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Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/ctbllib/data/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 12.2.2024 mit Größe 3 MB image not shown  

Quelle  ctodefno.tbl   Sprache: unbekannt

 
#############################################################################
##
#W  ctodefno.tbl                GAP table library               Thomas Breuer
##
##  This file contains ordinary character tables of defect normalizers
##  in central extensions of sporadic simple groups.
##

MOT("NDG(12.M22,3^2)",
[
"origin: Dixon's Algorithm"
],
[864,864,144,24,864,864,144,36,36,36,864,864,144,24,864,864,144,144,144,72,72,
72,36,36,36,24,24,48,48,48,48,864,864,864,864,144,144,144,144,72,72,72,36,36,
36,36,36,36,24,24,48,48,48,48,48,48,48,48],
[,[1,1,1,1,6,5,7,8,9,10,2,2,2,2,6,5,7,6,5,7,7,7,8,9,10,6,5,13,13,13,13,16,15,
16,15,17,17,16,15,17,17,17,23,23,24,24,25,25,16,15,39,38,39,38,39,38,39,38],[1
,2,3,4,1,1,1,1,1,1,12,11,13,14,2,2,2,3,3,3,3,3,2,2,2,4,4,29,28,30,31,12,12,11,
11,12,11,13,13,13,13,13,12,11,12,11,12,11,14,14,29,29,28,28,30,30,31,31]],
[[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,-1,1,1,-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,-1,1,1,1,1],
[TENSOR,[2,3]],[2,2,2,0,2,2,2,-1,-1,-1,2,2,2,0,2,2,2,2,2,2,2,2,-1,-1,-1,0,0,0
,0,0,0,2,2,2,2,2,2,2,2,2,2,2,-1,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[5,2]],[2,2,2,0,2,2,-1,2,-1,-1,2,2,2,0,2,2,-1,2,2,-1,-1,-1,2,-1,-1,0,
0,0,0,0,0,2,2,2,2,-1,-1,2,2,-1,-1,-1,2,2,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[7,2]],[2,2,-2,0,2,2,-1,-1,-1,2,-2,-2,2,0,2,2,-1,-2,-2,1,1,1,-1,-1,2,
0,0,0,0,0,0,-2,-2,-2,-2,1,1,2,2,-1,-1,-1,1,1,1,1,-2,-2,0,0,0,0,0,0,0,0,0,0],[2
,2,-2,0,2,2,-1,-1,2,-1,-2,-2,2,0,2,2,-1,-2,-2,1,1,1,-1,2,-1,0,0,0,0,0,0,-2,-2,
-2,-2,1,1,2,2,-1,-1,-1,1,1,-2,-2,1,1,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[9,2]],
[TENSOR,[10,2]],[2,-2,0,0,2,2,2,-1,-1,-1,-2*E(4),2*E(4),0,0,-2,-2,-2,0,0,0,0,
0,1,1,1,0,0,-E(8)+E(8)^3,E(8)-E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,-2*E(4),-2*E(4),
2*E(4),2*E(4),-2*E(4),2*E(4),0,0,0,0,0,E(4),-E(4),E(4),-E(4),E(4),-E(4),0,0,
-E(8)+E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,
-E(8)-E(8)^3,-E(8)-E(8)^3],
[TENSOR,[13,4]],
[TENSOR,[13,2]],
[TENSOR,[13,3]],[3,3,1,-1,3,3,3,0,0,0,-3,-3,-1,1,3,3,3,1,1,1,1,1,0,0,0,-1,-1,
-1,-1,1,1,-3,-3,-3,-3,-3,-3,-1,-1,-1,-1,-1,0,0,0,0,0,0,1,1,-1,-1,-1,-1,1,1,1,1
],
[TENSOR,[17,4]],
[TENSOR,[17,3]],
[TENSOR,[17,2]],[3,3,-3,-1,3*E(3)^2,3*E(3),0,0,0,0,-3,-3,3,1,3*E(3)^2,3*E(3),
0,-3*E(3)^2,-3*E(3),0,0,0,0,0,0,-E(3)^2,-E(3),1,1,-1,-1,-3*E(3)^2,-3*E(3),
-3*E(3)^2,-3*E(3),0,0,3*E(3)^2,3*E(3),0,0,0,0,0,0,0,0,0,E(3)^2,E(3),E(3)^2,
E(3),E(3)^2,E(3),-E(3)^2,-E(3),-E(3)^2,-E(3)],
[GALOIS,[21,2]],
[TENSOR,[21,4]],
[TENSOR,[22,4]],
[TENSOR,[21,3]],
[TENSOR,[22,3]],
[TENSOR,[21,2]],
[TENSOR,[22,2]],[3,3,1,-1,3*E(3)^2,3*E(3),0,0,0,0,-3,-3,-1,1,3*E(3)^2,3*E(3),
0,E(3)^2,E(3),-2,-2*E(3)^2,-2*E(3),0,0,0,-E(3)^2,-E(3),-1,-1,1,1,-3*E(3)^2,
-3*E(3),-3*E(3)^2,-3*E(3),0,0,-E(3)^2,-E(3),2,2*E(3)^2,2*E(3),0,0,0,0,0,0,
E(3)^2,E(3),-E(3)^2,-E(3),-E(3)^2,-E(3),E(3)^2,E(3),E(3)^2,E(3)],
[GALOIS,[29,2]],
[TENSOR,[29,4]],
[TENSOR,[30,4]],
[TENSOR,[29,3]],
[TENSOR,[30,3]],
[TENSOR,[29,2]],
[TENSOR,[30,2]],[4,-4,0,0,4,4,4,1,1,1,-4*E(4),4*E(4),0,0,-4,-4,-4,0,0,0,0,0,
-1,-1,-1,0,0,0,0,0,0,-4*E(4),-4*E(4),4*E(4),4*E(4),-4*E(4),4*E(4),0,0,0,0,0,
-E(4),E(4),-E(4),E(4),-E(4),E(4),0,0,0,0,0,0,0,0,0,0],
[TENSOR,[37,2]],[4,-4,0,0,4,4,-2,-2,1,1,-4*E(4),4*E(4),0,0,-4,-4,2,0,0,0,0,0,
2,-1,-1,0,0,0,0,0,0,-4*E(4),-4*E(4),4*E(4),4*E(4),2*E(4),-2*E(4),0,0,0,0,0,
2*E(4),-2*E(4),-E(4),E(4),-E(4),E(4),0,0,0,0,0,0,0,0,0,0],
[TENSOR,[39,2]],[4,-4,0,0,4,4,-2,1,-2,1,-4*E(4),4*E(4),0,0,-4,-4,2,0,0,0,0,0,
-1,2,-1,0,0,0,0,0,0,-4*E(4),-4*E(4),4*E(4),4*E(4),2*E(4),-2*E(4),0,0,0,0,0,
-E(4),E(4),2*E(4),-2*E(4),-E(4),E(4),0,0,0,0,0,0,0,0,0,0],
[TENSOR,[41,2]],[4,-4,0,0,4,4,-2,1,1,-2,-4*E(4),4*E(4),0,0,-4,-4,2,0,0,0,0,0,
-1,-1,2,0,0,0,0,0,0,-4*E(4),-4*E(4),4*E(4),4*E(4),2*E(4),-2*E(4),0,0,0,0,0,
-E(4),E(4),-E(4),E(4),2*E(4),-2*E(4),0,0,0,0,0,0,0,0,0,0],
[TENSOR,[43,2]],[6,6,-2,0,6,6,-3,0,0,0,6,6,-2,0,6,6,-3,-2,-2,1,1,1,0,0,0,0,0,
0,0,0,0,6,6,6,6,-3,-3,-2,-2,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[45,2]],[6,-6,0,0,6*E(3)^2,6*E(3),0,0,0,0,-6*E(4),6*E(4),0,0,
-6*E(3)^2,-6*E(3),0,0,0,0,0,0,0,0,0,0,0,E(8)-E(8)^3,-E(8)+E(8)^3,-E(8)-E(8)^3,
E(8)+E(8)^3,-6*E(12)^11,-6*E(12)^7,6*E(12)^11,6*E(12)^7,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,-E(24)+E(24)^19,E(24)^11-E(24)^17,E(24)-E(24)^19,-E(24)^11+E(24)^17,
-E(24)-E(24)^19,-E(24)^11-E(24)^17,E(24)+E(24)^19,E(24)^11+E(24)^17],
[TENSOR,[47,4]],
[TENSOR,[47,2]],
[TENSOR,[47,3]],
[GALOIS,[47,5]],
[TENSOR,[51,4]],
[TENSOR,[51,2]],
[TENSOR,[51,3]],[6,6,-2,0,6*E(3)^2,6*E(3),0,0,0,0,6,6,-2,0,6*E(3)^2,6*E(3),0,
-2*E(3)^2,-2*E(3),-2,-2*E(3)^2,-2*E(3),0,0,0,0,0,0,0,0,0,6*E(3)^2,6*E(3),
6*E(3)^2,6*E(3),0,0,-2*E(3)^2,-2*E(3),-2,-2*E(3)^2,-2*E(3),0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0],
[GALOIS,[55,2]],
[TENSOR,[55,2]],
[TENSOR,[56,2]]],
[( 9,10)(24,25)(45,47)(46,48),( 8, 9)(23,24)(43,45)(44,46),
(28,29)(30,31)(51,53)(52,54)(55,57)(56,58),
(11,12)(30,31)(32,34)(33,35)(36,37)(43,44)(45,46)(47,48)(55,57)(56,58),
( 5, 6)(15,16)(18,19)(21,22)(26,27)(32,33)(34,35)(38,39)(41,42)(49,50)(51,52)
(53,54)(55,56)(57,58)
]);
ALF("NDG(12.M22,3^2)","(A4x3):2",[1,1,3,8,1,1,2,5,6,7,1,1,3,8,1,1,2,3,3,4,
4,4,5,6,7,8,8,9,9,9,9,1,1,1,1,2,2,3,3,4,4,4,5,5,6,6,7,7,8,8,9,9,9,9,9,9,9,
9]);
ALF("NDG(12.M22,3^2)","2x(A4x3):2",[1,1,12,8,1,1,2,5,6,7,10,10,3,17,1,1,2,
12,12,13,13,13,5,6,7,8,8,18,18,9,9,10,10,10,10,11,11,3,3,4,4,4,14,14,15,
15,16,16,17,17,18,18,18,18,9,9,9,9]);
ALF("NDG(12.M22,3^2)","3.(A4x3):2",[1,1,2,14,3,4,8,10,7,9,1,1,2,14,3,4,8,
6,5,11,12,13,10,7,9,16,17,15,15,15,15,3,4,3,4,8,8,6,5,11,12,13,10,10,7,7,
9,9,16,17,19,18,19,18,19,18,19,18]);
ALF("NDG(12.M22,3^2)","Isoclinic(2x(2.A4x3).2)",[1,3,20,28,1,1,2,7,8,9,16,
18,5,13,3,3,4,20,20,21,21,21,10,11,12,28,28,14,15,29,30,16,16,18,18,17,19,
5,5,6,6,6,22,25,23,26,24,27,13,13,14,14,15,15,29,29,30,30]);
ALF("NDG(12.M22,3^2)","2x3.(A4x3):2",[1,1,4,27,5,7,15,19,13,17,2,2,3,28,5,
7,15,12,10,22,24,26,19,13,17,31,33,30,30,29,29,6,8,6,8,16,16,11,9,21,23,
25,20,20,14,14,18,18,32,34,38,36,38,36,37,35,37,35]);
ALF("NDG(12.M22,3^2)","12.M22",[1,7,13,13,5,9,19,19,19,19,4,10,16,16,11,3,
21,17,15,44,48,46,21,21,21,17,15,29,29,29,29,8,12,2,6,22,20,14,18,47,45,
49,22,20,22,20,22,20,14,18,30,31,30,31,30,31,30,31]);

MOT("12.M22N3",
[
"origin: Dixon's Algorithm"
],
[864,864,864,864,864,864,864,864,864,864,864,864,96,96,96,96,96,96,96,96,96,96
,96,96,36,36,36,36,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48
,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48],
[,[1,1,2,2,9,9,10,10,5,5,6,6,1,1,2,2,9,9,10,10,5,5,6,6,25,25,26,26,13,13,14,14
,21,21,22,22,17,17,18,18,15,15,16,16,23,23,24,24,19,19,20,20,15,15,16,16,23,23
,24,24,19,19,20,20],[1,2,4,3,1,2,4,3,1,2,4,3,13,14,16,15,13,14,16,15,13,14,16,
15,1,2,4,3,29,30,32,31,29,30,32,31,29,30,32,31,43,44,41,42,43,44,41,42,43,44,
41,42,56,55,54,53,56,55,54,53,56,55,54,53]],
[[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,-1,-1,1,1,-1,-1,-1,-1,1,
1,-1,-1,1,1,-1,-1,1,1,-E(4),-E(4),E(4),E(4),-E(4),-E(4),E(4),E(4),-E(4),-E(4),
E(4),E(4),E(4),E(4),-E(4),-E(4),E(4),E(4),-E(4),-E(4),E(4),E(4),-E(4),-E(4)],[
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],
[GALOIS,[2,3]],
[TENSOR,[1,3]],
[TENSOR,[1,4]],
[TENSOR,[1,1]],
[TENSOR,[1,2]],[2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,2
,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
],
[TENSOR,[9,2]],[8,8,8,8,8,8,8,8,8,8,8,8,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,-1,-1,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[11,2]],[3,3,3,3,3*E(3),3*E(3),3*E(3),3*E(3),3*E(3)^2,3*E(3)^2,
3*E(3)^2,3*E(3)^2,-1,-1,-1,-1,-E(3),-E(3),-E(3),-E(3),-E(3)^2,-E(3)^2,-E(3)^2,
-E(3)^2,0,0,0,0,-1,-1,-1,-1,-E(3),-E(3),-E(3),-E(3),-E(3)^2,-E(3)^2,-E(3)^2,
-E(3)^2,-1,-1,-1,-1,-E(3),-E(3),-E(3),-E(3),-E(3)^2,-E(3)^2,-E(3)^2,-E(3)^2,1,
1,1,1,E(3),E(3),E(3),E(3),E(3)^2,E(3)^2,E(3)^2,E(3)^2],
[TENSOR,[13,8]],
[TENSOR,[13,1]],
[TENSOR,[13,2]],
[TENSOR,[13,3]],
[TENSOR,[13,4]],
[TENSOR,[13,5]],
[TENSOR,[13,6]],
[GALOIS,[13,2]],
[TENSOR,[21,8]],
[TENSOR,[21,1]],
[TENSOR,[21,2]],
[TENSOR,[21,3]],
[TENSOR,[21,4]],
[TENSOR,[21,5]],
[TENSOR,[21,6]],[6,6,6,6,6*E(3),6*E(3),6*E(3),6*E(3),6*E(3)^2,6*E(3)^2,
6*E(3)^2,6*E(3)^2,2,2,2,2,2*E(3),2*E(3),2*E(3),2*E(3),2*E(3)^2,2*E(3)^2,
2*E(3)^2,2*E(3)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],
[TENSOR,[29,2]],
[GALOIS,[29,2]],
[TENSOR,[31,2]],[1,-1,-E(4),E(4),1,-1,-E(4),E(4),1,-1,-E(4),E(4),1,-1,-E(4),
E(4),1,-1,-E(4),E(4),1,-1,-E(4),E(4),1,-1,-E(4),E(4),-1,1,-E(4),E(4),-1,1,
-E(4),E(4),-1,1,-E(4),E(4),-E(8)^3,E(8)^3,-E(8),E(8),-E(8)^3,E(8)^3,-E(8),E(8)
,-E(8)^3,E(8)^3,-E(8),E(8),E(8)^3,-E(8)^3,-E(8),E(8),E(8)^3,-E(8)^3,-E(8),E(8)
,E(8)^3,-E(8)^3,-E(8),E(8)],
[TENSOR,[33,5]],
[TENSOR,[33,6]],
[TENSOR,[33,8]],
[TENSOR,[1,34]],
[TENSOR,[1,33]],
[TENSOR,[1,36]],
[TENSOR,[1,35]],
[TENSOR,[9,33]],
[TENSOR,[9,35]],
[TENSOR,[21,38]],
[TENSOR,[21,37]],
[TENSOR,[21,40]],
[TENSOR,[21,39]],
[TENSOR,[13,38]],
[TENSOR,[13,37]],
[TENSOR,[13,40]],
[TENSOR,[13,39]],
[TENSOR,[21,34]],
[TENSOR,[21,33]],
[TENSOR,[21,36]],
[TENSOR,[21,35]],
[TENSOR,[13,34]],
[TENSOR,[13,33]],
[TENSOR,[13,36]],
[TENSOR,[13,35]],
[TENSOR,[31,33]],
[TENSOR,[29,33]],
[TENSOR,[31,35]],
[TENSOR,[29,35]],
[TENSOR,[11,33]],
[TENSOR,[11,35]]],
[
(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)
(63,64)
,
(41,53)(42,54)(43,56)(44,55)(45,57)(46,58)(47,60)(48,59)(49,61)(50,62)(51,64)
(52,63)
,
(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(53,54)(55,56)(57,58)(59,60)(61,62)
(63,64)
,
( 5, 9)( 6,10)( 7,11)( 8,12)(17,21)(18,22)(19,23)(20,24)(33,37)(34,38)(35,39)
(36,40)(45,49)(46,50)(47,51)(48,52)(57,61)(58,62)(59,63)(60,64)
,
( 3, 4)( 7, 8)(11,12)(15,16)(19,20)(23,24)(27,28)(31,32)(35,36)(39,40)(41,43)
(42,44)(45,47)(46,48)(49,51)(50,52)(53,56)(54,55)(57,60)(58,59)(61,64)(62,63)
]);
ALF("12.M22N3","3^2:Q8",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,
3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,
6,6,6]);
ALF("12.M22N3","Isoclinic(2x3^2:Q8)",[1,1,2,2,1,1,2,2,1,1,2,2,3,3,4,4,3,3,
4,4,3,3,4,4,5,5,6,6,7,7,8,8,7,7,8,8,7,7,8,8,9,9,10,10,9,9,10,10,9,9,10,10,
11,11,12,12,11,11,12,12,11,11,12,12]);
ALF("12.M22N3","3^(1+2)_+:Q8",[1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,
6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,
13,13,14,14,14,14,15,15,15,15,16,16,16,16]);
ALF("12.M22N3","Isoclinic(4x3^2:Q8)",[1,13,7,19,1,13,7,19,1,13,7,19,2,14,
8,20,2,14,8,20,2,14,8,20,3,15,9,21,6,18,24,12,6,18,24,12,6,18,24,12,4,16,
10,22,4,16,10,22,4,16,10,22,5,17,23,11,5,17,23,11,5,17,23,11]);
ALF("12.M22N3","Isoclinic(2x3^(1+2)_+:Q8)",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,
8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,
21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32]);
ALF("12.M22N3","12_1.L3(4)",[1,7,10,4,5,11,2,8,9,3,6,12,13,13,16,16,17,17,
14,14,15,15,18,18,19,21,20,22,26,26,23,23,24,24,27,27,28,28,25,25,32,32,
32,32,33,33,33,33,34,34,34,34,29,29,29,29,30,30,30,30,31,31,31,31],[
"fusion map determined using the groups 4.M22N3 and 4_1.L3(4)"
]);
ALF("12.M22N3","12.M22",[1,7,10,4,5,11,2,8,9,3,6,12,13,13,16,16,17,17,14,
14,15,15,18,18,19,21,20,22,23,23,26,26,27,27,24,24,25,25,28,28,29,29,29,
29,30,30,30,30,31,31,31,31,29,29,29,29,30,30,30,30,31,31,31,31],[
"fusion map determined by factorization through 12_1.L3(4) and more"
]);

MOT("3xIsoclinic(2x5:8)",
0,
0,
0,
0,
[
(31,37)(32,38)(33,39)(34,40)(35,41)(36,42)(43,46)(44,47)(45,48)(49,52)(50,53)
(51,54)(55,58)(56,59)(57,60)
,
(19,22)(20,23)(21,24)(25,28)(26,29)(27,30)(49,52)(50,53)(51,54)(55,58)(56,59)
(57,60)
,
(19,55)(20,56)(21,57)(22,58)(23,59)(24,60)(25,52)(26,53)(27,54)(28,49)(29,50)
(30,51)
,
(13,16)(14,17)(15,18)(19,25)(20,26)(21,27)(22,28)(23,29)(24,30)(43,46)(44,47)
(45,48)(49,55)(50,56)(51,57)(52,58)(53,59)(54,60)
,
( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)
(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)
],
["ConstructDirectProduct",[["Isoclinic(2x5:8)"],["Cyclic",3]]]);
ALF("3xIsoclinic(2x5:8)","5:4",[1,1,1,2,2,2,1,1,1,2,2,2,4,4,4,4,4,4,3,3,3,
3,3,3,5,5,5,5,5,5,1,1,1,2,2,2,1,1,1,2,2,2,4,4,4,4,4,4,3,3,3,3,3,3,5,5,5,5,
5,5]);
ALF("3xIsoclinic(2x5:8)","2x5:4",[1,1,1,2,2,2,1,1,1,2,2,2,4,4,4,4,4,4,3,3,
3,3,3,3,5,5,5,5,5,5,6,6,6,7,7,7,6,6,6,7,7,7,9,9,9,9,9,9,8,8,8,8,8,8,10,10,
10,10,10,10]);
ALF("3xIsoclinic(2x5:8)","5:4x3",[1,2,3,4,5,6,1,2,3,4,5,6,10,11,12,10,11,
12,7,8,9,7,8,9,13,14,15,13,14,15,1,2,3,4,5,6,1,2,3,4,5,6,10,11,12,10,11,
12,7,8,9,7,8,9,13,14,15,13,14,15]);
ALF("3xIsoclinic(2x5:8)","Isoclinic(2x5:8)",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,
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]);
ALF("3xIsoclinic(2x5:8)","6x5:4",[1,21,11,2,22,12,1,21,11,2,22,12,4,24,14,
4,24,14,3,23,13,3,23,13,5,25,15,5,25,15,16,6,26,17,7,27,16,6,26,17,7,27,
19,9,29,19,9,29,18,8,28,18,8,28,20,10,30,20,10,30]);
ALF("3xIsoclinic(2x5:8)","C3",[1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,
1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,
2,3]);
ALF("3xIsoclinic(2x5:8)","12.M22",[1,5,9,32,36,40,7,11,3,38,42,34,16,14,
18,16,14,18,29,30,31,29,30,31,29,30,31,29,30,31,10,2,6,41,33,37,4,8,12,35,
39,43,13,17,15,13,17,15,29,30,31,29,30,31,29,30,31,29,30,31],[
"compatible with 2x5:4 -> 2.M22"
]);
ALN("3xIsoclinic(2x5:8)",["12.M22N5"]);

MOT("12x7:3",
0,
0,
0,
0,
[
(13,25)(14,26)(15,27)(16,28)(17,29)(18,30)(19,31)(20,32)(21,33)(22,34)(23,35)
(24,36)
,
(37,41,45)(38,42,46)(39,43,47)(40,44,48)(49,57,53)(50,58,54)(51,59,55)
(52,60,56)
,
(37,49)(38,50)(39,51)(40,52)(41,53)(42,54)(43,55)(44,56)(45,57)(46,58)(47,59)
(48,60)
,
( 2, 6)( 3,11)( 5, 9)( 8,12)(14,18)(15,23)(17,21)(20,24)(26,30)(27,35)(29,33)
(32,36)(38,42)(39,47)(41,45)(44,48)(50,54)(51,59)(53,57)(56,60)
,
( 2, 8)( 4,10)( 6,12)(14,20)(16,22)(18,24)(26,32)(28,34)(30,36)(38,44)(40,46)
(42,48)(50,56)(52,58)(54,60)
],
["ConstructDirectProduct",[["7:3"],["Cyclic",12]]]);
ALF("12x7:3","7:3",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,
3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5]);
ALF("12x7:3","2x7:3",[1,2,1,2,1,2,1,2,1,2,1,2,3,4,3,4,3,4,3,4,3,4,3,4,5,6,
5,6,5,6,5,6,5,6,5,6,7,8,7,8,7,8,7,8,7,8,7,8,9,10,9,10,9,10,9,10,9,10,9,10]);
ALF("12x7:3","7:3x3",[1,2,3,1,2,3,1,2,3,1,2,3,4,5,6,4,5,6,4,5,6,4,5,6,7,8,
9,7,8,9,7,8,9,7,8,9,10,11,12,10,11,12,10,11,12,10,11,12,13,14,15,13,14,15,
13,14,15,13,14,15]);
ALF("12x7:3","4x7:3",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,7,8,5,6,7,8,5,6,7,8,9,
10,11,12,9,10,11,12,9,10,11,12,13,14,15,16,13,14,15,16,13,14,15,16,17,18,
19,20,17,18,19,20,17,18,19,20]);
ALF("12x7:3","6x7:3",[1,6,11,16,21,26,1,6,11,16,21,26,2,7,12,17,22,27,2,7,
12,17,22,27,3,8,13,18,23,28,3,8,13,18,23,28,4,9,14,19,24,29,4,9,14,19,24,
29,5,10,15,20,25,30,5,10,15,20,25,30]);
ALF("12x7:3","12.M22",[1,2,3,4,5,6,7,8,9,10,11,12,50,51,52,53,54,55,56,57,
58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,19,20,21,22,19,20,21,22,
19,20,21,22,19,20,21,22,19,20,21,22,19,20,21,22],[
"fusion map is unique up to table aut."
]);
ALN("12x7:3",["12.M22N7"]);

MOT("12x11:5",
0,
0,
0,
0,
[
(13,25)(14,26)(15,27)(16,28)(17,29)(18,30)(19,31)(20,32)(21,33)(22,34)(23,35)
(24,36)
,
(37,49,73,61)(38,50,74,62)(39,51,75,63)(40,52,76,64)(41,53,77,65)(42,54,78,66)
(43,55,79,67)(44,56,80,68)(45,57,81,69)(46,58,82,70)(47,59,83,71)(48,60,84,72)
,
( 2, 6)( 3,11)( 5, 9)( 8,12)(14,18)(15,23)(17,21)(20,24)(26,30)(27,35)(29,33)
(32,36)(38,42)(39,47)(41,45)(44,48)(50,54)(51,59)(53,57)(56,60)(62,66)(63,71)
(65,69)(68,72)(74,78)(75,83)(77,81)(80,84)
,
( 2, 8)( 4,10)( 6,12)(14,20)(16,22)(18,24)(26,32)(28,34)(30,36)(38,44)(40,46)
(42,48)(50,56)(52,58)(54,60)(62,68)(64,70)(66,72)(74,80)(76,82)(78,84)
],
["ConstructDirectProduct",[["11:5"],["Cyclic",12]]]);
ALF("12x11:5","11:5",[1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,
3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,
6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7]);
ALF("12x11:5","2x11:5",[1,8,1,8,1,8,1,8,1,8,1,8,2,9,2,9,2,9,2,9,2,9,2,9,3,
10,3,10,3,10,3,10,3,10,3,10,4,11,4,11,4,11,4,11,4,11,4,11,5,12,5,12,5,12,
5,12,5,12,5,12,6,13,6,13,6,13,6,13,6,13,6,13,7,14,7,14,7,14,7,14,7,14,7,
14]);
ALF("12x11:5","3x11:5",[1,8,15,1,8,15,1,8,15,1,8,15,2,9,16,2,9,16,2,9,16,
2,9,16,3,10,17,3,10,17,3,10,17,3,10,17,4,11,18,4,11,18,4,11,18,4,11,18,5,
12,19,5,12,19,5,12,19,5,12,19,6,13,20,6,13,20,6,13,20,6,13,20,7,14,21,7,
14,21,7,14,21,7,14,21]);
ALF("12x11:5","4x11:5",[1,2,3,4,1,2,3,4,1,2,3,4,5,6,7,8,5,6,7,8,5,6,7,8,9,
10,11,12,9,10,11,12,9,10,11,12,13,14,15,16,13,14,15,16,13,14,15,16,17,18,
19,20,17,18,19,20,17,18,19,20,21,22,23,24,21,22,23,24,21,22,23,24,25,26,
27,28,25,26,27,28,25,26,27,28]);
ALF("12x11:5","6x11:5",[1,2,3,4,5,6,1,2,3,4,5,6,7,8,9,10,11,12,7,8,9,10,
11,12,13,14,15,16,17,18,13,14,15,16,17,18,19,20,21,22,23,24,19,20,21,22,
23,24,25,26,27,28,29,30,25,26,27,28,29,30,31,32,33,34,35,36,31,32,33,34,
35,36,37,38,39,40,41,42,37,38,39,40,41,42]);
ALF("12x11:5","12.M22",[1,2,3,4,5,6,7,8,9,10,11,12,86,87,88,89,90,91,92,
93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,32,33,34,35,
36,37,38,39,40,41,42,43,32,33,34,35,36,37,38,39,40,41,42,43,32,33,34,35,
36,37,38,39,40,41,42,43,32,33,34,35,36,37,38,39,40,41,42,43],[
"fusion map is unique up to table aut."
]);
ALN("12x11:5",["12.M22N11"]);

MOT("3x2.M22N2",
0,
0,
0,
0,
[(88,91)(89,92)(90,93),(82,85)(83,86)(84,87),(76,79)(77,80)(78,81),
(43,46)(44,47)(45,48)(70,73)(71,74)(72,75),
(37,40)(38,41)(39,42)(70,73)(71,74)(72,75),
(31,34)(32,35)(33,36)(55,58)(56,59)(57,60),
(19,25)(20,26)(21,27)(22,28)(23,29)(24,30)(37,43)(38,44)(39,45)(40,46)(41,47)
(42,48)(61,64)(62,65)(63,66)(76,82)(77,83)(78,84)(79,85)(80,86)(81,87)
,
( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)
(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)
(68,69)(71,72)(74,75)(77,78)(80,81)(83,84)(86,87)(89,90)(92,93)
],
["ConstructDirectProduct",[["2.M22N2"],["Cyclic",3]]]);
ALF("3x2.M22N2","2^4:D8",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,
5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,
10,10,11,11,11,12,12,12,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,16,
16,16,16,16,16,17,17,17,17,17,17]);
ALF("3x2.M22N2","2.M22N2",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,
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]);
ALF("3x2.M22N2","C3",[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,
3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,
1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1,2,3]);
ALF("3x2.M22N2","3xMcLN2",[1,2,3,1,2,3,4,5,6,4,5,6,7,8,9,7,8,9,10,11,12,
10,11,12,13,14,15,13,14,15,19,20,21,19,20,21,22,23,24,22,23,24,16,17,18,
16,17,18,25,26,27,25,26,27,31,32,33,31,32,33,37,38,39,28,29,30,34,35,36,
40,41,42,40,41,42,46,47,48,46,47,48,43,44,45,43,44,45,49,50,51,49,50,51]);
ALF("3x2.M22N2","6.M22",[1,5,3,4,2,6,10,8,12,7,11,9,7,11,9,10,8,12,10,8,
12,7,11,9,7,11,9,10,8,12,7,11,9,10,8,12,7,11,9,10,8,12,7,11,9,10,8,12,18,
16,20,15,19,17,18,16,20,15,19,17,21,22,23,21,22,23,21,22,23,18,16,20,15,
19,17,15,19,17,18,16,20,21,22,23,21,22,23,48,52,50,51,49,53]);
ALN("3x2.M22N2",["6.M22N2"]);

MOT("2x3.(A4x3):2",
0,
0,
0,
0,
[(27,28)(29,30)(31,32)(33,34)(35,36)(37,38),(17,19)(18,20),(13,17)(14,18),
( 5, 7)( 6, 8)( 9,11)(10,12)(23,25)(24,26)(31,33)(32,34)(35,37)(36,38)],
["ConstructDirectProduct",[["3.(A4x3):2"],["Cyclic",2]]]);
ALF("2x3.(A4x3):2","3.(A4x3):2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,
10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19]);
ALF("2x3.(A4x3):2","2x(A4x3):2",[1,10,3,12,1,10,1,10,3,12,3,12,6,15,2,11,
7,16,5,14,4,13,4,13,4,13,8,17,9,18,8,17,8,17,9,18,9,18]);
ALF("2x3.(A4x3):2","(A4x3):2",[1,1,3,3,1,1,1,1,3,3,3,3,6,6,2,2,7,7,5,5,4,
4,4,4,4,4,8,8,9,9,8,8,8,8,9,9,9,9]);
ALF("2x3.(A4x3):2","6.M22",[1,4,10,7,5,2,3,6,12,9,8,11,13,14,13,14,13,14,
13,14,33,30,31,34,35,32,7,10,21,21,11,8,9,12,23,23,22,22]);

MOT("(GL(2,3)x2F4(2)').2",
[
"origin: Dixon's Algorithm"
],
[1725235200,1725235200,983040,983040,147456,147456,10368,10368,18432,18432,
12288,12288,6144,6144,4800,4800,1152,1152,3072,3072,3072,3072,768,768,960,960,
576,576,624,624,768,768,768,768,30720,30720,4608,3072,768,384,288,288,384,384,
480,480,287539200,163840,24576,1728,3072,2048,1024,800,192,512,512,128,160,96,
104,128,128,10240,10240,1536,1024,256,128,96,96,128,128,160,160,215654400,
215654400,122880,122880,18432,18432,1296,1296,2304,2304,1536,1536,768,768,600,
600,144,144,384,384,384,384,96,96,120,120,72,72,78,78,96,96,96,96,7680,7680,
7680,7680,1152,1152,768,768,192,192,96,96,72,72,72,72,96,96,96,96,120,120,120,
120,143769600,81920,12288,864,1536,1024,512,400,96,256,256,64,80,48,52,64,64,
5120,5120,768,512,128,64,48,48,64,64,80,80,143769600,81920,12288,864,1536,1024
,512,400,96,256,256,128,128,80,96,96,104,104,128,128,128,128,5120,5120,768,512
,128,64,48,48,64,64,80,80],
[,[1,1,1,1,1,1,7,7,5,5,3,3,5,5,15,15,7,7,11,11,11,11,13,13,15,15,17,17,29,29,
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--> --------------------

--> maximum size reached

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

[ Dauer der Verarbeitung: 0.19 Sekunden  (vorverarbeitet)  ]