,-1,0,0]],]);
ARC("U4(2)","isSimple",true);
ARC("U4(2)","extInfo",["2","2"]);
ARC("U4(2)","tomfusion",rec(name:="U4(2)",map:=[1,2,3,4,4,5,6,7,12,13,15,
15,16,16,17,20,33,33,41,41],text:=[
"fusion map is unique"
]));
ALF("U4(2)","U4(2).2",[1,2,3,4,4,5,6,7,8,9,10,10,11,11,12,13,14,14,15,15]);
ALF("U4(2)","U4(3)",[1,2,2,3,3,4,5,7,8,9,10,10,11,11,12,11,18,19,20,20],[
"fusion map is unique up to table autom."
],"tom:378");
ALN("U4(2)",["u4q2"]);
MOT("U4(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]"
],
[51840,1152,192,648,216,108,96,16,10,72,36,36,24,9,12,1440,96,96,32,36,36,12,
8,10,12],
[,[1,1,1,4,5,6,2,3,9,4,5,6,5,14,10,1,1,3,3,5,6,6,7,9,13],[1,2,3,1,1,1,7,8,9,2,
2,2,3,4,7,16,17,18,19,16,16,17,23,24,18],,[1,2,3,4,5,6,7,8,1,10,11,12,13,14,
15,16,17,18,19,20,21,22,23,16,25]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[10,-6,2,1,-2,4,2,-2,0,-3,0,0,2,1,-1,0,0,
0,0,0,0,0,0,0,0],[6,-2,2,-3,3,0,2,0,1,1,1,-2,-1,0,-1,4,0,-2,2,1,-2,0,0,-1,1],
[TENSOR,[4,2]],[20,4,-4,-7,2,2,4,0,0,1,-2,-2,2,-1,1,0,0,0,0,0,0,0,0,0,0],[15,
-1,-1,6,3,0,3,-1,0,2,-1,2,-1,0,0,5,-3,1,1,-1,2,0,-1,0,1],
[TENSOR,[7,2]],[15,7,3,-3,0,3,-1,1,0,1,-2,1,0,0,-1,5,1,3,-1,2,-1,1,-1,0,0],
[TENSOR,[9,2]],[20,4,4,2,5,-1,0,0,0,-2,1,1,1,-1,0,10,2,2,2,1,1,-1,0,0,-1],
[TENSOR,[11,2]],[24,8,0,6,0,3,0,0,-1,2,2,-1,0,0,0,4,4,0,0,-2,1,1,0,-1,0],
[TENSOR,[13,2]],[30,-10,2,3,3,3,-2,0,0,-1,-1,-1,-1,0,1,10,-2,-4,0,1,1,1,0,0,
-1],
[TENSOR,[15,2]],[60,12,4,-3,-6,0,4,0,0,-3,0,0,-2,0,1,0,0,0,0,0,0,0,0,0,0],[80,
-16,0,-10,-4,2,0,0,0,2,2,2,0,-1,0,0,0,0,0,0,0,0,0,0,0],[90,-6,-6,9,0,0,2,2,0,
-3,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0],[60,-4,4,6,-3,-3,0,0,0,2,-1,-1,1,0,0,10,2,
-2,-2,1,1,-1,0,0,1],
[TENSOR,[20,2]],[64,0,0,-8,4,-2,0,0,-1,0,0,0,0,1,0,16,0,0,0,-2,-2,0,0,1,0],
[TENSOR,[22,2]],[81,9,-3,0,0,0,-3,-1,1,0,0,0,0,0,0,9,-3,3,-1,0,0,0,1,-1,0],
[TENSOR,[24,2]]],
[]);
ARC("U4(2).2","CAS",[rec(name:="o6m2.2",
permchars:=( 3, 5, 4)( 6,12,11,10, 7, 8, 9)(17,19,25,24,23,21,18,22,20),
permclasses:=( 4, 6,12,13,11,10, 7)( 5, 9,15, 8)(20,21,24,25,22,23),
text:=Concatenation(
"names:=o6m2; pom6[2,-], w(e6)\n",
" 2d3(2) (lie-not.)\n",
" order: 2^7.3^4.5 = 51,840\n",
" number of classes: 25\n",
" source:private communication\n",
" with gabrysch, th.\n",
" univ. of bielefeld (1981)\n",
" test: 1 .o.r., sym 2 decompose correctly\n",
" comments: o6m2 is isomorhic to u4q2 \n",
"")),rec(name:="s6f2s1",
permchars:=( 2,16,20,10,23,21,25,22, 6,11, 4)( 3,15, 5,17,14,24, 7)
( 8,18,13, 9)(12,19),
permclasses:=( 2, 3)( 4,11, 7)( 5, 6, 9,15,13, 8)(10,12)(18,19)(20,21,22,23)
(24,25),
text:=Concatenation(
"names:=s6f2s1; [3..3,2,1]', [3..3,2,1]\n",
" order: 2^7.3^4.5 = 51,840\n",
" number of classes: 25\n",
" source:frame, j.s.\n",
" the classes and representations of the groups\n",
" of 27 lines and 28 bitangents,\n",
" annali di mathematica 4\n",
" [1923],83-119\n",
" comments:subgroup of index 28 in s6f2 \n",
""))]);
ARC("U4(2).2","projectives",["2.U4(2).2",[[8,0,0,-1,-4,2,4,0,-2,-3,0,0,0,-1,1,
0,0,0,0,0,0,0,0,0,0],[20,0,0,-7,2,2,2,0,0,3,0,0,0,-1,-1,0,0,2*E(8)+2*E(8)^3,0,
0,0,0,E(8)+E(8)^3,0,-E(8)-E(8)^3],[40,0,0,13,4,4,4,0,0,3,0,0,0,1,1,0,0,0,0,0,
0,0,0,0,0],[40,0,0,4,-8,-2,4,0,0,0,0,0,0,1,-2,0,0,0,0,0,0,0,0,0,0],[72,0,0,-9,
0,0,4,0,2,-3,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],[60,0,0,-3,-6,0,-2,0,0,3,0,0,0,0,
1,0,0,2*E(8)+2*E(8)^3,0,0,0,0,-E(8)-E(8)^3,0,-E(8)-E(8)^3],[120,0,0,3,0,6,-4,
0,0,-3,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0],[64,0,0,-8,4,-2,0,0,-1,0,0,0,0,1,0,0,0,
0,0,0,0,0,0,E(20)+E(20)^9-E(20)^13-E(20)^17,0],[80,0,0,8,2,-4,0,0,0,0,0,0,0,
-1,0,0,0,4*E(8)+4*E(8)^3,0,0,0,0,0,0,E(8)+E(8)^3]],]);
ARC("U4(2).2","tomfusion",rec(name:="U4(2).2",map:=[1,3,4,6,7,8,13,19,23,26,
34,33,35,73,89,2,5,11,18,32,27,38,60,74,83],text:=[
"fusion map is unique"
]));
ALF("U4(2).2","L4(3)",[1,3,2,4,5,6,9,10,11,14,15,16,12,18,23,2,3,8,10,12,
13,16,17,20,21],[
"fusion map is unique up to table autom."
],"tom:814");
ALF("U4(2).2","S4xU4(2).2",[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25],[
"fusion map determined as that of a direct factor"
]);
ALF("U4(2).2","S6(2)",[1,3,4,7,6,8,9,13,14,17,16,20,18,25,29,2,5,10,11,15,
19,21,23,26,27],[
"fusion map is unique"
]);
ALF("U4(2).2","U4(3).2_1",[1,2,2,3,4,5,7,8,9,10,11,12,11,17,18,20,20,21,
22,24,25,25,27,28,31],[
"fusion map is unique up to table autom."
],"tom:980");
ALN("U4(2).2",["w(e6)","o6m2.2","s6f2s1"]);
MOT("U5(2)",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"
],
[13685760,82944,4608,77760,77760,3888,3888,1944,324,1152,384,96,15,1728,1728,
1296,1296,432,432,288,288,216,144,144,108,108,36,16,54,54,27,27,11,11,144,144,
72,72,36,24,24,24,24,15,15,18,18],
[,[1,1,1,5,4,7,6,8,9,2,2,3,13,5,4,7,6,7,6,5,4,8,7,6,9,9,9,11,30,29,32,31,34,
33,15,14,19,18,22,21,20,19,18,45,44,30,29],[1,2,3,1,1,1,1,1,1,10,11,12,13,2,2,
2,2,2,2,3,3,2,3,3,2,2,3,28,6,7,6,7,33,34,10,10,10,10,10,12,12,11,11,13,13,16,
17],,[1,2,3,5,4,7,6,8,9,10,11,12,1,15,14,17,16,19,18,21,20,22,24,23,26,25,27,
28,30,29,32,31,33,34,36,35,38,37,39,41,40,43,42,4,5,47,46],,,,,,[1,2,3,5,4,7,
6,8,9,10,11,12,13,15,14,17,16,19,18,21,20,22,24,23,26,25,27,28,30,29,32,31,1,
1,36,35,38,37,39,41,40,43,42,45,44,47,46]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1],[10,-6,2,-5,-5,1,1,4,-2,2,-2,-2,0,3,3,3,3,-3,-3,-1,-1,0,-1,
-1,0,0,2,0,-2,-2,1,1,-1,-1,-1,-1,-1,-1,2,1,1,1,1,0,0,0,0],[11,-5,3,
-5*E(3)+E(3)^2,E(3)-5*E(3)^2,4*E(3)+E(3)^2,E(3)+4*E(3)^2,2,2,3,-1,-1,1,
3*E(3)+E(3)^2,E(3)+3*E(3)^2,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,E(3)^2,E(3),
-E(3)+E(3)^2,E(3)-E(3)^2,-2,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,-2*E(3)^2,-2*E(3),0,
1,-E(3),-E(3)^2,-E(3),-E(3)^2,0,0,-E(3)+E(3)^2,E(3)-E(3)^2,2*E(3)+E(3)^2,
E(3)+2*E(3)^2,0,-1,-1,-E(3)^2,-E(3),E(3),E(3)^2,E(3),E(3)^2],
[GALOIS,[3,2]],[44,12,-4,14,14,-1,-1,5,2,4,4,0,-1,6,6,3,3,3,3,2,2,-3,-1,-1,0,
0,2,0,2,2,-1,-1,0,0,-2,-2,1,1,1,0,0,1,1,-1,-1,0,0],[55,23,7,10,10,1,1,10,1,-1,
-1,3,0,2,2,5,5,5,5,-2,-2,2,1,1,-1,-1,1,-1,1,1,1,1,0,0,2,2,-1,-1,2,0,0,-1,-1,0,
0,-1,-1],[55,7,-1,5*E(3)+20*E(3)^2,20*E(3)+5*E(3)^2,-4*E(3)+2*E(3)^2,
2*E(3)-4*E(3)^2,1,1,7,3,-1,0,-3*E(3)+4*E(3)^2,4*E(3)-3*E(3)^2,-2,-2,-2*E(3)^2,
-2*E(3),E(3)+4*E(3)^2,4*E(3)+E(3)^2,1,2,2,3*E(3)+E(3)^2,E(3)+3*E(3)^2,-1,1,
E(3)^2,E(3),E(3)^2,E(3),0,0,E(3),E(3)^2,-2*E(3),-2*E(3)^2,1,-E(3),-E(3)^2,0,0,
0,0,E(3)^2,E(3)],
[GALOIS,[7,2]],[66,18,10,6*E(3)+15*E(3)^2,15*E(3)+6*E(3)^2,-3*E(3)+6*E(3)^2,
6*E(3)-3*E(3)^2,3,3,2,-2,2,1,-2*E(3)-E(3)^2,-E(3)-2*E(3)^2,3*E(3)+6*E(3)^2,
6*E(3)+3*E(3)^2,E(3)+2*E(3)^2,2*E(3)+E(3)^2,2*E(3)-E(3)^2,-E(3)+2*E(3)^2,3,
-E(3)+2*E(3)^2,2*E(3)-E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,1,0,0,0,0,0,0,0,
2*E(3)+3*E(3)^2,3*E(3)+2*E(3)^2,-E(3),-E(3)^2,-1,-E(3)^2,-E(3),E(3),E(3)^2,
E(3)^2,E(3),0,0],
[GALOIS,[9,2]],[110,-2,-10,-25,-25,2,2,2,2,6,-6,2,0,7,7,-2,-2,-2,-2,-1,-1,-2,
2,2,-2,-2,2,0,-1,-1,-1,-1,0,0,3,3,0,0,0,-1,-1,0,0,0,0,1,1],[110,30,6,
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3*E(3)+9*E(3)^2,9*E(3)+3*E(3)^2,-3*E(3)+6*E(3)^2,6*E(3)-3*E(3)^2,-3*E(3),
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2*E(3)^2,2*E(3),-E(3)^2,-E(3),0,0,-E(3)+E(3)^2,E(3)-E(3)^2,-E(3)-2*E(3)^2,
-2*E(3)-E(3)^2,0,-1,-1,-E(3),-E(3)^2,0,0,0,0],
[GALOIS,[12,2]],[110,-34,6,-5*E(3)+10*E(3)^2,10*E(3)-5*E(3)^2,-5*E(3)+E(3)^2,
E(3)-5*E(3)^2,11,2,-2,2,-2,0,3*E(3)+2*E(3)^2,2*E(3)+3*E(3)^2,E(3)-5*E(3)^2,
-5*E(3)+E(3)^2,3*E(3)+5*E(3)^2,5*E(3)+3*E(3)^2,-E(3)-2*E(3)^2,-2*E(3)-E(3)^2,
-1,E(3)-E(3)^2,-E(3)+E(3)^2,2*E(3)^2,2*E(3),0,0,-E(3),-E(3)^2,-E(3),-E(3)^2,0,
0,-E(3)+2*E(3)^2,2*E(3)-E(3)^2,1,1,1,E(3),E(3)^2,-1,-1,0,0,-E(3),-E(3)^2],
[GALOIS,[14,2]],[120,24,8,30,30,12,12,3,3,8,0,0,0,6,6,6,6,0,0,2,2,3,2,2,3,3,
-1,0,0,0,0,0,-1,-1,2,2,2,2,-1,0,0,0,0,0,0,0,0],[165,-27,5,30,30,3,3,3,-6,5,5,
-3,0,6,6,-9,-9,3,3,2,2,3,-1,-1,0,0,2,1,0,0,0,0,0,0,2,2,-1,-1,-1,0,0,-1,-1,0,0,
0,0],[176,-16,16,-4,-4,14,14,-4,5,0,0,0,1,-4,-4,2,2,2,2,4,4,-4,-2,-2,-1,-1,1,
0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,1,1,-1,-1],[220,-36,-4,-10*E(3)-40*E(3)^2,
-40*E(3)-10*E(3)^2,-7*E(3)-10*E(3)^2,-10*E(3)-7*E(3)^2,7,1,4,-4,0,0,
-2*E(3)+8*E(3)^2,8*E(3)-2*E(3)^2,3*E(3)+6*E(3)^2,6*E(3)+3*E(3)^2,
E(3)+2*E(3)^2,2*E(3)+E(3)^2,2*E(3),2*E(3)^2,3,3*E(3)+2*E(3)^2,2*E(3)+3*E(3)^2,
E(3)-E(3)^2,-E(3)+E(3)^2,-1,0,-2*E(3)^2,-2*E(3),E(3)^2,E(3),0,0,-2*E(3),
-2*E(3)^2,E(3),E(3)^2,1,0,0,-E(3),-E(3)^2,0,0,0,0],
[GALOIS,[19,2]],[220,-4,12,20*E(3)-10*E(3)^2,-10*E(3)+20*E(3)^2,
2*E(3)+17*E(3)^2,17*E(3)+2*E(3)^2,-5,4,4,4,0,0,4*E(3)-2*E(3)^2,
-2*E(3)+4*E(3)^2,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,-2*E(3)+E(3)^2,E(3)-2*E(3)^2,
4*E(3)+2*E(3)^2,2*E(3)+4*E(3)^2,-1,2*E(3)+E(3)^2,E(3)+2*E(3)^2,2,2,0,0,E(3)^2,
E(3),E(3)^2,E(3),0,0,-2*E(3)^2,-2*E(3),E(3)^2,E(3),1,0,0,E(3)^2,E(3),0,0,
-E(3)^2,-E(3)],
[GALOIS,[21,2]],[264,-24,-8,-30*E(3)+24*E(3)^2,24*E(3)-30*E(3)^2,-6,-6,3,3,8,
0,0,-1,10*E(3)+8*E(3)^2,8*E(3)+10*E(3)^2,-6*E(3)^2,-6*E(3),-2*E(3)+2*E(3)^2,
2*E(3)-2*E(3)^2,-2*E(3),-2*E(3)^2,3,-2*E(3)^2,-2*E(3),E(3)-E(3)^2,
-E(3)+E(3)^2,1,0,0,0,0,0,0,0,2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,-1,0,0,0,0,-E(3),
-E(3)^2,0,0],
[GALOIS,[23,2]],[320,-64,0,-40,-40,-4,-4,14,-4,0,0,0,0,8,8,8,8,-4,-4,0,0,2,0,
0,2,2,0,0,-1,-1,-1,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,-1,-1],[330,-6,2,
-15*E(3)-60*E(3)^2,-60*E(3)-15*E(3)^2,3*E(3)+12*E(3)^2,12*E(3)+3*E(3)^2,-3,-3,
10,-2,2,0,-7*E(3)+4*E(3)^2,4*E(3)-7*E(3)^2,3*E(3),3*E(3)^2,-E(3)+4*E(3)^2,
4*E(3)-E(3)^2,-3*E(3)-4*E(3)^2,-4*E(3)-3*E(3)^2,-3,-E(3),-E(3)^2,-E(3)+E(3)^2,
E(3)-E(3)^2,-1,0,0,0,0,0,0,0,E(3),E(3)^2,E(3),E(3)^2,1,-E(3),-E(3)^2,E(3),
E(3)^2,0,0,0,0],
[GALOIS,[26,2]],[440,88,8,-10,-10,8,8,17,-1,-8,0,0,0,-2,-2,-2,-2,4,4,2,2,1,2,
2,1,1,-1,0,-1,-1,-1,-1,0,0,-2,-2,-2,-2,1,0,0,0,0,0,0,1,1],[440,-40,8,
70*E(3)+40*E(3)^2,40*E(3)+70*E(3)^2,-2*E(3)-14*E(3)^2,-14*E(3)-2*E(3)^2,-1,-1,
8,0,0,0,-2*E(3)-8*E(3)^2,-8*E(3)-2*E(3)^2,-8*E(3)-2*E(3)^2,-2*E(3)-8*E(3)^2,2,
2,2*E(3),2*E(3)^2,-1,2*E(3)^2,2*E(3),-1,-1,-1,0,-E(3),-E(3)^2,-E(3),-E(3)^2,0,
0,2*E(3),2*E(3)^2,2*E(3),2*E(3)^2,-1,0,0,0,0,0,0,-E(3),-E(3)^2],
[GALOIS,[29,2]],[495,-81,15,-45*E(3),-45*E(3)^2,9*E(3),9*E(3)^2,9,0,-1,-1,-1,
0,3*E(3),3*E(3)^2,9*E(3),9*E(3)^2,-3*E(3),-3*E(3)^2,3*E(3),3*E(3)^2,-3,
-3*E(3),-3*E(3)^2,0,0,0,-1,0,0,0,0,0,0,-E(3),-E(3)^2,-E(3),-E(3)^2,-1,-E(3),
-E(3)^2,-E(3),-E(3)^2,0,0,0,0],
[GALOIS,[31,2]],[495,63,-9,-45*E(3)^2,-45*E(3),9*E(3)^2,9*E(3),9,0,-1,-5,-1,0,
3*E(3)^2,3*E(3),-9*E(3)^2,-9*E(3),-3*E(3)^2,-3*E(3),3*E(3)^2,3*E(3),-3,
3*E(3)^2,3*E(3),0,0,0,1,0,0,0,0,0,0,-E(3)^2,-E(3),-E(3)^2,-E(3),-1,-E(3)^2,
-E(3),E(3)^2,E(3),0,0,0,0],
[GALOIS,[33,2]],[660,84,20,30,30,-15,-15,3,3,-4,4,0,0,6,6,3,3,-3,-3,2,2,3,-1,
-1,-3,-3,-1,0,0,0,0,0,0,0,2,2,-1,-1,-1,0,0,1,1,0,0,0,0],[704,64,0,
40*E(3)+64*E(3)^2,64*E(3)+40*E(3)^2,4*E(3)-8*E(3)^2,-8*E(3)+4*E(3)^2,2,2,0,0,
0,-1,-8*E(3),-8*E(3)^2,-8,-8,4*E(3),4*E(3)^2,0,0,-2,0,0,-2*E(3),-2*E(3)^2,0,0,
-E(3),-E(3)^2,-E(3),-E(3)^2,0,0,0,0,0,0,0,0,0,0,0,-E(3),-E(3)^2,E(3),E(3)^2],
[GALOIS,[36,2]],[880,48,16,20*E(3)-40*E(3)^2,-40*E(3)+20*E(3)^2,
-4*E(3)-10*E(3)^2,-10*E(3)-4*E(3)^2,-8,-5,0,0,0,0,4*E(3)+8*E(3)^2,
8*E(3)+4*E(3)^2,-6*E(3)^2,-6*E(3),4*E(3)+2*E(3)^2,2*E(3)+4*E(3)^2,4*E(3),
4*E(3)^2,0,-2*E(3)^2,-2*E(3),E(3)-E(3)^2,-E(3)+E(3)^2,1,0,-2*E(3),-2*E(3)^2,
E(3),E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[38,2]],[891,27,-21,81,81,0,0,0,0,3,3,-1,1,9,9,0,0,0,0,-3,-3,0,0,0,0,
0,0,-1,0,0,0,0,0,0,-3,-3,0,0,0,-1,-1,0,0,1,1,0,0],[891,27,-21,81*E(3),
81*E(3)^2,0,0,0,0,3,3,-1,1,9*E(3),9*E(3)^2,0,0,0,0,-3*E(3),-3*E(3)^2,0,0,0,0,
0,0,-1,0,0,0,0,0,0,-3*E(3),-3*E(3)^2,0,0,0,-E(3),-E(3)^2,0,0,E(3)^2,E(3),0,0],
[GALOIS,[41,2]],[990,-18,6,45*E(3),45*E(3)^2,18*E(3),18*E(3)^2,-9,0,-2,-6,-2,
0,-3*E(3),-3*E(3)^2,0,0,-6*E(3),-6*E(3)^2,-3*E(3),-3*E(3)^2,3,0,0,0,0,0,0,0,0,
0,0,0,0,E(3),E(3)^2,-2*E(3),-2*E(3)^2,1,E(3),E(3)^2,0,0,0,0,0,0],
[GALOIS,[43,2]],[1024,0,0,64,64,16,16,-8,4,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,-2,-2,1,1,1,1,0,0,0,0,0,0,0,0,0,-1,-1,0,0],[1215,-81,-9,0,0,0,0,0,0,-9,3,
3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,E(11)+E(11)^3+E(11)^4+E(11)^5
+E(11)^9,E(11)^2+E(11)^6+E(11)^7+E(11)^8+E(11)^10,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[46,2]]],
[(33,34),( 4, 5)( 6, 7)(14,15)(16,17)(18,19)(20,21)(23,24)(25,26)(29,30)
(31,32)(35,36)(37,38)(40,41)(42,43)(44,45)(46,47)]);
ARC("U5(2)","CAS",[rec(name:="u5q2",
permchars:=( 6, 8)(12,14)(19,21)(23,24)(32,34)(40,42,41)(43,44),
permclasses:=( 4, 8,30,38,27,33,46,39,32,42,28, 7,19,23,24,25,34,47,40,16,20,
12, 6,18,22,31,41,17,21,13,43,29,37,26,35,14,10)( 5, 9,36,15,11),
text:=Concatenation(
"names:u5q2; psu5[2], su5(2)\n",
"2a4(2) (lie-not.)\n",
"order: 2^10.3^5.5.11 = 13,685,760\n",
"number of classes: 47\n",
"source:hunt, d.c.\n",
"character tables of certain finite simple groups,\n",
"bull.austral.math.soc 5\n",
"(1971),1-42\n",
"text: 1. o.r., sym 2 decompose correctly\n",
"comments: - \n",
""))]);
ARC("U5(2)","maxes",["2^{1+6}:3^{1+2}:2A4","3xU4(2)","2^(4+4):(3xA5)",
"3^4:S5","S3x3^(1+2)+:2A4","L2(11)"]);
ARC("U5(2)","isSimple",true);
ARC("U5(2)","extInfo",["","2"]);
ARC("U5(2)","tomfusion",rec(name:="U5(2)",map:=[1,2,3,4,4,5,5,6,7,12,14,13,15,
19,19,20,20,24,24,22,22,21,23,23,25,25,26,41,49,49,50,50,52,52,65,65,66,66,67,
69,69,68,68,72,72,116,116],text:=[
"fusion map is unique"
]));
ALF("U5(2)","U5(2).2",[1,2,3,4,4,5,5,6,7,8,9,10,11,12,12,13,13,14,14,15,
15,16,17,17,18,18,19,20,21,21,22,22,23,23,24,24,25,25,26,27,27,28,28,29,
29,30,30]);
ALF("U5(2)","Suz",[1,2,2,4,4,5,5,5,5,7,8,9,12,13,13,14,15,16,16,13,13,16,
15,14,15,14,16,20,22,23,22,23,26,26,27,27,28,28,28,29,29,31,31,37,37,38,
39],[
"fusion is unique up to table automorphisms,\n",
"the representative is equal to the fusion map on the CAS table"
]);
ALF("U5(2)","U6(2)",[1,2,3,5,5,6,6,5,7,8,9,13,15,18,18,16,17,17,16,20,20,
18,19,19,21,21,22,25,29,30,29,30,33,34,37,37,36,35,37,43,43,39,38,44,44,
45,46],[
"fusion map is unique up to table automorphisms"
]);
ALN("U5(2)",["u5q2"]);
MOT("U5(2).2",
[
"origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11]"
],
[27371520,165888,9216,77760,3888,3888,648,2304,768,192,30,1728,1296,432,288,
432,144,108,72,32,54,27,11,144,72,72,24,24,15,18,1440,96,36,36,192,192,32,10,
12,16,16,24,24],
[,[1,1,1,4,5,6,7,2,2,3,11,4,5,5,4,6,5,7,7,9,21,22,23,12,14,16,15,14,29,21,1,3,
6,7,8,8,8,11,19,20,20,26,26],[1,2,3,1,1,1,1,8,9,10,11,2,2,2,3,2,3,2,3,20,5,5,
23,8,8,8,10,9,11,13,31,32,31,31,35,36,37,38,32,40,41,35,36],,[1,2,3,4,5,6,7,8,
9,10,1,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,4,30,31,32,33,34,36,
35,37,31,39,41,40,43,42],,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,1,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[10,-6,2,-5,1,4,-2,2,-2,-2,0,3,3,-3,-1,0,-1,
0,2,0,-2,1,-1,-1,-1,2,1,1,0,0,0,0,0,0,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,0,0,0,
E(8)+E(8)^3,-E(8)-E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3],
[TENSOR,[3,2]],[22,-10,6,4,-5,4,4,6,-2,-2,2,-4,-1,-1,0,-4,3,2,0,2,1,1,0,0,-3,
0,-2,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[44,12,-4,14,-1,5,2,4,4,0,-1,6,3,3,2,
-3,-1,0,2,0,2,-1,0,-2,1,1,0,1,-1,0,4,0,1,-2,4,4,0,-1,0,0,0,1,1],
[TENSOR,[6,2]],[55,23,7,10,1,10,1,-1,-1,3,0,2,5,5,-2,2,1,-1,1,-1,1,1,0,2,-1,2,
0,-1,0,-1,5,1,2,-1,-3,-3,1,0,1,-1,-1,0,0],
[TENSOR,[8,2]],[110,14,-2,-25,2,2,2,14,6,-2,0,-1,-4,2,-5,2,4,-4,-2,2,-1,-1,0,
-1,2,2,1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[132,36,20,-21,-3,6,6,4,-4,4,2,3,
-9,-3,-1,6,-1,0,2,0,0,0,0,-5,1,-2,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[110,
-2,-10,-25,2,2,2,6,-6,2,0,7,-2,-2,-1,-2,2,-2,2,0,-1,-1,0,3,0,0,-1,0,0,1,0,0,0,
0,2*E(8)+2*E(8)^3,-2*E(8)-2*E(8)^3,0,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3,E(8)+E(8)^3],
[TENSOR,[12,2]],[220,60,12,-20,-5,16,-8,12,4,4,0,-12,-3,3,0,0,-3,0,0,0,-2,1,0,
0,3,0,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[220,-68,12,-5,4,22,4,-4,4,-4,0,-5,
4,-8,3,-2,0,-2,0,0,1,1,0,-1,2,2,-1,-2,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[120,24,
8,30,12,3,3,8,0,0,0,6,6,0,2,3,2,3,-1,0,0,0,-1,2,2,-1,0,0,0,0,10,2,1,1,2,2,2,0,
-1,0,0,-1,-1],
[TENSOR,[16,2]],[165,-27,5,30,3,3,-6,5,5,-3,0,6,-9,3,2,3,-1,0,2,1,0,0,0,2,-1,
-1,0,-1,0,0,5,-3,-1,2,1,1,1,0,0,-1,-1,1,1],
[TENSOR,[18,2]],[176,-16,16,-4,14,-4,5,0,0,0,1,-4,2,2,4,-4,-2,-1,1,0,-1,-1,0,
0,0,0,0,0,1,-1,4,4,-2,1,0,0,0,-1,1,0,0,0,0],
[TENSOR,[20,2]],[440,-72,-8,50,17,14,2,8,-8,0,0,-6,-9,-3,-2,6,-5,0,-2,0,2,-1,
0,2,-1,2,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[440,-8,24,-10,-19,-10,8,8,8,0,0,
-2,1,1,-6,-2,-3,4,0,0,-1,-1,0,2,-1,2,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[528,
-48,-16,6,-12,6,6,16,0,0,-2,-18,6,0,2,6,2,0,2,0,0,0,0,-2,-2,-2,0,0,1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],[320,-64,0,-40,-4,14,-4,0,0,0,0,8,8,-4,0,2,0,2,0,0,-1,-1,
1,0,0,0,0,0,0,-1,0,0,0,0,4*E(8)+4*E(8)^3,-4*E(8)-4*E(8)^3,0,0,0,0,0,
E(8)+E(8)^3,-E(8)-E(8)^3],
[TENSOR,[25,2]],[660,-12,4,75,-15,-6,-6,20,-4,4,0,3,-3,-3,7,-6,1,0,-2,0,0,0,0,
-1,-1,2,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[440,88,8,-10,8,17,-1,-8,0,0,0,-2,
-2,4,2,1,2,1,-1,0,-1,-1,0,-2,-2,1,0,0,0,1,10,2,1,1,-2,-2,-2,0,-1,0,0,1,1],
[TENSOR,[28,2]],[880,-80,16,-110,16,-2,-2,16,0,0,0,10,10,4,-2,-2,-2,-2,-2,0,1,
1,0,-2,-2,-2,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[990,-162,30,45,-9,18,0,-2,-2,
-2,0,-3,-9,3,-3,-6,3,0,0,-2,0,0,0,1,1,-2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[
990,126,-18,45,-9,18,0,-2,-10,-2,0,-3,9,3,-3,-6,-3,0,0,2,0,0,0,1,1,-2,1,-1,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],[660,84,20,30,-15,3,3,-4,4,0,0,6,3,-3,2,3,-1,-3,
-1,0,0,0,0,2,-1,-1,0,1,0,0,10,-2,1,1,2,2,-2,0,1,0,0,-1,-1],
[TENSOR,[33,2]],[1408,128,0,-104,4,4,4,0,0,0,-2,8,-16,-4,0,-4,0,2,0,0,1,1,0,0,
0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0],[1760,96,32,20,14,-16,-10,0,0,0,0,-12,
6,-6,-4,0,2,0,2,0,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[891,27,-21,
81,0,0,0,3,3,-1,1,9,0,0,-3,0,0,0,0,-1,0,0,0,-3,0,0,-1,0,1,0,9,-3,0,0,-3,-3,1,
-1,0,1,1,0,0],
[TENSOR,[37,2]],[1782,54,-42,-81,0,0,0,6,6,-2,2,-9,0,0,3,0,0,0,0,-2,0,0,0,3,0,
0,1,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1980,-36,12,-45,-18,-18,0,-4,-12,-4,0,
3,0,6,3,6,0,0,0,0,0,0,0,-1,2,2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[1024,0,0,
64,16,-8,4,0,0,0,-1,0,0,0,0,0,0,0,0,0,-2,1,1,0,0,0,0,0,-1,0,16,0,-2,-2,0,0,0,
1,0,0,0,0,0],
[TENSOR,[41,2]],[2430,-162,-18,0,0,0,0,-18,6,6,0,0,0,0,0,0,0,0,0,2,0,0,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(35,36)(40,41)(42,43)]);
ALF("U5(2).2","Suz.2",[1,2,2,4,5,5,5,7,8,9,12,13,14,15,13,15,14,14,15,19,
21,21,24,25,26,26,27,29,33,34,39,40,43,43,48,48,49,53,55,58,58,63,63],[
"fusion map is unique"
]);
LIBTABLE.LOADSTATUS.ctounit3:="userloaded";
ALN:= NotifyCharTableName;
#############################################################################
##
#E
|