SSL ctodefno.tbl   Interaktion und
Portierbarkeitunbekannt

#############################################################################
##
#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,
19,19,21,21,3,3,5,3,11,9,17,17,19,21,25,25,2,2,2,8,6,4,6,16,8,12,12,14,16,18,
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E(104)^5+E(104)^7+E(104)^15+E(104)^21-E(104)^23-E(104)^29+E(104)^31+E(104)^37
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[(181,182)(183,184),(177,178),(174,175),
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(110,111)(112,113)(114,115)(116,117)(118,119)(120,121)(122,123)(124,125)
(126,127)(128,129)(130,131)(132,133)
,(179,180),
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(151,152)(159,160)(161,162)(172,173)(181,184)(182,183)(185,186)(193,194)
(195,196)
]);
ALF("(GL(2,3)x2F4(2)').2","S4x2F4(2)'.2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,
9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,19,20,21,22,23,24,
25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
49,50,51,52,53,54,55,56,57,58,59,59,60,60,61,61,62,62,63,63,64,64,65,65,
66,66,67,67,68,68,69,69,70,70,71,71,72,72,73,73,74,74,75,75,76,76,77,77,
78,78,79,79,80,80,81,81,82,82,83,83,84,84,85,85,86,86,87,87,88,89,90,91,
92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,
112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,128,
129,130,130,131,131,132,132,133,133,134,135,136,137,138,139,140,141,142,
143,144,145]);
ALF("(GL(2,3)x2F4(2)').2","2.B",[1,2,5,4,7,7,10,11,17,16,14,14,16,17,23,24,
38,37,46,46,46,46,52,52,64,63,79,78,97,98,109,109,109,109,12,12,20,18,43,
49,92,92,110,110,130,130,6,6,6,40,22,19,22,65,40,50,50,49,65,93,168,110,
110,19,19,22,19,50,52,93,93,109,109,135,135,8,9,30,29,36,36,10,11,84,83,
80,80,83,84,105,106,39,39,157,157,157,157,160,160,182,181,89,88,211,212,
232,232,232,232,75,75,75,75,91,91,82,82,155,155,159,159,94,95,94,95,233,
233,233,233,240,240,240,240,3,7,7,31,20,18,20,62,39,50,50,52,68,92,169,
113,113,15,15,22,19,48,52,93,93,113,113,134,134,21,21,21,96,21,21,21,138,
96,55,55,57,57,138,96,96,234,235,114,114,114,114,21,21,21,21,55,57,96,96,
114,114,138,138],[
"fusion map is unique up to table automorphisms"
]);
ALN("(GL(2,3)x2F4(2)').2",["2.BM16"]);

MOT("D8x2F4(2)'.2",
[
"normalizer of a defect group of type D8 in B"
],
0,
0,
0,
[( 24, 25)( 53, 54)( 82, 83)(111,112)(140,141),
( 18, 47)( 19, 48)( 20, 49)( 21, 50)( 22, 51)( 23, 52)( 24, 53)( 25, 54)
( 26, 55)( 27, 56)( 28, 57)( 29, 58)
,
( 10, 11)( 16, 17)( 18, 19)( 26, 27)( 28, 29)( 39, 40)( 45, 46)( 47, 48)
( 55, 56)( 57, 58)( 68, 69)( 74, 75)( 76, 77)( 84, 85)( 86, 87)( 97, 98)
(103,104)(105,106)(113,114)(115,116)(126,127)(132,133)(134,135)(142,143)
(144,145)
,
( 88,117)( 89,118)( 90,119)( 91,120)( 92,121)( 93,122)( 94,123)( 95,124)
( 96,125)( 97,126)( 98,127)( 99,128)(100,129)(101,130)(102,131)(103,132)
(104,133)(105,134)(106,135)(107,136)(108,137)(109,138)(110,139)(111,140)
(112,141)(113,142)(114,143)(115,144)(116,145)
],
["ConstructDirectProduct",[["D8"],["2F4(2)'.2"]]]);
ALF("D8x2F4(2)'.2","B",[1,3,5,7,12,10,12,18,28,35,35,41,49,60,75,83,83,8,
8,15,13,32,38,71,71,84,84,99,99,4,4,4,30,17,14,17,50,30,39,39,38,50,72,
129,84,84,14,14,17,14,39,41,72,72,83,83,104,104,16,16,16,74,16,16,16,106,
74,43,43,45,106,74,176,88,88,16,16,16,16,43,45,74,74,88,88,106,106,2,5,5,
23,15,13,15,48,29,39,39,41,52,71,130,87,87,11,11,17,14,37,41,72,72,87,87,
103,103,4,4,4,30,17,14,17,50,30,39,39,38,50,72,129,84,84,14,14,17,14,39,
41,72,72,83,83,104,104]);
ALN("D8x2F4(2)'.2",["NDG(B,D8)"]);

MOT("QD16.2",
[
"auxiliary table for the construction of (QD16x2F4(2)').2,\n",
"origin: Dixon's Algorithm"
],
[32,32,16,16,16,8,8,8,8,8,8],
[,[1,1,1,2,2,4,4,1,2,2,2]],
[[1,1,1,1,1,1,1,1,1,1,1],[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]],[1,1,1,1,1,-1,-1,1,1,-1,-1],
[TENSOR,[2,5]],
[TENSOR,[3,5]],
[TENSOR,[2,7]],[2,2,2,-2,-2,0,0,0,0,0,0],
[TENSOR,[9,2]],[4,-4,0,0,0,0,0,0,0,0,0]],
[(6,7)(10,11)]);
ALF("QD16.2","2.A6.2_1",[1,2,11,3,12,8,13,11,3,12,3],[
"fusion map is unique up to table aut."
]);
ALF("QD16.2","2.A7.2",[1,2,14,3,15,8,16,14,3,15,3],[
"fusion map is unique up to table aut."
]);

MOT("(QD16x2F4(2)').2",
[
"normalizer of a defect group of type QD16 in 2.B and M,\n",
"origin: Dixon's Algorithm"
],
[575078400,575078400,327680,327680,49152,49152,3456,3456,6144,6144,4096,4096,
2048,2048,1600,1600,384,384,1024,1024,1024,1024,256,256,320,320,192,192,208,
208,256,256,256,256,10240,10240,1536,1024,256,128,96,96,128,128,160,160,
287539200,163840,24576,1728,3072,2048,1024,800,192,512,512,128,160,96,104,128,
128,10240,10240,1536,1024,256,128,96,96,128,128,160,160,143769600,81920,12288,
864,1536,1024,512,400,96,256,256,128,128,80,96,96,104,104,128,128,128,128,5120
,5120,768,512,128,64,48,48,64,64,80,80,143769600,81920,12288,864,1536,1024,512
,400,96,256,256,64,80,48,52,64,64,5120,5120,768,512,128,64,48,48,64,64,80,80,
143769600,81920,12288,864,1536,1024,512,400,96,256,256,64,80,48,52,64,64,5120,
5120,768,512,128,64,48,48,64,64,80,80],
[,[1,1,1,1,1,1,7,7,5,5,3,3,5,5,15,15,7,7,11,11,11,11,13,13,15,15,18,18,29,29,
19,19,21,21,3,3,5,3,11,10,18,18,19,21,25,25,2,2,2,8,6,4,6,16,8,12,12,14,16,17,
30,20,22,4,4,6,4,12,9,17,17,20,22,26,26,47,47,47,50,49,48,49,54,50,52,52,53,53
,54,55,55,61,61,56,56,57,57,48,48,49,48,52,51,55,55,56,57,59,59,1,1,1,7,5,3,5,
15,7,11,11,13,15,18,29,19,21,4,4,6,4,12,9,17,17,20,22,26,26,2,2,2,8,6,4,6,16,8
,12,12,14,16,17,30,20,22,4,4,6,4,12,9,17,17,20,22,26,26],[1,2,3,4,5,6,1,2,9,10
,11,12,13,14,15,16,6,5,21,22,19,20,23,24,25,26,10,9,29,30,33,34,31,32,36,35,37
,38,39,40,37,37,44,43,46,45,47,48,49,47,51,52,53,54,49,57,56,58,59,51,61,63,62
,65,64,66,67,68,69,66,66,73,72,75,74,76,77,78,76,80,81,82,83,78,86,85,87,88,89
,80,80,92,93,96,97,94,95,99,98,100,101,102,103,100,100,107,106,109,108,110,111
,112,110,114,115,116,117,112,120,119,121,122,114,124,126,125,128,127,129,130,
131,132,129,129,136,135,138,137,139,140,141,139,143,144,145,146,141,149,148,
150,151,143,153,155,154,157,156,158,159,160,161,158,158,165,164,167,166],,[1,2
,3,4,5,6,7,8,9,10,11,12,13,14,1,2,17,18,19,20,21,22,23,24,3,4,27,28,29,30,31,
32,33,34,35,36,37,38,39,40,42,41,43,44,35,36,47,48,49,50,51,52,53,47,55,56,57,
58,48,60,61,62,63,64,65,66,67,68,69,71,70,72,73,64,65,76,77,78,79,80,81,82,76,
84,85,86,88,87,77,90,91,92,93,94,95,96,97,98,99,100,101,102,103,105,104,106,
107,98,99,110,111,112,113,114,115,116,110,118,119,120,121,111,123,124,125,126,
127,128,129,130,131,132,134,133,135,136,127,128,139,140,141,142,143,144,145,
139,147,148,149,150,140,152,153,154,155,156,157,158,159,160,161,163,162,164,
165,156,157],,,,,,,,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,
23,24,25,26,27,28,1,2,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49
,50,51,52,53,54,55,56,57,58,59,60,47,62,63,64,65,66,67,68,69,70,71,72,73,74,75
,76,77,78,79,80,81,82,83,84,85,86,88,87,89,91,90,76,76,94,95,96,97,98,99,100,
101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,
120,121,122,123,110,125,126,127,128,129,130,131,132,133,134,135,136,137,138,
139,140,141,142,143,144,145,146,147,148,149,150,151,152,139,154,155,156,157,
158,159,160,161,162,163,164,165,166,167]],
0,
[(94,95)(96,97),(92,93),(90,91),(87,88),
( 41, 42)( 70, 71)(104,105)(133,134)(162,163),
( 19, 21)( 20, 22)( 31, 33)( 32, 34)( 35, 36)( 43, 44)( 45, 46)( 56, 57)
( 62, 63)( 64, 65)( 72, 73)( 74, 75)( 85, 86)( 94, 96)( 95, 97)( 98, 99)
(106,107)(108,109)(119,120)(125,126)(127,128)(135,136)(137,138)(148,149)
(154,155)(156,157)(164,165)(166,167)
],
[ "ConstructIndexTwoSubdirectProduct", "M11N2", "QD16.2", "2F4(2)'",
  "2F4(2)'.2",
  [ 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 134, 135, 136, 137, 138,
      139, 140, 141, 142, 143, 144, 145, 192, 193, 194, 195, 196, 197, 198,
      199, 200, 201, 202, 203, 250, 251, 252, 253, 254, 255, 256, 257, 258,
      259, 260, 261, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318,
      319 ], (2,3,5,10,19,4,7,13,25,16,31,28,22,9,18)(6,11,21,8,15,29,24,14,
    27,20)(12,23)(17,33,32,30,26)(35,47,59,83,119,46,58,82,118,45,57,81,117,
    44,56,80,116,43,55,79,115,42,54,78,114,41,53,77,113,40,52,76,112,39,51,63,
    87,123,67,91,139,105,153,136,102,150,133,99,147,130,74,110,37,49,61,85,
    121,65,89,125,69,93,141,107,155,138,104,152,135,101,149,132,98,146,129,73,
    96,144,127,71,95,143,109,36,48,60,84,120,64,88,124,68,92,140,106,154,137,
    103,151,134,100,148,131,75,111,38,50,62,86,122,66,90,126,70,94,142,
    108)(72,97,145,128), (1,30,88)(2,31,89)(3,32,90)(4,33,91)(5,34,92)(6,35,
    93)(7,36,94)(8,37,95)(9,38,96)(10,39,97)(11,40,98)(12,41,99)(13,42,
    100)(14,43,101)(15,44,102)(16,45,103)(17,46,104)(18,47,105)(19,48,106)(20,
    49,107)(21,50,108)(22,51,109)(23,52,110)(24,53,111)(25,54,112)(26,55,
    113)(27,56,114)(28,57,115)(29,58,116)(117,146,124,153,131,160,138,167,145,
    123,152,130,159,137,166,144,122,151,129,157,135,163,141,119,148,126,156,
    134,164,142,120,150,128,158,136,165,143,121,149,127,155,133,161,139)(118,
    147,125,154,132,162,140) ]);
ALF("(QD16x2F4(2)').2","D8x2F4(2)'.2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,
10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,19,20,21,22,23,24,25,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,70,71,72,
72,73,73,74,74,75,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,
93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,
113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,
131,132,133,134,135,136,137,138,139,140,141,142,143,144,145]);
ALF("(QD16x2F4(2)').2","2.B",[1,2,5,4,7,7,10,11,16,17,14,14,16,17,23,24,37,
38,46,46,46,46,52,52,64,63,79,78,97,98,109,109,109,109,12,12,20,18,43,49,
92,92,110,110,130,130,6,6,6,40,22,19,22,65,40,50,50,49,65,93,168,110,110,
19,19,22,19,50,52,93,93,109,109,135,135,21,21,21,96,21,21,21,138,96,55,55,
57,57,138,96,96,234,235,114,114,114,114,21,21,21,21,55,57,96,96,114,114,
138,138,3,7,7,31,20,18,20,62,39,50,50,52,68,92,169,113,113,15,15,22,19,48,
52,93,93,113,113,134,134,6,6,6,40,22,19,22,65,40,50,50,49,65,93,168,110,
110,19,19,22,19,50,52,93,93,109,109,135,135],[
"fusion map is unique up to table automorphisms"
]);
ALF("(QD16x2F4(2)').2","M",[1,2,3,2,3,3,5,16,7,9,9,9,7,9,11,29,14,17,21,
21,21,21,22,22,30,29,42,36,45,89,54,54,54,54,7,7,9,9,21,24,43,43,54,54,64,
64,8,8,8,41,10,8,10,65,41,25,25,24,65,40,144,54,54,8,8,10,8,25,22,40,40,
54,54,65,65,23,23,23,84,23,23,23,123,84,23,23,26,26,123,84,84,189,190,56,
56,56,56,23,23,23,23,23,26,84,84,56,56,123,123,2,3,3,16,9,9,9,29,17,25,25,
22,30,43,89,54,54,8,8,10,8,25,22,40,40,54,54,65,65,8,8,8,41,10,8,10,65,41,
25,25,24,65,40,144,54,54,8,8,10,8,25,22,40,40,54,54,65,65]);
ALN("(QD16x2F4(2)').2",["NDG(2.B,QD16)","NDG(M,QD16)"]);

MOT("2.(3^2:D8xU4(3).2^2).2",
[
"origin: Dixon's Algorithm"
],
[3762339840,3762339840,1327104,1327104,6718464,6718464,559872,559872,93312,
93312,110592,110592,9216,5760,5760,82944,82944,20736,20736,4032,4032,4608,7776
,7776,13824,13824,3483648,414720,331776,36864,62208,5184,5184,4608,2880,20736,
5184,2016,7464960,165888,27648,13824,93312,31104,15552,10368,2592,2304,1440,
3456,1728,1296,418037760,418037760,147456,147456,746496,746496,62208,62208,
10368,10368,12288,12288,1024,640,640,9216,9216,2304,2304,448,448,512,864,864,
1536,1536,387072,46080,36864,4096,6912,576,576,512,320,2304,576,224,829440,
18432,3072,1536,10368,3456,1728,1152,288,256,160,384,192,144,156764160,55296,
279936,46656,46656,3888,4608,768,240,3456,1728,1728,168,384,648,1296,1296,576,
290304,34560,27648,3072,5184,864,864,432,384,240,1728,864,864,168,1244160,
2488320,2488320,27648,27648,4608,4608,2304,4608,4608,15552,31104,31104,5184,
10368,10368,2592,5184,5184,1728,3456,3456,432,432,384,384,240,480,480,576,576,
288,576,576,216,432,432,470292480,470292480,165888,165888,839808,839808,139968
,139968,139968,139968,11664,11664,13824,13824,1152,720,720,10368,10368,5184,
5184,5184,5184,504,504,576,1944,1944,1944,1944,1728,1728,435456,51840,41472,
4608,7776,1296,1296,648,576,360,2592,1296,1296,252,1866240,1866240,41472,41472
,6912,6912,3456,3456,23328,46656,46656,7776,7776,3888,3888,2592,2592,648,1296,
1296,576,576,360,360,864,1728,1728,432,432,324,648,648,104509440,36864,186624,
15552,2592,3072,512,160,2304,576,112,256,216,384,193536,46080,46080,36864,
36864,2048,3456,576,576,288,512,512,320,320,2304,2304,576,576,224,224,414720,
9216,1536,768,5184,1728,864,576,144,128,80,192,96,72,78382080,27648,139968,
23328,23328,1944,2304,384,120,1728,864,864,84,192,324,648,648,288,145152,17280
,13824,1536,2592,432,432,216,192,120,864,432,432,84,622080,1244160,1244160,
13824,13824,2304,2304,1152,2304,2304,7776,15552,15552,2592,5184,5184,1296,2592
,2592,864,1728,1728,216,216,192,192,120,240,240,288,288,144,288,288,108,216,
216,96768,96768,1536,1536,160,768,768,256,256,1728,1728,192,192,144,144,80,80,
96,96,112,112,112,112,5760,384,144,144,384,128,32,40,96,96,96,96,96768,1536,
320,768,256,1728,192,144,80,96,112,112,11520,768,144,1536,1536,256,128,128,160
,160,96,192,192,96768,1536,320,768,256,1728,192,144,80,96,112,112,11520,768,
144,1536,1536,256,128,128,160,160,96,192,192],
[,[1,1,1,1,5,5,7,7,9,9,4,4,3,14,14,5,5,7,7,20,20,12,23,23,16,16,1,2,4,4,5,8,9,
12,15,16,18,20,1,1,4,3,5,7,7,7,9,11,14,16,19,23,1,1,1,1,5,5,7,7,9,9,4,4,3,14,
14,5,5,7,7,20,20,12,23,23,16,16,1,2,4,4,5,8,9,12,15,16,18,20,1,1,4,3,5,7,7,7,9
,11,14,16,19,23,1,1,5,7,7,9,4,3,14,5,7,7,20,12,23,23,23,16,2,1,3,3,6,7,7,10,11
,14,17,19,19,21,2,1,1,2,1,3,4,4,3,3,6,5,5,8,7,7,8,7,7,8,7,7,10,9,12,11,15,14,
14,17,16,18,19,19,24,23,23,174,174,174,174,178,178,180,180,182,182,184,184,177
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177,176,176,178,178,178,182,180,180,182,182,180,184,184,184,186,186,189,189,
191,191,191,194,196,200,202,202,54,54,58,60,62,55,56,67,58,60,73,63,76,69,54,
53,53,55,55,55,58,59,59,62,63,63,66,66,69,69,71,71,73,73,53,53,56,55,57,59,59,
59,61,63,66,68,71,75,174,174,178,180,182,184,177,176,189,178,180,182,197,187,
200,202,202,191,175,174,176,176,179,180,182,185,186,189,192,194,196,198,175,
174,174,175,174,176,177,177,176,176,179,178,178,183,180,180,181,182,182,183,
180,180,185,184,187,186,190,189,189,192,191,193,196,196,201,202,202,79,79,79,
79,80,81,81,81,81,83,83,83,83,85,85,87,87,88,88,90,90,90,90,53,56,61,61,63,63,
65,66,68,68,78,78,266,266,267,270,269,272,272,275,278,281,284,285,252,253,256,
257,257,257,258,258,259,259,260,265,265,266,266,267,270,269,272,272,275,278,
281,284,285,252,253,256,257,257,257,258,258,259,259,260,265,265],[1,2,3,4,1,2,
1,2,1,2,11,12,13,14,15,4,3,4,3,20,21,22,5,6,12,11,27,28,29,30,27,28,27,34,35,
29,29,38,39,40,41,42,39,39,39,40,40,48,49,41,42,43,53,54,55,56,53,54,53,54,53,
54,63,64,65,66,67,56,55,56,55,72,73,74,57,58,64,63,79,80,81,82,79,80,79,86,87,
81,81,90,91,92,93,94,91,91,91,92,92,100,101,93,94,95,105,106,105,105,105,105,
111,112,113,106,106,106,117,118,107,107,107,111,123,124,125,126,123,124,124,
123,131,132,125,125,125,136,137,138,139,140,141,142,143,144,145,146,137,138,
139,137,138,139,137,139,138,140,141,141,140,141,161,162,163,164,165,142,143,
144,145,146,147,149,148,1,2,3,4,1,2,1,2,1,2,1,2,11,12,13,14,15,4,3,4,3,4,3,20,
21,22,5,6,5,6,12,11,27,28,29,30,27,28,28,27,34,35,29,29,29,38,39,39,40,40,41,
41,42,42,39,39,39,39,39,39,39,40,40,40,40,40,48,48,49,49,41,41,41,42,42,43,43,
43,252,253,252,252,252,257,258,259,253,253,262,263,254,257,266,267,268,269,270
,271,266,267,268,266,276,277,278,279,269,270,269,270,284,285,286,287,288,289,
286,286,286,287,287,295,296,288,289,290,105,106,105,105,105,105,111,112,113,
106,106,106,117,118,107,107,107,111,123,124,125,126,123,124,124,123,131,132,
125,125,125,136,137,138,139,140,141,142,143,144,145,146,137,138,139,137,138,
139,137,139,138,140,141,141,140,141,161,162,163,164,165,142,143,144,145,146,
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,0,-8,8,0,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[447,3]],[10080,-10080,-224,224,-288,288,144,-144,0,0,-96,96,0,0,0,32
,-32,-16,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,-240,240,0,0,0,0,0,-8,8,0,-24,24,0,12,-12,0,-12,12,0,-12,12,0,0,
0,0,0,0,0,0,0,0,4,-4,0,0,0,-1260,1260,28,-28,36,-36,-18,18,-18,18,0,0,12,-12,0
,0,0,-4,4,2,-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,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,120,-120,0,0,0,0,0,4
,-4,0,12,-12,0,-6,6,0,6,-6,0,6,-6,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
],
[TENSOR,[449,3]],[14336,-14336,0,0,512,-512,-64,64,-64,64,0,0,0,16,-16,0,0,0,
0,0,0,0,-16,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,256,-256,0,0,0,0,0,0,0,0,-32,32,0,16,-16,0,8,-8,0,0,0,0,0,0,0,0,-4,4,0,
0,0,0,0,0,-4,4,-1792,1792,0,0,-64,64,8,-8,8,-8,8,-8,0,0,0,-2,2,0,0,0,0,0,0,0,0
,0,2,-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
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-128,128,0,0,0,0,0,0,0,0,16,-16,0,-8,8,0,
-4,4,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[451,3]],[20480,-20480,0,0,-256,256,-256,256,32,-32,0,0,0,0,0,0,0,0,0
,-16,16,0,32,-32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,-2560,2560,0,0,32,-32,32,-32,32,-32,-4,4,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,-4,4,
-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],
[(284,285)(388,390)(389,391)(414,415)(439,440),(394,395),(238,239),
(384,385)(424,425)(449,450),(120,121)(229,230)(245,246)(250,251)(315,316),
(400,401)(402,403),
(404,429)(405,430)(406,431)(407,432)(408,433)(409,434)(410,435)(411,436)
(412,437)(413,438)(414,439)(415,440)(416,441)(417,442)(418,443)(419,444)
(420,445)(421,446)(422,447)(423,448)(424,449)(425,450)(426,451)(427,452)
(428,453)
,
(120,121)(138,139)(145,146)(148,149)(151,152)(154,155)(157,158)(164,165)
(169,170)(172,173)(315,316)(333,334)(340,341)(343,344)(346,347)(349,350)
(352,353)(359,360)(364,365)(367,368)(384,385)(419,420)(422,423)(427,428)
(444,445)(447,448)(452,453)
,
(120,121)(138,139)(145,146)(148,149)(151,152)(154,155)(157,158)(164,165)
(169,170)(172,173)(315,316)(333,334)(340,341)(343,344)(346,347)(349,350)
(352,353)(359,360)(364,365)(367,368)(369,370)(371,372)(374,375)(376,377)
(378,379)(380,381)(382,383)(384,385)(386,387)(388,389)(390,391)
]);
ALF("2.(3^2:D8xU4(3).2^2).2","(3^2:D8xU4(3).2^2).2",[1,1,2,2,3,3,4,4,5,5,
6,6,7,8,8,9,9,10,10,11,11,12,13,13,14,14,15,16,17,18,19,20,21,22,23,24,25,
26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,41,42,42,43,43,44,44,45,
45,46,46,47,48,48,49,49,50,50,51,51,52,53,53,54,54,55,56,57,58,59,60,61,
62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,
86,87,88,89,90,91,92,93,94,95,96,96,97,98,99,100,101,102,103,104,105,106,
107,108,109,110,111,112,113,113,114,115,116,117,118,119,119,120,121,121,
122,123,123,124,125,125,126,127,127,128,129,130,131,132,133,133,134,135,
136,137,137,138,139,139,140,140,141,141,142,142,143,143,144,144,145,145,
146,146,147,148,148,149,149,150,150,151,151,152,152,153,154,154,155,155,
156,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,
173,174,175,176,177,178,179,180,180,181,182,183,184,185,186,187,188,188,
189,190,191,192,193,194,194,195,196,197,198,198,199,200,201,202,203,204,
205,206,207,208,209,210,211,212,213,214,214,215,215,216,217,218,218,219,
220,220,221,221,222,222,223,223,224,224,225,226,227,228,229,230,231,232,
233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,
251,252,253,254,254,255,256,257,258,259,260,261,262,263,264,265,266,267,
268,269,270,271,271,272,273,274,275,276,277,277,278,279,279,280,281,281,
282,283,283,284,285,285,286,287,288,289,290,291,291,292,293,294,295,295,
296,297,297,298,298,299,299,300,301,301,302,302,303,303,304,304,305,305,
306,306,307,307,308,308,309,309,310,311,312,312,313,314,315,316,317,317,
318,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,
334,335,336,336,337,337,338,339,339,340,341,342,343,344,345,346,347,348,
349,350,351,352,353,354,355,355,356,357,357,358,358,359,360,360]);
ALF("2.(3^2:D8xU4(3).2^2).2","2.B",[1,2,4,5,10,11,8,9,8,9,13,13,19,23,24,
35,34,30,29,41,42,44,60,61,74,74,3,6,13,12,31,33,27,45,65,74,73,99,3,7,13,
15,31,28,27,32,36,47,62,74,77,120,4,5,7,7,34,35,29,30,29,30,18,18,19,63,
64,37,38,36,36,102,103,44,122,123,90,90,7,6,18,18,39,33,36,45,65,90,82,
104,7,7,18,19,39,32,36,32,36,47,68,90,86,124,3,7,31,28,27,28,14,19,62,39,
32,36,100,47,121,120,120,87,6,7,15,15,40,36,32,33,45,68,85,77,81,101,6,4,
5,6,7,15,14,18,19,19,40,34,35,33,29,30,33,30,29,33,36,36,33,32,47,44,65,
63,64,85,87,82,86,86,127,123,122,8,9,29,30,8,9,10,11,8,9,10,11,76,76,86,
105,106,30,29,35,34,30,29,141,142,151,60,61,60,61,76,76,28,33,73,75,28,40,
33,31,152,180,73,74,73,219,28,27,32,36,73,76,81,77,28,27,27,27,31,31,28,
36,39,39,37,38,154,153,178,179,73,76,76,85,81,120,120,120,13,18,74,73,76,
20,22,133,90,82,172,51,205,92,14,19,19,16,17,20,87,86,86,80,51,51,135,135,
78,79,83,84,173,173,15,19,22,20,85,77,81,86,86,51,134,93,91,206,27,36,27,
31,28,31,80,86,179,36,39,32,220,153,121,120,120,80,33,32,81,81,33,39,36,
40,152,183,81,85,77,221,33,29,30,33,36,81,80,82,86,86,33,29,30,33,34,35,
40,30,29,33,37,38,40,39,154,151,180,181,182,81,80,90,86,86,127,123,122,16,
17,20,20,21,51,51,51,51,89,88,94,95,84,83,138,138,164,164,177,176,177,176,
19,22,86,86,51,51,55,135,93,93,164,164,43,48,55,49,52,156,161,155,216,158,
238,239,45,51,152,54,53,56,57,57,214,214,164,162,163,43,48,55,49,52,156,
161,155,216,158,238,239,45,51,152,54,53,56,57,57,214,214,164,162,163],[
"fusion map is unique up to table automorphisms"
]);
ALN("2.(3^2:D8xU4(3).2^2).2",["2.BM14"]);

MOT("2xBN5",
[
"Sylow 5 normalizer in 2.B"
],
0,
0,
0,
[(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(95,96)(97,98)(99,100
)(101,102)(103,104)(105,106)(107,108)(109,110),(9,10)(11,12)(13,14)(15,16)(25,
26)(27,28)(29,30)(31,32)(91,92)(93,94)(99,100)(101,102)(107,108)(109,110)(111,
112)(113,114),(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(
26,28)(29,31)(30,32)(91,93)(92,94)(95,97)(96,98)(99,101)(100,102)(103,105)(104
,106)(107,109)(108,110)(111,113)(112,114)],
["ConstructDirectProduct",[["BN5"],["Cyclic",2]]]);
ALF("2xBN5","2.B",[1,2,7,7,7,7,7,7,22,22,22,22,22,22,22,22,22,22,22,22,22,
22,22,22,22,22,22,22,22,22,22,22,25,26,25,26,25,26,25,26,25,26,23,24,25,
26,23,24,25,26,25,26,25,26,25,26,23,24,23,24,25,26,25,26,23,24,69,70,69,
70,69,70,69,70,69,70,69,70,68,68,70,69,70,69,68,68,68,68,70,69,140,140,
140,140,140,140,140,140,140,140,140,140,140,140,140,140,140,140,140,140,
140,140,140,140,166,167],[
"fusion map is unique"
]);
ALN("2xBN5",["2.BN5"]);

MOT("(5^2:4S4x2.A5):2",
[
"origin: Dixon's Algorithm"
],
[576000,576000,19200,28800,28800,24000,24000,28800,9600,14400,23040,23040,768,
1152,1152,960,960,1152,384,576,19200,19200,640,960,960,800,800,960,320,480,
2880,2880,96,144,144,120,120,144,96,96,144,144,23040,23040,768,1152,1152,960,
960,1152,384,576,23040,23040,768,1152,1152,960,960,1152,384,576,9600,640,480,
800,800,960,320,480,9600,640,480,800,800,960,320,480,1920,128,96,160,160,192,
64,96,1920,128,96,160,160,192,64,96,3840,3840,128,192,192,160,160,192,64,96,
24000,24000,800,1200,1200,1000,1000,1200,400,600,2880,2880,96,144,144,120,120,
144,96,96,144,144,960,64,48,80,80,96,32,48,960,64,48,80,80,96,32,48,4800,4800,
160,240,240,200,200,240,80,120,2880,2880,96,144,144,120,120,144,96,96,144,144,
2880,2880,96,144,144,120,120,144,96,96,144,144,2400,160,120,200,200,240,80,120
,2400,160,120,200,200,240,80,120],
[,[1,1,2,4,4,6,6,1,3,4,1,1,2,4,4,6,6,1,3,4,1,1,2,4,4,6,6,1,3,4,31,31,32,34,34,
36,36,31,33,33,34,34,11,11,12,15,15,17,17,11,13,15,11,11,12,15,15,17,17,11,13,
15,21,22,25,27,27,22,23,24,21,22,25,27,27,22,23,24,21,22,25,27,27,22,23,24,21,
22,25,27,27,22,23,24,11,11,12,15,15,17,17,11,13,15,105,105,106,108,108,110,110
,105,107,108,31,31,32,34,34,36,36,31,33,33,34,34,53,54,57,59,59,54,55,56,43,44
,47,49,49,44,45,46,105,105,106,108,108,110,110,105,107,108,115,115,116,119,119
,121,121,115,117,117,119,119,115,115,116,119,119,121,121,115,117,117,119,119,
143,144,147,149,149,144,145,146,143,144,147,149,149,144,145,146],[1,2,3,1,2,6,
7,8,9,8,11,12,13,12,11,16,17,18,19,18,21,22,23,22,21,26,27,28,29,28,1,2,3,1,2,
6,7,8,9,9,8,8,53,54,55,54,53,58,59,60,61,60,43,44,45,44,43,48,49,50,51,50,71,
72,71,75,74,76,77,76,63,64,63,67,66,68,69,68,87,88,87,91,90,92,93,92,79,80,79,
83,82,84,85,84,95,96,97,96,95,100,101,102,103,102,105,106,107,105,106,110,111,
112,113,112,11,12,13,12,11,16,17,18,19,19,18,18,135,136,135,139,138,140,141,
140,127,128,127,131,130,132,133,132,143,144,145,144,143,148,149,150,151,150,53
,54,55,54,53,58,59,60,61,61,60,60,43,44,45,44,43,48,49,50,51,51,50,50,185,186,
185,189,188,190,191,190,177,178,177,181,180,182,183,182],,[1,2,3,4,5,1,2,8,9,
10,11,12,13,14,15,12,11,18,19,20,21,22,23,24,25,22,21,28,29,30,31,32,33,34,35,
31,32,38,39,40,41,42,43,44,45,46,47,44,43,50,51,52,53,54,55,56,57,54,53,60,61,
62,63,64,65,63,63,68,69,70,71,72,73,71,71,76,77,78,79,80,81,79,79,84,85,86,87,
88,89,87,87,92,93,94,95,96,97,98,99,96,95,102,103,104,1,2,3,4,5,1,2,8,9,10,115
,116,117,118,119,116,115,122,123,124,125,126,127,128,129,127,127,132,133,134,
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[TENSOR,[191,15]]],
[( 41, 42)(125,126)(163,164)(175,176),
( 66, 67)( 74, 75)( 82, 83)( 90, 91)(130,131)(138,139)(180,181)(188,189),
( 39, 40)(123,124)(161,162)(173,174),
( 43, 53)( 44, 54)( 45, 55)( 46, 56)( 47, 57)( 48, 58)( 49, 59)( 50, 60)
( 51, 61)( 52, 62)( 63, 71)( 64, 72)( 65, 73)( 66, 74)( 67, 75)( 68, 76)
( 69, 77)( 70, 78)( 79, 87)( 80, 88)( 81, 89)( 82, 90)( 83, 91)( 84, 92)
( 85, 93)( 86, 94)(127,135)(128,136)(129,137)(130,138)(131,139)(132,140)
(133,141)(134,142)(153,165)(154,166)(155,167)(156,168)(157,169)(158,170)
(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)(177,185)(178,186)
(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)
]);
ALF("(5^2:4S4x2.A5):2","5^2:4S4xS5",[1,1,2,3,3,4,4,5,6,7,8,8,9,10,10,11,
11,12,13,14,15,15,16,17,17,18,18,19,20,21,22,22,23,24,24,25,25,26,27,27,
28,28,29,29,30,31,31,32,32,33,34,35,36,36,37,38,38,39,39,40,41,42,43,44,
45,46,46,47,48,49,50,51,52,53,53,54,55,56,57,58,59,60,60,61,62,63,64,65,
66,67,67,68,69,70,71,71,72,73,73,74,74,75,76,77,78,78,79,80,80,81,81,82,
83,84,85,85,86,87,87,88,88,89,90,90,91,91,92,93,94,95,95,96,97,98,99,100,
101,102,102,103,104,105,106,106,107,108,108,109,109,110,111,112,113,113,
114,115,115,116,116,117,118,118,119,119,120,120,121,122,122,123,123,124,
125,125,126,126,127,128,129,130,130,131,132,133,134,135,136,137,137,138,
139,140]);
ALF("(5^2:4S4x2.A5):2","2.B",[1,2,6,8,9,25,26,3,21,28,7,7,6,36,36,69,70,7,
21,32,5,4,6,29,30,66,67,7,21,32,10,11,40,10,11,107,108,31,96,96,31,31,17,
16,22,83,84,136,137,20,21,91,17,16,22,83,84,136,137,20,21,91,12,19,75,131,
131,15,21,77,12,19,75,131,131,15,21,77,18,19,82,139,139,19,21,86,18,19,82,
139,139,19,21,86,16,17,22,84,83,137,136,20,21,91,23,24,65,105,106,23,24,
62,138,178,38,37,40,39,39,184,185,39,96,96,37,38,49,52,159,217,218,52,57,
160,49,52,159,218,217,52,57,160,64,63,65,181,182,63,64,68,138,183,79,78,
93,88,89,242,243,92,96,96,95,94,79,78,93,88,89,242,243,92,96,96,95,94,130,
135,240,130,130,134,138,241,130,135,240,130,130,134,138,241]);
ALN("(5^2:4S4x2.A5):2",["2.BM23"]);

MOT("2.BN7",
[
"origin: Dixon's Algorithm,\n",
"Sylow 7 normalizer in 2.B"
],
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1152,1152,96,576,28224,588,72,72,72,504,84,576,576,96,504,84,72,96,576,576,96,
96,96,96,48,48,48,48,96,96,96,96,96,96,96,96,48,48,48,48,24,24,48,48,48,48,24,
48,288,14112,588,588,72,72,72,72,72,504,84,72,504,84,288,288,48,504,84,72,48,
288,288,72,504,84],
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12,13,14,13,14,17,18,19,20,21,22,23,24,25,26,25,26,29,30,31,32,33,34,35,36,37,
38,39,39,41,42,43,44,44,46,47,48,49,49,51,52,53,54,55,56,57,58,59,60,61,62,63,
64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,84,84,87,88,89,
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E(8)-E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,E(8)-E(8)^3,-E(8)+E(8)^3,0,0,0,0,0,0,0,0,
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,[85,2]],
[TENSOR,[85,10]],
[TENSOR,[85,6]],
[TENSOR,[85,9]],
[TENSOR,[85,5]],[8,-8,8,-8,8,-8,0,0,-2,2,-2,2,2,-2,2,-2,2,-2,0,0,-8,8,-8,8,2,
-2,2,-2,2,-2,0,0,8,-8,8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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[TENSOR,[91,6]],
[TENSOR,[91,5]],[48,48,-1,-1,0,0,0,0,0,0,0,0,6,6,-1,-1,0,0,0,0,0,0,0,0,6,6,-1
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[TENSOR,[94,3]],[48,48,-1,-1,0,0,0,0,0,0,0,0,6,6,-1,-1,0,0,0,0,0,0,0,0,6,6,-1
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-1,0,0,0,0,0,-6,1],
[TENSOR,[96,3]],
[TENSOR,[94,6]],
[TENSOR,[94,5]],
[TENSOR,[94,8]],
[TENSOR,[94,7]],
[TENSOR,[96,5]],
[TENSOR,[96,6]],
[TENSOR,[96,7]],
[TENSOR,[96,8]],[96,-96,-2,2,0,0,0,0,0,0,0,0,12,-12,-2,2,0,0,0,0,0,0,0,0,12,
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[TENSOR,[106,6]],
[TENSOR,[106,5]]],
[(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72),
(55,57)(56,58)(59,60)(61,62)(63,65)(64,66)(67,69)(68,70)(71,72)(73,74)(77,78)
(79,80)
,
( 85, 86)( 87, 90)( 88, 89)( 91, 94)( 92, 95)( 93, 96)(100,107)(101,108)
(102,106)
,
( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 32)( 20, 31)
( 21, 34)( 22, 33)( 23, 36)( 24, 35)( 43, 51)( 44, 49)( 45, 50)( 46, 54)
( 47, 53)( 48, 52)( 61, 71)( 62, 72)( 63, 70)( 64, 69)( 65, 68)( 66, 67)
( 76, 81)( 77, 80)( 78, 79)( 87, 90)( 88, 89)( 91,102)( 92,100)( 93,101)
( 94,106)( 95,107)( 96,108)( 97,105)( 98,104)( 99,103)
]);
ALF("2.BN7","2.B",[1,2,41,42,7,7,22,22,11,10,37,38,8,9,141,142,36,36,93,
93,37,38,11,10,8,9,141,142,36,36,93,93,38,37,10,11,20,6,6,101,40,40,33,33,
221,40,40,92,33,221,33,92,40,40,53,54,53,54,21,21,96,96,162,163,162,163,
163,162,163,162,96,96,57,57,22,93,165,165,165,165,93,22,7,3,99,100,31,39,
39,31,32,28,219,36,27,220,39,31,93,28,219,32,93,31,39,36,27,220],[
"fusion map determined up to table autom. by factoriz. of the fusion\n",
"from 2xThN7 through 2xTh and 2.BN7 to 2.B"
]);

MOT("(3^2x2).U4(3).D8",
[
"origin: Dixon's Algorithm"
],
[470292480,470292480,117573120,117573120,117573120,117573120,41472,41472,41472
,41472,165888,165888,209952,209952,209952,209952,839808,839808,11664,11664,
23328,23328,1296,1296,3456,3456,3456,3456,13824,13824,288,1152,288,180,180,180
,180,720,720,2592,2592,2592,2592,10368,10368,648,648,1296,1296,1296,1296,2592,
2592,126,126,126,126,504,504,144,144,576,324,324,324,324,324,324,432,432,432,
432,1728,1728,48384,11520,11520,9216,9216,512,864,144,144,72,128,128,80,80,576
,576,144,144,56,56,48384,48384,768,768,80,384,384,128,128,864,864,96,96,72,72,
40,40,48,48,56,56,56,56,311040,311040,622080,622080,3456,6912,576,1152,1152,
1152,576,576,7776,7776,7776,7776,7776,7776,1296,1296,2592,2592,648,648,1296,
1296,288,288,36,48,96,60,60,120,120,144,144,144,72,72,144,144,108,108,108,108,
108,108,4320,8640,576,288,36,576,576,1152,1152,96,192,48,48,96,96,60,60,120,
120,72,72,72,144,144,144,144,144,144],
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,58,58,26,28,30,63,63,65,65,67,67,43,43,41,41,45,45,2,1,1,12,12,12,18,21,21,24
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,6,2,12,10,24,26,26,30,30,26,30,33,33,32,32,37,37,39,39,44,40,40,71,71,71,71,
73,73],[1,2,1,2,1,2,11,12,11,12,11,12,1,2,1,2,1,2,1,2,1,2,1,2,29,30,29,30,29,
30,32,32,32,38,39,38,39,38,39,12,11,12,11,12,11,12,11,12,11,12,11,12,11,58,59,
58,59,58,59,62,62,62,15,16,15,16,15,16,30,29,30,29,30,29,75,76,77,78,79,80,75,
76,77,75,85,86,87,88,79,78,79,78,93,94,95,96,97,98,99,100,101,102,103,96,95,97
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127,126,127,120,121,120,121,120,121,121,120,121,120,121,120,121,120,123,123,
123,148,148,151,152,151,152,125,125,125,127,126,127,126,130,131,130,131,130,
131,167,167,168,168,167,173,174,173,174,176,176,179,180,179,180,183,184,183,
184,168,168,168,173,174,173,174,173,174],,[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,3,4,5,6,1,2,40,41,42,43
,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69
,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,77,76,89,90,91,92,94,93,96
,95,98,97,99,101,100,103,102,105,104,107,106,109,108,99,99,113,112,117,116,115
,114,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,
136,137,138,139,140,141,142,143,144,145,146,147,148,119,118,121,120,153,154,
155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,172,171,174,
173,175,176,178,177,180,179,166,166,167,167,185,186,187,191,190,189,188,193,
192],,[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
,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53
,5,6,3,4,1,2,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81
,82,83,84,85,86,87,88,89,90,91,92,75,75,96,95,98,97,99,101,100,103,102,105,104
,107,106,109,108,110,111,113,112,95,96,95,96,118,119,120,121,122,123,124,125,
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,
164,165,166,167,168,169,170,172,171,174,173,175,176,178,177,180,179,181,182,
183,184,185,187,186,189,188,191,190,193,192]],
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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,
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,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[21,21,21,21,21,21,5,5,5,5,5,5,-6,-6,-6,-6,
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[TENSOR,[6,2]],
[TENSOR,[6,3]],
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[TENSOR,[192,2]]],
[(186,187)(188,190)(189,191),(110,111)(181,182)(183,184),
( 93, 94)(114,116)(115,117),
( 95, 96)( 97, 98)(100,101)(102,103)(104,105)(106,107)(108,109)(112,113)
(114,115)(116,117)(171,172)(173,174)(177,178)(179,180)(186,187)(188,189)
(190,191)(192,193)
,
( 95, 96)( 97, 98)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)
(112,113)(114,115)(116,117)(118,119)(120,121)(126,127)(128,129)(130,131)
(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)(149,150)
(151,152)(154,155)(156,157)(158,159)(160,161)(162,163)(164,165)
]);
ALF("(3^2x2).U4(3).D8","3^2.U4(3).D8",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,
9,10,10,11,11,12,12,13,13,14,14,15,15,16,17,18,19,19,20,20,21,21,22,22,23,
23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,33,34,35,35,36,36,
37,37,38,38,39,39,40,40,41,42,42,43,43,44,45,46,46,47,48,48,49,49,50,50,
51,51,52,52,53,53,54,54,55,56,56,57,57,58,58,59,59,60,60,61,61,62,62,63,
63,64,64,65,65,66,66,67,68,69,70,71,71,72,72,73,73,74,74,75,75,76,76,77,
77,78,78,79,79,80,80,81,82,83,84,84,85,85,86,87,87,88,88,89,89,90,90,91,
91,92,92,93,94,95,96,97,98,98,99,99,100,101,102,102,103,103,104,104,105,
105,106,107,107,108,108,109,109,110,110]);
ALF("(3^2x2).U4(3).D8","2.Co1",[1,2,9,10,7,8,37,36,30,29,4,3,9,10,11,12,7,
8,11,12,9,10,13,14,72,73,78,79,15,16,86,20,75,102,103,98,99,25,26,36,37,
38,39,29,30,38,39,32,33,34,35,36,37,120,121,122,123,43,44,132,135,47,55,
56,57,58,59,60,77,76,79,78,73,72,5,6,6,20,20,20,31,40,40,41,48,48,69,69,
75,75,86,86,93,93,21,21,21,21,22,54,54,54,54,80,80,80,80,89,89,117,117,
136,136,143,144,144,143,32,33,3,4,40,6,81,17,18,19,84,85,38,39,29,30,34,
35,37,36,33,32,39,38,37,36,40,40,42,137,48,150,149,66,65,74,88,87,83,82,
85,84,111,112,109,110,113,114,31,5,20,75,41,132,132,47,47,132,47,136,136,
54,54,147,147,64,64,75,86,86,135,135,135,135,132,132]);

MOT("NDG(2.Co1,3^3)",
[
"origin: Dixon's Algorithm"
],
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17280,3456,384,288,288,288,192,2160,155520,17280,17280,12960,7776,7776,3888,
3888,864,864,864,864,432,432,432,432,324,324,144,72,72,36,36,5760,5760,5760,
5760,1728,192,192,192,64,64,64,64,64,64,48,48,2160,240,240,8640,8640,1728,432,
432,432,432,288,288,288,288,216,216,216,216,192,144,144,96,72,72,72,72,72,72,
72,72,72,72,72,72,72,72,36,36,1080,90,240,240,240,240,864,144,144,144,144,144,
144,144,144,96,96,96,72,48,48,24,1080,120,120,90,80,80,80,80,80,80,80,80,120,
120,120,120],
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10,10,11,11,12,13,7,8,8,12,12,15,15,15,15,16,16,17,17,14,14,21,21,21,21,17,16,
22,22,22,24,24,23,32,32,33,33,24,24,25,25,36,36,37,37,23,26,26,25,32,32,36,36,
36,36,28,28,34,34,38,38,38,38,40,40,100,101,63,63,63,63,67,68,68,68,68,71,71,
71,71,67,80,80,81,80,80,81,100,100,100,101,104,104,105,105,104,104,105,105,123
,123,123,123],[1,2,3,4,5,1,1,1,1,1,1,1,1,14,15,16,17,18,19,20,21,22,2,3,4,2,2,
2,2,2,4,3,3,4,4,3,3,4,2,2,5,5,5,5,5,46,47,48,49,50,51,52,53,54,55,56,57,58,59,
60,61,62,63,64,14,15,16,15,14,14,15,18,18,20,20,15,14,14,15,17,16,19,21,18,18,
18,18,18,18,19,19,20,20,20,20,20,20,19,19,22,22,102,103,104,105,50,48,49,46,47
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[(102,103)(104,105)(126,129)(127,128)(130,133)(131,132)(134,135)(136,137),
( 72, 73)( 74, 75)( 86, 89)( 87, 88)( 94, 96)( 95, 97)(119,120),
( 52, 53)( 56, 58)( 57, 59)(116,117),
( 46, 47)( 48, 49)( 54, 55)( 56, 59)( 57, 58)(107,108)(109,110)(111,112)
(113,114)(126,127)(128,129)(130,131)(132,133)
,( 42, 43)( 44, 45)( 84, 85)( 86, 88)( 87, 89),
( 90, 91)( 92, 93)( 94, 95)( 96, 97)( 98, 99),
( 46, 48)( 47, 49)( 56, 58)( 57, 59)( 84, 85)( 86, 88)( 87, 89)( 92, 93)
( 94, 95)( 96, 97)(107,109)(108,110)(111,113)(112,114)(126,130)(127,131)
(128,132)(129,133)
]);
ALF("NDG(2.Co1,3^3)","2.Co1",[1,2,4,3,6,7,13,9,7,11,9,13,13,15,16,5,5,17,
5,20,20,23,8,30,29,14,10,8,12,10,36,37,30,29,38,39,37,36,14,14,42,40,40,
42,42,47,47,47,47,21,21,21,21,48,48,54,54,54,54,21,21,24,62,61,72,73,31,
79,78,72,73,74,74,75,75,77,76,78,79,31,41,41,75,81,81,87,87,88,88,31,31,
75,75,86,86,86,86,41,41,96,100,115,115,116,116,80,135,135,135,135,132,132,
132,132,80,80,80,89,80,80,89,97,146,145,101,163,163,164,164,164,164,163,
163,166,166,167,167]);

MOT("NDG(Co1,5^2)",
[
"origin: Dixon's Algorithm"
],
[36000,3000,3000,1440,720,720,2400,600,600,2400,16,16,24,24,48,48,96,200,200,
2400,48,48,40,160,40,160,100,50,50,100,50,50,30,30,250,250,1500,250,250,60,72,
72,144,144,48,48,36,36,150,150,1800,72,30,120,30,120,24,24,36,36,72,72],
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,33,33,35,36,37,38,39,37,6,6,4,4,4,4,47,47,49,50,51,51,49,51,50,51,52,52,48,48
,52,52],[1,2,3,4,1,4,7,8,9,10,12,11,16,15,16,15,17,18,19,20,17,20,23,24,25,26,
27,28,29,30,31,32,37,40,35,36,37,38,39,40,44,43,44,43,46,45,1,4,3,2,1,4,8,7,9,
10,45,46,43,44,43,44],,[1,1,1,4,5,6,7,7,10,10,11,12,13,14,15,16,17,20,20,20,21
,22,24,24,26,26,7,7,7,10,10,10,5,6,1,1,1,1,1,4,41,42,43,44,45,46,47,48,51,51,
51,52,54,54,56,56,57,58,59,60,61,62]],
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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,
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-E(4),E(4),1,-1,1,1,1,-1,-1,-1,1,1,E(4),-E(4),-E(4),E(4),-E(4),E(4)],
[TENSOR,[5,4]],
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[TENSOR,[21,4]],
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[TENSOR,[21,2]],
[TENSOR,[21,8]],
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[TENSOR,[29,2]],
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,
[TENSOR,[33,3]],
[TENSOR,[33,5]],
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,-2],
[TENSOR,[37,3]],
[TENSOR,[37,5]],
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[TENSOR,[43,2]],[12,12,12,-12,-6,6,0,0,0,0,0,0,0,0,0,0,4,-4,-4,-4,-2,2,0,0,0,
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[TENSOR,[48,2]],
[TENSOR,[47,2]],[36,6,-9,0,0,0,-12,3,0,0,0,0,0,0,0,0,0,3,-2,-12,0,0,0,0,-1,4,
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[TENSOR,[52,2]],
[TENSOR,[51,2]],[48,-12,8,0,0,0,0,0,-4,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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[TENSOR,[55,2]],[48,8,-12,0,0,0,-16,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,
-1,-1,0,0,0,0,0,-2,-2,-12,3,3,0,0,0,0,0,0,0,0,0,-3,2,12,0,1,-4,0,0,0,0,0,0,0,0
],
[TENSOR,[57,2]],[60,-15,10,0,0,0,0,0,-5,20,0,0,0,0,0,0,0,2,-3,12,0,0,-1,4,0,0
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[TENSOR,[59,2]],[60,10,-15,0,0,0,-20,5,0,0,0,0,0,0,0,0,0,-3,2,12,0,0,0,0,1,-4
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[TENSOR,[61,2]]],
[(28,29)(31,32)(35,36)(38,39),
(11,12)(13,14)(15,16)(41,42)(43,44)(45,46)(57,58)(59,60)(61,62),
( 2, 3)( 7,10)( 8, 9)(11,12)(18,19)(23,25)(24,26)(27,30)(28,31,29,32)
(35,38,36,39)(45,46)(49,50)(53,55)(54,56)(57,58)
]);
ALF("NDG(Co1,5^2)","Co1",[1,16,15,3,8,25,2,38,40,3,14,14,57,57,14,14,4,39,
40,3,26,25,43,4,39,3,38,42,41,39,40,39,63,91,15,16,15,17,16,39,56,56,13,
13,13,13,8,25,61,62,5,19,89,18,90,19,50,50,56,56,50,50]);

MOT("NDG(2.Co1,5^2)",
[
"origin: Dixon's Algorithm"
],
[72000,6000,6000,1440,4800,1200,72000,6000,6000,1440,4800,1200,4800,1200,1440,
2880,4800,1200,1440,2880,48,96,40,160,160,40,48,200,2400,200,48,96,32,48,96,32
,32,48,96,32,48,96,60,500,500,3000,500,500,100,100,200,60,500,500,3000,500,500
,100,100,200,100,200,100,60,120,100,200,100,60,120,72,144,48,48,144,72,300,300
,3600,72,240,60,300,300,3600,72,240,60,60,240,72,144,60,240,72,144,72,144,48,
72,144,48,48,144,72,48,144,72],
[,[1,2,3,4,1,3,1,2,3,4,1,3,7,8,10,7,7,8,10,7,4,1,2,1,7,9,10,8,7,9,21,22,22,21,
22,22,22,21,22,22,21,22,43,44,45,46,47,48,47,48,46,43,44,45,46,47,48,47,48,46,
54,55,53,52,55,54,55,53,52,55,15,16,16,20,20,19,83,84,85,86,85,84,83,84,85,86,
85,84,77,79,80,79,77,79,80,79,91,92,92,91,92,92,96,96,95,96,96,95],[1,2,3,1,5,
6,7,8,9,7,11,12,17,18,20,20,13,14,16,16,22,22,23,24,25,26,29,28,29,30,39,39,37
,42,42,40,33,32,32,36,35,35,46,44,45,46,47,48,49,50,51,55,53,54,55,56,57,58,59
,60,66,67,68,70,70,61,62,63,65,65,75,75,74,73,72,72,8,9,7,7,11,12,2,3,1,1,5,6,
14,13,16,16,18,17,20,20,72,72,73,72,72,73,74,75,75,74,75,75],,[1,1,1,4,5,5,7,7
,7,10,11,11,13,13,15,16,17,17,19,20,21,22,24,24,25,25,27,29,29,29,31,32,33,34,
35,36,37,38,39,40,41,42,4,1,1,1,1,1,5,5,5,10,7,7,7,7,7,11,11,11,13,13,13,15,16
,17,17,17,19,20,71,72,73,74,75,76,79,79,79,80,81,81,85,85,85,86,87,87,90,90,91
,92,94,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108]],
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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,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1
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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,
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-1,-1,1,1,-1,-1,1,1,1,1,-1,1,1,-1,-1,1,1,-1,1,1],
[TENSOR,[2,3]],[1,1,1,1,-1,-1,1,1,1,1,-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),1
,1,1,1,1,1,-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),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)],
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[TENSOR,[103,2]],[72,12,-18,0,-24,6,-72,-12,18,0,24,-6,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,12,-3,-3,1,1,-4,0,-2,-2,-12,3,3,-1
,-1,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[105,2]],[72,-18,12,0,0,0,-72,18,-12,0,0,0,-24*E(4),6*E(4),0,0,
24*E(4),-6*E(4),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,-3,-3,12,2,2
,0,0,0,0,3,3,-12,-2,-2,0,0,0,E(4),-4*E(4),E(4),0,0,-E(4),4*E(4),-E(4),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,[107,2]]],
[(44,45)(47,48)(49,50)(53,54)(56,57)(58,59)(61,63)(66,68),
(31,34)(32,35)(33,36)(37,40)(38,41)(39,42),
( 97,100)( 98,101)( 99,102)(103,106)(104,107)(105,108),
(  5, 11)(  6, 12)( 13, 17)( 14, 18)( 33, 36)( 37, 40)( 49, 58)( 50, 59)
( 51, 60)( 61, 66)( 62, 67)( 63, 68)( 81, 87)( 82, 88)( 89, 93)( 90, 94)
( 97,100)( 98,101)(104,107)(105,108)
,
( 13, 17)( 14, 18)( 15, 19)( 16, 20)( 31, 38)( 32, 39)( 33, 37)( 34, 41)
( 35, 42)( 36, 40)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 71, 76)
( 72, 75)( 73, 74)( 89, 93)( 90, 94)( 91, 95)( 92, 96)( 97,105)( 98,104)
( 99,103)(100,108)(101,107)(102,106)
]);
ALF("NDG(2.Co1,5^2)","2.Co1",[1,25,23,13,3,61,2,26,24,14,4,62,5,64,41,5,5,
64,41,5,42,6,69,6,5,63,41,64,5,63,90,22,22,90,22,22,22,90,22,22,90,22,100,
23,25,23,25,27,65,67,61,101,24,26,24,26,28,66,68,62,64,63,63,148,63,64,63,
63,148,63,89,21,21,21,21,89,99,97,8,14,30,146,98,96,7,13,29,145,147,31,41,
31,147,31,41,31,89,80,80,89,80,80,80,80,89,80,80,89]);

MOT("2xCo1N3",
[
"Sylow 3 normalizer in 2.Co1"
],
0,
0,
0,
[
(  9, 10)( 11, 12)( 13, 14)( 15, 16)(167,168)(169,170)(175,176)(177,178)
(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)
(203,204)(205,206)(207,208)(209,210)
,
( 27, 29, 33)( 28, 30, 34)( 37, 45, 49)( 38, 46, 50)( 39, 51, 47)( 40, 52, 48)
( 81, 95, 99)( 82, 96,100)(101,109,119)(102,110,120)(103,115,129)(104,116,130)
(105,131,117)(106,132,118)(107,137,147)(108,138,148)(121,157,135)(122,158,136)
(125,149,141)(126,150,142)(127,133,151)(128,134,152)(143,153,145)(144,154,146)
(229,233,231)(230,234,232)(251,253,255)(252,254,256)
,
(  5,  6)(  7,  8)( 11, 12)( 15, 16)( 79, 80)( 83, 84)( 85, 86)( 87, 88)
( 89, 90)( 91, 92)( 93, 94)( 97, 98)(101,102)(103,104)(105,106)(107,108)
(109,110)(115,116)(117,118)(119,120)(123,124)(127,128)(129,130)(131,132)
(133,134)(137,138)(143,144)(145,146)(147,148)(151,152)(153,154)(159,160)
(161,162)(163,164)(169,170)(171,172)(175,176)(179,180)(181,182)(185,186)
(191,192)(193,194)(197,198)(199,200)(203,204)(205,206)(241,242)(243,244)
(247,248)(251,252)(253,254)(255,256)
,
(  3,  4)(  7,  8)( 11, 12)( 13, 14)( 77, 78)( 79, 80)( 81, 82)( 83, 84)
( 93, 94)( 95, 96)( 97, 98)( 99,100)(103,104)(107,108)(111,112)(113,114)
(115,116)(121,122)(125,126)(127,128)(129,130)(133,134)(135,136)(137,138)
(139,140)(141,142)(147,148)(149,150)(151,152)(155,156)(157,158)(159,160)
(163,164)(165,166)(167,168)(169,170)(173,174)(179,180)(181,182)(183,184)
(189,190)(193,194)(195,196)(197,198)(203,204)(209,210)(239,240)(241,242)
(243,244)(245,246)(247,248)(249,250)
],
["ConstructDirectProduct",[["Co1N3"],["Cyclic",2]]]);
ALF("2xCo1N3","2.Co1",[1,2,3,4,3,4,3,4,6,6,6,6,6,6,6,6,11,12,11,12,9,10,9,
10,7,8,7,8,9,10,9,10,11,12,11,12,11,12,11,12,9,10,9,10,9,10,9,10,11,12,9,
10,11,12,11,12,11,12,9,10,9,10,13,14,13,14,11,12,11,12,13,14,13,14,13,14,
38,39,38,39,34,35,29,30,34,35,38,39,32,33,29,30,32,33,29,30,34,35,32,33,
29,30,34,35,34,35,29,30,32,33,38,39,36,37,36,37,36,37,38,39,34,35,36,37,
38,39,32,33,38,39,36,37,36,37,36,37,36,37,36,37,36,37,36,37,38,39,38,39,
32,33,38,39,38,39,29,30,38,39,36,37,38,39,38,39,38,39,40,40,40,40,36,37,
36,37,40,40,40,40,36,37,38,39,38,39,38,39,40,40,40,40,40,40,40,40,40,40,
40,40,40,40,40,40,42,42,42,42,42,42,42,42,55,56,57,58,55,56,57,58,59,60,
59,60,55,56,59,60,57,58,55,56,57,58,59,60,57,58,57,58,109,110,111,112,109,
110,111,112,113,114,113,114,109,110,113,114,111,112],[
"fusion map determined using the fusion Co1N3 -> Co1"
]);
ALN("2xCo1N3",["2.Co1N3"]);

MOT("2xCo1N5",
[
"Sylow 5 normalizer in 2.Co1"
],
0,
0,
0,
[
(21,23)(22,24)(25,29)(26,30)(27,31)(28,32)(47,71)(48,72)(49,73)(50,74)(51,67)
(52,68)(53,69)(54,70)(55,65)(56,66)(57,61)(58,62)(59,63)(60,64)
,
(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)
(69,70)(71,72)(73,74)
,
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(55,56)(57,58)(59,60)(61,62)(63,64)
(65,66)
],
["ConstructDirectProduct",[["Co1N5"],["Cyclic",2]]]);
ALF("2xCo1N5","Co1N5",[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,
24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,
36,37,37]);
ALF("2xCo1N5","2.Co1",[1,2,27,28,25,26,25,26,27,28,23,24,25,26,27,28,6,6,
69,69,22,22,22,22,22,22,117,117,22,22,117,117,6,6,69,69,67,68,61,62,65,66,
3,4,67,68,118,119,18,19,19,18,119,118,22,22,22,22,117,117,22,22,117,117,
22,22,19,18,119,118,118,119,18,19],[
"fusion map determined by factorization through 2.Co1M19"
]);
ALN("2xCo1N5",["2.Co1N5"]);

MOT("2x5^(1+2):GL2(5)",
0,
0,
0,
0,
[(69,73)(70,74)(71,75)(72,76),
(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)
(75,76)
,
(11,13)(12,14)(39,41)(40,42)(45,47)(46,48)(53,55)(54,56)(57,59)(58,60)(61,63)
(62,64)(65,67)(66,68)(69,71)(70,72)(73,75)(74,76)
],
["ConstructDirectProduct",[["5^(1+2):GL2(5)"],["Cyclic",2]]]);
ALF("2x5^(1+2):GL2(5)","5^(1+2):GL2(5)",[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,
21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,
33,34,34,35,35,36,36,37,37,38,38]);
ALF("2x5^(1+2):GL2(5)","2.Co1",[1,2,27,28,25,26,3,4,67,68,18,19,18,19,6,6,
11,12,19,18,27,28,23,24,25,26,27,28,34,35,67,68,61,62,65,66,69,69,82,83,
82,83,104,105,118,119,118,119,119,118,151,152,22,22,22,22,22,22,22,22,52,
53,52,53,117,117,117,117,138,139,138,139,138,139,138,139]);

MOT("2x7^2:(3x2A4)",
[
"Sylow 7 normalizer in 2.Co1"
],
0,
0,
0,
[
( 5, 9)( 6,10)( 7,11)( 8,12)(13,15)(14,16)(23,25)(24,26)(27,37)(28,38)(29,35)
(30,36)(39,41)(40,42)(43,45)(44,46)(47,51)(48,52)(49,53)(50,54)
,
( 5,11)( 6,12)( 7, 9)( 8,10)(17,19)(18,20)(27,35)(28,36)(29,37)(30,38)(31,33)
(32,34)(39,41)(40,42)(47,53)(48,54)(49,51)(50,52)
],
["ConstructDirectProduct",[["7^2:(3x2A4)"],["Cyclic",2]]]);
ALF("2x7^2:(3x2A4)","7^2:(3x2A4)",[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]);
ALF("2x7^2:(3x2A4)","2.Co1",[1,2,6,6,9,10,9,10,13,14,13,14,13,14,13,14,13,
14,13,14,22,22,42,42,42,42,40,40,40,40,42,42,42,42,42,42,42,42,43,44,45,
46,90,90,90,90,122,123,122,123,124,125,124,125],[
"fusion map is unique"
]);
ALN("2x7^2:(3x2A4)",["2.Co1N7","2xCo1N7"]);

MOT("2.HS.2N3",
[
"origin: Dixon's Algorithm"
],
[1152,1152,288,128,128,96,96,48,48,32,144,576,64,64,64,48,32,16,8,144,72,72,48
,48,24,24,32,32,32,32,16,16,16,16,72,24],
[,[1,1,1,1,1,1,1,1,1,1,11,2,2,4,4,2,5,4,4,11,11,11,11,11,11,11,17,17,17,17,13,
13,15,15,20,20],[1,2,3,4,5,6,7,8,9,10,1,12,13,14,15,16,17,18,19,2,3,3,6,7,8,9,
30,29,28,27,32,31,33,34,12,16]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,
1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,1,1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,
1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,
-1,-1,1,1],[1,1,-1,1,1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,
1,1,1,1,-1,-1,1,1],[1,1,-1,1,1,-1,-1,1,1,-1,1,1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1
,1,1,-1,-1,-1,-1,1,1,1,1,1,-1],
[TENSOR,[2,5]],
[TENSOR,[2,4]],
[TENSOR,[2,3]],[2,2,-2,2,2,0,0,0,0,-2,2,2,2,-2,-2,0,-2,2,0,2,-2,-2,0,0,0,0,0,
0,0,0,0,0,0,0,2,0],
[TENSOR,[9,4]],[2,2,0,2,2,-2,-2,0,0,0,2,-2,-2,2,2,2,-2,0,0,2,0,0,-2,-2,0,0,0,
0,0,0,0,0,0,0,-2,2],
[TENSOR,[11,2]],[2,2,0,2,2,0,0,-2,2,0,2,-2,-2,-2,-2,0,2,0,0,2,0,0,0,0,-2,2,0,
0,0,0,0,0,0,0,-2,0],
[TENSOR,[13,2]],[2,2,2,-2,-2,0,0,0,0,-2,2,2,-2,0,0,0,0,0,0,2,2,2,0,0,0,0,
-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,-E(8)-E(8)^3,0,0,-E(8)-E(8)^3,E(8)+E(8)^3
,2,0],
[TENSOR,[15,3]],
[TENSOR,[15,4]],
[TENSOR,[15,5]],[2,-2,0,2,-2,2,-2,0,0,0,2,0,0,-2,2,0,0,0,0,-2,0,0,2,-2,0,0,
-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)^3,0,0
,0,0],
[TENSOR,[19,3]],
[TENSOR,[19,5]],
[TENSOR,[19,2]],[4,4,0,-4,-4,0,0,0,0,0,4,-4,4,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,-4,0],[4,-4,0,4,-4,0,0,0,0,0,4,0,0,4,-4,0,0,0,0,-4,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0],[4,-4,0,-4,4,0,0,0,0,0,4,0,0,0,0,0,0,0,0,-4,0,0,0,0,0,0,
-2*E(4),2*E(4),-2*E(4),2*E(4),0,0,0,0,0,0],
[TENSOR,[25,3]],[8,8,8,0,0,-2,-2,-2,-2,0,-1,8,0,0,0,-2,0,0,0,-1,-1,-1,1,1,1,1
,0,0,0,0,0,0,0,0,-1,1],
[TENSOR,[27,2]],
[TENSOR,[27,5]],
[TENSOR,[27,4]],[8,8,0,0,0,2,2,-2,2,0,-1,-8,0,0,0,-2,0,0,0,-1,-3,3,-1,-1,1,-1
,0,0,0,0,0,0,0,0,1,1],
[TENSOR,[31,2]],
[TENSOR,[31,5]],
[TENSOR,[31,4]],[16,-16,0,0,0,-4,4,0,0,0,-2,0,0,0,0,0,0,0,0,2,0,0,2,-2,0,0,0,
0,0,0,0,0,0,0,0,0],
[TENSOR,[35,2]]],
[(27,28)(29,30)(33,34),( 8, 9)(21,22)(25,26),(27,30)(28,29)(31,32),
( 6, 7)(23,24)(27,30)(28,29)]);
ALF("2.HS.2N3","2.HS.2",[1,2,34,3,4,3,4,34,35,35,6,5,5,10,10,5,9,37,10,7,
40,39,18,19,40,41,42,42,42,42,38,38,23,23,17,17]);

MOT("2.HSN2",
[
"origin: Dixon's Algorithm"
],
[1024,1024,1024,1024,512,512,256,256,64,128,128,32,64,64,64,64,64,64,512,512,
256,256,256,256,256,256,256,128,128,128,128,128,128,128,128,128,128,64,64,32,
64,64,32,32,16,16,32,32,32,32,16,16,32,32,32,32,32,32],
[,[1,1,1,1,1,1,1,1,2,1,1,2,1,1,2,2,1,1,3,3,3,6,6,3,3,6,6,7,7,7,7,7,7,6,6,7,7,4
,3,4,3,3,5,6,11,10,23,23,22,22,38,38,24,24,25,25,21,21]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,
-1,-1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,
1,1,-1,-1,1,1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,-1,-1,1,1,1,1,1,1
,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,
1],
[TENSOR,[2,3]],[1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,
-1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1],
[TENSOR,[2,5]],
[TENSOR,[3,5]],
[TENSOR,[2,7]],[2,2,2,2,2,2,-2,-2,2,-2,-2,0,0,0,0,0,0,0,-2,-2,-2,-2,-2,2,2,-2
,-2,0,0,0,0,0,0,2,2,0,0,-2,2,0,0,0,0,0,0,0,2*E(4),2*E(4),-2*E(4),-2*E(4),0,0,0
,0,0,0,0,0],
[TENSOR,[9,5]],[2,2,2,2,2,2,-2,-2,2,2,2,0,0,0,0,0,0,0,-2,-2,-2,2,2,2,2,2,2,0,
0,0,0,0,0,-2,-2,0,0,-2,-2,0,0,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[11,3]],[2,2,2,2,2,2,-2,-2,-2,2,2,0,2,2,-2,-2,0,0,-2,-2,-2,-2,-2,2,2,
-2,-2,0,0,0,0,0,0,2,2,0,0,2,-2,0,0,0,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[13,2]],[2,2,2,2,2,2,-2,-2,-2,-2,-2,0,0,0,0,0,0,0,-2,-2,-2,2,2,2,2,2,
2,0,0,0,0,0,0,-2,-2,0,0,2,2,0,0,0,0,0,0,0,0,0,0,0,-2,2,0,0,0,0,0,0],
[TENSOR,[15,2]],[2,2,2,2,2,2,2,2,2,-2,-2,2,0,0,0,0,0,0,2,2,2,-2,-2,2,2,-2,-2,
0,0,0,0,0,0,-2,-2,0,0,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,0,0,0,0],
[TENSOR,[17,3]],[2,2,2,2,2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,-2,
-2,-2,-2,-2,-2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2],
[TENSOR,[19,2]],[2,2,2,2,2,2,2,2,-2,2,2,0,0,0,0,0,2,2,2,2,2,-2,-2,2,2,-2,-2,0
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ALF("2.HSN2","HSN2",[1,1,2,2,3,3,4,4,5,6,6,7,8,8,9,9,10,10,11,11,12,13,13,
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29,30,30,31,32,33,33,34,34,35,35]);
ALF("2.HSN2","2.HS",[1,2,4,3,3,4,4,3,5,3,4,5,3,4,5,5,3,4,8,9,10,10,10,10,
10,9,8,8,9,10,10,10,10,10,10,10,10,11,10,11,10,10,11,10,10,11,24,25,25,24,
26,27,25,24,24,25,25,24]);
ALF("2.HSN2","2.HS.2N2",[1,3,2,4,5,6,7,8,36,9,10,53,17,18,48,48,15,16,29,
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47,56,55,71,72,71,72,74,74,70,70,66,66,69,69]);

MOT("2.HS.2N2",
[
"origin: Dixon's Algorithm"
],
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0,0,0,0,0,0,0,0,0]],
[(22,23)(67,68),(22,23)(42,43),(17,18)(71,72),(17,18)(44,45),(15,16)(37,38),
(11,12),
( 3, 4)(17,22)(18,23)(30,32)(31,33)(35,36)(42,44)(43,45)(46,50)(47,51)(48,52)
(53,54)(55,57)(56,58)(60,61)(62,63)(64,65)(67,71)(68,72)(73,74)
,
( 9,10)(13,14)(20,21)(40,41)(42,43)(44,45)(55,56)(57,58)(60,61)(62,63)(64,65)
(67,68)(71,72)
]);
ALF("2.HS.2N2","2.HS.2",[1,4,2,3,3,4,4,3,3,4,34,34,35,34,3,4,3,4,35,35,34,
34,35,35,35,9,9,9,8,9,9,9,8,9,10,5,9,9,36,36,36,8,9,9,9,10,9,5,37,37,36,
37,5,10,10,9,37,36,37,43,42,42,43,42,43,22,43,42,22,22,22,22,38,23]);

MOT("NDG(2.HS,Q8)",
[
"normalizer in 2.HS of a 2-defect group of the type Q8"
],
0,
0,
0,
[(16,26)(17,27)(18,28)(19,29)(20,30)(21,31)(22,32)(23,33)(24,34)(25,35),
( 3, 5)( 8,10)(13,15)(18,20)(23,25)(28,30)(33,35),
( 3, 8)( 5,10)(18,23)(20,25)(28,33)(30,35)],
["ConstructDirectProduct",[["2.L2(3)"],["5:4"]]]);
ALF("NDG(2.HS,Q8)","5:4xA4",[1,5,9,13,17,1,5,9,13,17,2,6,10,14,18,3,7,11,
15,19,3,7,11,15,19,4,8,12,16,20,4,8,12,16,20]);
ALF("NDG(2.HS,Q8)","2.HS",[1,14,8,4,9,2,15,9,3,8,5,30,11,5,11,6,37,36,21,
35,7,38,35,20,36,6,37,36,21,35,7,38,35,20,36]);
ALF("NDG(2.HS,Q8)","NDG(2.HS,Q8).2",[1,12,7,4,8,2,16,7,3,8,6,22,10,9,11,5,
21,17,15,20,13,23,18,14,19,5,21,18,15,19,13,23,17,14,20]);

MOT("NDG(2.HS,Q8).2",
[
"origin: Dixon's Algorithm"
],
[960,960,192,192,120,160,96,96,32,32,32,240,120,24,24,240,24,24,24,24,30,40,30
,80,16,16,16,80,16,16,16,20,40,40],
[,[1,1,1,1,5,2,4,4,2,3,3,12,5,5,5,12,15,15,15,15,21,16,21,1,1,3,3,6,6,9,9,12,
22,22],[1,2,3,4,1,6,8,7,9,11,10,12,2,3,4,16,8,8,7,7,12,22,16,24,25,27,26,28,29
,31,30,32,34,33],,[1,2,3,4,5,6,7,8,9,10,11,1,13,14,15,2,18,17,20,19,5,6,13,24,
25,26,27,28,29,30,31,24,28,28]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[1,1
,1,1,1,1,-1,-1,1,-1,-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]],[1,1,-1,-1,1,1,-E(4),E(4),-1,-E(4),E(4),1,1,-1,-1,1,-E(4),
-E(4),E(4),E(4),1,1,1,-1,1,-E(4),E(4),-1,1,-E(4),E(4),-1,-1,-1],
[TENSOR,[3,5]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],[2,2,2,2,-1,2,-2,-2,2,-2,-2,2,-1,-1,-1,2,1,1,1,1,-1,2,-1,0,0,0
,0,0,0,0,0,0,0,0],
[TENSOR,[9,3]],
[TENSOR,[9,6]],
[TENSOR,[9,5]],[3,3,3,3,0,-1,3,3,-1,-1,-1,3,0,0,0,3,0,0,0,0,0,-1,0,-1,-1,-1,
-1,1,1,1,1,-1,1,1],
[TENSOR,[13,2]],
[TENSOR,[13,4]],
[TENSOR,[13,3]],
[TENSOR,[13,6]],
[TENSOR,[13,5]],
[TENSOR,[13,8]],
[TENSOR,[13,7]],[4,-4,-4,4,-2,0,0,0,0,0,0,4,2,2,-2,-4,0,0,0,0,-2,0,2,0,0,0,0,
0,0,0,0,0,0,0],
[TENSOR,[21,5]],[4,4,0,0,4,4,0,0,0,0,0,-1,4,0,0,-1,0,0,0,0,-1,-1,-1,-4,0,0,0,
-4,0,0,0,1,1,1],
[TENSOR,[23,2]],[4,-4,-4,4,1,0,0,0,0,0,0,4,-1,-1,1,-4,-E(3)+E(3)^2,
E(3)-E(3)^2,E(3)-E(3)^2,-E(3)+E(3)^2,1,0,-1,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[25,3]],
[TENSOR,[25,6]],
[TENSOR,[25,5]],[8,8,0,0,-4,8,0,0,0,0,0,-2,-4,0,0,-2,0,0,0,0,1,-2,1,0,0,0,0,0
,0,0,0,0,0,0],[8,-8,0,0,-4,0,0,0,0,0,0,-2,4,0,0,2,0,0,0,0,1,0,-1,0,0,0,0,0,0,0
,0,0,-E(40)^7-E(40)^13+E(40)^21-E(40)^23+E(40)^29+E(40)^31-E(40)^37+E(40)^39,
E(40)^7+E(40)^13-E(40)^21+E(40)^23-E(40)^29-E(40)^31+E(40)^37-E(40)^39],
[TENSOR,[30,2]],[12,12,0,0,0,-4,0,0,0,0,0,-3,0,0,0,-3,0,0,0,0,0,1,0,4,0,0,0,
-4,0,0,0,-1,1,1],
[TENSOR,[32,2]],[16,-16,0,0,4,0,0,0,0,0,0,-4,-4,0,0,4,0,0,0,0,-1,0,1,0,0,0,0,
0,0,0,0,0,0,0]],
[(33,34),(17,18)(19,20),( 7, 8)(10,11)(17,19)(18,20)(26,27)(30,31)]);
ALF("NDG(2.HS,Q8).2","2.HS.2",[1,2,3,4,6,5,8,8,5,10,10,13,7,18,19,14,29,
29,29,29,30,26,31,34,35,37,37,38,38,38,38,44,50,51],[
"fusion map is unique up to table aut."
]);
ALF("NDG(2.HS,Q8).2","HN",[1,2,2,3,4,7,6,6,7,7,7,9,14,14,15,22,31,31,31,
31,34,41,48,2,3,7,7,18,18,18,18,22,53,54],[
"fusion map is unique up to table aut."
]);

MOT("5^(1+2):8:4",
[
"origin: Dixon's Algorithm"
],
[4000,4000,1000,1000,100,100,50,50,160,160,40,40,32,32,32,32,16,16,16,16,16,16
,16,16,80,80,40,40,40,40,80,80,20,20],
[,[1,1,3,3,5,5,7,7,1,1,3,3,10,10,10,10,13,13,15,15,14,14,16,16,9,9,11,11,11,11
,2,2,6,6],,,[1,2,1,2,1,2,1,2,9,10,9,10,13,14,15,16,17,18,19,20,21,22,23,24,25,
26,25,26,25,26,31,32,31,32]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,1,1,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1],[
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1
,-1],
[TENSOR,[2,3]],[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),1,1,1,1,1,1,-1,-1,-1,-1],
[TENSOR,[2,5]],
[TENSOR,[3,5]],
[TENSOR,[2,7]],[2,2,2,2,2,2,2,2,-2,-2,-2,-2,2*E(4),2*E(4),-2*E(4),-2*E(4),0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[9,5]],[8,8,8,8,3,3,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,-4,-4,1,1],
[TENSOR,[11,2]],[16,16,16,16,-4,-4,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0],[20,20,-5,-5,0,0,0,0,4,4,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,1,
1,1,1,0,0,0,0],
[TENSOR,[14,2]],[20,20,-5,-5,0,0,0,0,-4,-4,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
-E(20)-E(20)^9+E(20)^13+E(20)^17,-E(20)-E(20)^9+E(20)^13+E(20)^17,
E(20)+E(20)^9-E(20)^13-E(20)^17,E(20)+E(20)^9-E(20)^13-E(20)^17,0,0,0,0],
[TENSOR,[16,2]],[1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-E(4),E(4),E(4),
-E(4),-1,1,-1,1,E(4),-E(4),E(4),-E(4),E(4),-E(4),-E(4),E(4),-E(4),E(4)],
[TENSOR,[3,18]],
[TENSOR,[2,19]],
[TENSOR,[2,18]],
[TENSOR,[5,21]],
[TENSOR,[2,22]],
[TENSOR,[3,23]],
[TENSOR,[2,24]],
[TENSOR,[9,18]],
[TENSOR,[9,22]],
[TENSOR,[11,19]],
[TENSOR,[11,18]],
[TENSOR,[13,18]],
[TENSOR,[14,18]],
[TENSOR,[14,19]],
[TENSOR,[16,19]],
[TENSOR,[16,18]]],
[(27,29)(28,30),(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34),
(17,18)(19,20)(25,26)(27,28)(29,30)(31,32)(33,34),
(13,14)(15,16)(17,21)(18,22)(19,23)(20,24)(25,26)(27,28)(29,30),
(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,26)(27,28)(29,30)(31,32)(33,34)]
);
ALF("5^(1+2):8:4","5^(1+2):(8.2)",[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]);
ALF("5^(1+2):8:4","2.HS",[1,2,12,13,14,15,16,17,4,3,29,28,11,11,11,11,26,
26,26,26,27,27,27,27,8,9,39,40,41,42,5,5,30,30]);
ALF("5^(1+2):8:4","2.HS.2N5",[1,2,3,4,5,6,7,8,9,10,11,12,13,13,14,14,15,
16,17,18,15,16,17,18,19,19,20,21,21,20,22,23,24,25]);
ALN("5^(1+2):8:4",["2.HSN5"]);

MOT("2.J2N2",
[
"origin: Dixon's Algorithm"
],
[768,768,768,768,96,96,64,64,96,96,384,384,32,32,16,16,16,48,48,48,48,24,24,24
,24,24,24,48,48,48,48,24,24,24,24,24,24],
[,[1,1,1,1,1,1,3,3,3,3,1,1,11,11,8,8,2,28,28,28,28,28,28,30,30,28,28,18,18,18,
18,18,18,20,20,18,18],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,15,17,1,2,3,4,11,12
,9,10,6,5,1,2,3,4,11,12,9,10,6,5]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[
1,1,1,1,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,-1
,-1,-1,-1],[1,1,1,1,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,1,E(3)^2,E(3)^2,E(3)^2,
E(3)^2,E(3)^2,E(3)^2,-E(3)^2,-E(3)^2,-E(3)^2,-E(3)^2,E(3),E(3),E(3),E(3),E(3),
E(3),-E(3),-E(3),-E(3),-E(3)],
[GALOIS,[3,2]],
[TENSOR,[2,3]],
[TENSOR,[2,4]],[2,-2,2,-2,-2,2,2,-2,-2,2,-2,2,0,0,0,0,0,-1,1,-1,1,1,-1,1,-1,
-1,1,-1,1,-1,1,1,-1,1,-1,-1,1],
[TENSOR,[7,2]],
[TENSOR,[7,5]],
[TENSOR,[7,6]],
[TENSOR,[7,3]],
[TENSOR,[7,4]],[3,3,3,3,-3,-3,3,3,-3,-3,3,3,-1,-1,1,1,-1,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0],
[TENSOR,[13,2]],[4,4,4,4,-2,-2,0,0,2,2,-4,-4,0,0,0,0,0,1,1,1,1,-1,-1,-1,-1,1,
1,1,1,1,1,-1,-1,-1,-1,1,1],
[TENSOR,[15,2]],[4,-4,4,-4,-2,2,0,0,2,-2,4,-4,0,0,0,0,0,1,-1,1,-1,1,-1,-1,1,
-1,1,1,-1,1,-1,1,-1,-1,1,-1,1],
[TENSOR,[17,2]],[4,-4,-4,4,0,0,0,0,0,0,0,0,2,-2,0,0,0,-2,2,2,-2,0,0,0,0,0,0,
-2,2,2,-2,0,0,0,0,0,0],
[TENSOR,[15,5]],
[TENSOR,[15,6]],
[TENSOR,[15,3]],
[TENSOR,[15,4]],
[TENSOR,[17,5]],
[TENSOR,[17,6]],
[TENSOR,[17,3]],
[TENSOR,[17,4]],
[TENSOR,[19,3]],
[TENSOR,[19,4]],[6,6,6,6,0,0,-2,-2,0,0,6,6,-2,-2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0],[6,6,6,6,0,0,-2,-2,0,0,6,6,2,2,0,0,-2,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0],[6,-6,6,-6,0,0,-2,2,0,0,-6,6,0,0,-2*E(4),2*E(4),0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[32,2]],[8,8,-8,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,0,0,0,0,0,0,2,
2,-2,-2,0,0,0,0,0,0],
[TENSOR,[34,3]],
[TENSOR,[34,4]],[12,-12,-12,12,0,0,0,0,0,0,0,0,-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]],
[(18,28)(19,29)(20,30)(21,31)(22,32)(23,33)(24,34)(25,35)(26,36)(27,37),
(15,16),( 5, 6)( 9,10)(24,25)(26,27)(34,35)(36,37)]);
ALF("2.J2N2","J2N2",[1,1,2,2,4,4,9,9,8,8,3,3,10,10,17,17,5,6,6,12,12,13,
13,18,18,15,15,7,7,11,11,14,14,19,19,16,16]);
ALF("2.J2N2","2.J2",[1,2,3,4,3,4,10,11,11,10,3,4,10,11,26,25,5,6,7,20,21,
20,21,34,33,21,20,6,7,20,21,20,21,34,33,21,20]);

MOT("2.J2N3",
[
"origin: Dixon's Algorithm"
],
[432,48,48,48,18,24,24,18,24,24,48,432,48,48,24,24,16,16,16,16,16,16,16,16,216
,216],
[,[1,4,4,1,5,26,6,5,26,6,4,1,4,1,6,6,11,13,13,11,11,13,13,11,26,26],[1,3,2,4,1
,4,3,12,14,11,13,12,11,14,13,2,23,24,21,22,19,20,17,18,12,1]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[1,-1,-1,1,1,1,-1,-1,-1
,1,1,-1,1,-1,1,-1,-1,1,1,-1,1,-1,-1,1,-1,1],[1,-1,-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]],[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),1,1],
[TENSOR,[5,4]],
[TENSOR,[2,6]],
[TENSOR,[2,5]],[1,-E(4),E(4),-1,1,-1,-E(4),-1,1,E(4),-E(4),-1,E(4),1,-E(4),
E(4),-E(8)^3,-E(8),E(8),E(8)^3,E(8)^3,E(8),-E(8),-E(8)^3,-1,1],
[TENSOR,[9,4]],
[TENSOR,[5,9]],
[TENSOR,[5,10]],
[TENSOR,[2,12]],
[TENSOR,[2,11]],
[TENSOR,[2,10]],
[TENSOR,[2,9]],[6,-2,-2,-2,0,1,1,0,-1,-1,2,-6,2,2,-1,1,0,0,0,0,0,0,0,0,3,-3],
[TENSOR,[17,7]],
[TENSOR,[17,5]],
[TENSOR,[17,2]],
[TENSOR,[17,11]],
[TENSOR,[17,9]],
[TENSOR,[17,15]],
[TENSOR,[17,13]],[8,0,0,0,-1,0,0,-1,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,8,8],
[TENSOR,[25,2]]],
[(17,20)(18,19)(21,24)(22,23),(17,21)(18,22)(19,23)(20,24),
( 2, 3)( 7,16)(10,15)(11,13)(17,22)(18,21)(19,24)(20,23)]);
ALF("2.J2N3","3^(1+2):8",[1,5,6,2,4,7,13,4,7,13,6,1,5,2,12,12,8,11,9,10,8,
11,9,10,3,3]);
ALF("2.J2N3","2.J2",[1,10,10,3,8,20,33,9,21,34,11,2,11,4,34,33,26,26,26,
26,25,25,25,25,7,6]);

MOT("2.J2.2N5",
[
"origin: Dixon's Algorithm"
],
[1200,1200,80,80,80,80,48,48,24,24,48,48,48,48,16,16,16,16,100,100,100,100,24,
24,20,20,20,20,24,24,24,24],
[,[1,1,1,1,2,2,2,2,9,9,7,7,8,8,7,7,8,8,19,19,21,21,10,10,19,19,22,22,23,23,24,
24],[1,2,3,4,6,5,8,7,1,2,13,14,11,12,17,18,15,16,19,20,21,22,8,7,25,26,28,27,
13,14,11,12],,[1,2,3,4,5,6,7,8,9,10,12,11,14,13,16,15,18,17,1,2,1,2,23,24,3,4,
5,6,30,29,32,31]],
[[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),1,1,1,1,
-1,-1,1,1,-1,-1,E(4),E(4),-E(4),-E(4)],
[GALOIS,[1,3]],
[TENSOR,[1,1]],
[TENSOR,[1,2]],[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),1,1,1,1,-1,-1,-1,-1,1,1,-E(4),-E(4),E(4),E(4)],
[TENSOR,[5,3]],
[TENSOR,[1,5]],
[TENSOR,[1,6]],[2,2,0,0,0,0,-2,-2,-1,-1,-2*E(4),-2*E(4),2*E(4),2*E(4),0,0,0,0
,2,2,2,2,1,1,0,0,0,0,E(4),E(4),-E(4),-E(4)],
[TENSOR,[9,3]],
[TENSOR,[9,1]],
[TENSOR,[9,2]],[12,12,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,-3,2,2,0,0,-1,-1,0,0
,0,0,0,0],
[TENSOR,[13,5]],[12,12,0,0,4,4,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-3,-3,0,0,0,0,-1,
-1,0,0,0,0],
[TENSOR,[15,1]],[1,-1,-1,1,E(4),-E(4),-E(4),E(4),1,-1,E(8)^3,-E(8)^3,E(8),
-E(8),-E(8)^3,E(8)^3,-E(8),E(8),1,-1,1,-1,-E(4),E(4),-1,1,E(4),-E(4),E(8)^3,
-E(8)^3,E(8),-E(8)],
[TENSOR,[17,3]],
[TENSOR,[1,18]],
[TENSOR,[1,17]],
[TENSOR,[5,19]],
[TENSOR,[5,20]],
[TENSOR,[1,22]],
[TENSOR,[1,21]],
[TENSOR,[9,20]],
[TENSOR,[9,19]],
[TENSOR,[9,17]],
[TENSOR,[9,18]],
[TENSOR,[13,17]],
[TENSOR,[13,21]],
[TENSOR,[15,17]],
[TENSOR,[15,19]]],
[( 3, 4)( 5, 6)(15,16)(17,18)(25,26)(27,28),
(11,12)(13,14)(15,16)(17,18)(29,30)(31,32),
( 5, 6)( 7, 8)(11,13)(12,14)(15,17)(16,18)(23,24)(27,28)(29,31)(30,32)]);
ALF("2.J2.2N5","5^2:(4xS3)",[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]);
ALF("2.J2.2N5","2.J2.2",[1,2,3,4,5,5,5,5,8,9,31,32,32,31,31,32,32,31,14,
15,12,13,18,18,23,24,22,22,39,40,40,39]);
ALF("2.J2.2N5","Isoclinic(2.J2.2)",[1,2,3,4,5,5,5,5,8,9,31,32,31,32,31,32,
31,32,14,15,12,13,18,18,23,24,22,22,39,40,39,40],[
"fusion map is unique up to table aut."
]);
ALF("2.J2.2N5","2.G2(4).2",[1,2,3,4,5,5,5,5,8,9,43,44,43,44,43,44,43,44,
16,17,14,15,20,20,26,27,28,28,52,53,52,53],[
"determined by factorization through Isoclinic(2.J2.2)"
]);
ALF("2.J2.2N5","2.Suz",[1,2,3,4,5,5,5,5,10,11,16,16,16,16,16,16,16,16,17,
18,19,20,29,29,40,41,42,42,50,51,51,50],[
"fusion map is unique up to table aut."
]);
ALN("2.J2.2N5",["2.G2(4).2N5","2.SuzN5"]);

MOT("2.M12N2",
[
"origin: Dixon's Algorithm"
],
[128,32,16,16,64,16,16,128,16,16,16,16,16,16,16,16,32,128,64,32,16,32,128],
[,[1,1,5,1,1,5,1,1,18,18,20,22,23,23,20,22,1,1,1,23,18,23,1]],
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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,-1,1,1,1,-1,1,1],[1,-1,1,-1,1,
1,-1,1,1,-1,1,-1,-1,1,1,-1,-1,1,1,1,-1,1,1],
[TENSOR,[2,5]],
[TENSOR,[2,4]],
[TENSOR,[2,3]],[2,-2,0,0,2,0,0,2,0,0,0,0,0,0,0,0,-2,2,2,-2,2,-2,2],
[TENSOR,[9,2]],[2,0,0,0,-2,0,0,2,-2,0,0,0,0,2,0,0,0,2,-2,-2,0,2,2],[2,0,0,0,
-2,0,0,2,0,-2,0,0,2,0,0,0,0,2,-2,2,0,-2,2],
[TENSOR,[12,3]],
[TENSOR,[11,2]],[2,-2,0,0,2,0,0,2,0,0,-E(8)-E(8)^3,E(8)+E(8)^3,0,0,
E(8)+E(8)^3,-E(8)-E(8)^3,2,-2,-2,0,0,0,-2],
[TENSOR,[15,7]],
[TENSOR,[15,2]],
[TENSOR,[15,3]],[4,0,0,0,-4,0,0,4,0,0,0,0,0,0,0,0,0,-4,4,0,0,0,-4],[4,0,-2,0,
0,2,0,-4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,-4],[4,0,0,-2,0,0,2,-4,0,0,0,0,0,0,0,0,0,
-4,0,0,0,0,4],
[TENSOR,[21,4]],
[TENSOR,[20,2]]],
[(11,15)(12,16),(4,7),(3,6),( 2,17)(12,16),( 9,10)(11,12)(13,14)(15,16)(20,22)
]);
ALF("2.M12N2","M12N2",[1,4,11,8,3,12,8,2,6,7,15,16,14,13,15,16,4,1,3,10,5,
9,2]);
ALF("2.M12N2","2.M12",[1,4,11,4,4,10,5,5,3,3,17,20,10,11,18,19,5,2,5,10,3,
11,4],[
"compatible with M12N2 -> M12"
]);

MOT("2xM12N3",
[
"Sylow 3 normalizer in 2.M12"
],
0,
0,
0,
[( 5, 6)( 7, 8)(17,18)(19,20),( 3, 4)( 7, 8)(17,18)(21,22),
( 5, 7)( 6, 8)(11,13)(12,14)(17,19)(18,20)],
["ConstructDirectProduct",[["M12N3"],["Cyclic",2]]]);
ALF("2xM12N3","2.M12",[1,2,4,5,4,5,4,5,6,7,6,7,6,7,8,9,15,16,15,16,15,16],[
"fusion map is unique up to table automorphisms"
]);
ALN("2xM12N3",["2.M12N3"]);

MOT("2.RuN2",
[
"origin: Dixon's Algorithm"
],
[32768,32768,32768,32768,16384,16384,8192,8192,4096,4096,2048,2048,2048,2048,
1024,1024,1024,1024,512,512,512,512,256,256,256,256,256,256,256,1024,512,512,
1024,1024,512,512,1024,1024,512,512,512,1024,1024,1024,1024,1024,1024,256,256,
256,256,256,256,256,512,512,256,512,512,512,512,512,512,256,512,512,512,512,
256,256,512,512,512,512,256,256,256,256,128,256,256,256,256,128,256,256,256,
256,256,256,256,256,128,128,64,64,64,64,64,128,128,32,32,32,128,128,32,32,32,
32,32,64,64,64,64,64,64,64,64,64,64,64,64,64,64,32,32,32,32,32,32],
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,7,5,3,6,6,6,6,7,7,8,7,5,6,7,7,6,7,7,8,8,8,8,8,3,3,7,8,8,5,5,7,8,8,8,5,5,4,3,
14,14,10,10,10,14,14,5,14,14,3,3,14,14,10,10,16,16,12,11,14,9,12,16,16,22,18,
21,30,30,32,31,35,39,36,38,38,42,42,34,34,40,40,41,41,45,45,46,46,79,79,105,
105,106,106]],
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[TENSOR,[1,4]],
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[TENSOR,[11,1]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,0,0,-2,-2,0,-2,0,0,0,0
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[TENSOR,[13,3]],[2,2,2,2,2,2,2,2,2,2,2,2,2,2,-2,-2,2,2,0,0,2,2,0,-2,0,0,0,-2,
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[TENSOR,[21,1]],[4,4,4,4,4,4,4,4,4,4,4,4,-4,-4,0,0,0,0,-2,-2,0,0,2,0,2,-2,-2,
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[TENSOR,[128,1]],[32,-32,-32,32,0,0,0,0,0,0,0,0,0,0,8,-8,0,0,0,0,0,0,0,0,0,0,
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[GALOIS,[130,3]]],
[(126,127),( 62, 63)( 65, 66)( 67, 68)( 71, 72)(112,113)(122,123),
( 58, 59)( 73, 74)(114,115)(120,121)(124,125),
( 21, 22)( 58, 59)( 73, 74)( 77, 89)( 78, 90)( 80, 91)( 81, 92)( 82, 85)
( 83, 86)(102,104)(124,125)
,( 93,101)( 94,100)(118,119)(128,129)(130,131),
( 19, 20)( 55, 56)( 67, 68)( 71, 72)( 93,100)( 94,101)(122,123),
( 26, 27)( 93,100)( 94,101)(112,113)(122,123),
( 60, 61)( 93,101)( 94,100)(105,106)(116,117)(128,131)(129,130),
( 28, 29)( 60, 61)( 80, 81)( 82, 83)( 85, 86)( 87, 88)( 91, 92)( 93,101)
( 94,100)(105,106)(120,121)(124,125)(128,130)(129,131)
]);
ALF("2.RuN2","RuN2",[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,
13,14,15,15,16,16,17,18,19,20,20,21,22,23,23,24,25,26,27,27,28,28,29,29,
30,31,32,33,34,35,36,37,37,38,39,39,40,40,41,41,42,43,43,44,44,45,46,47,
47,48,48,49,50,51,51,52,53,53,54,54,55,56,56,57,57,58,58,59,59,60,60,61,
62,63,64,65,66,66,67,68,69,70,70,71,72,73,74,75,76,76,77,77,78,78,79,79,
80,80,81,81,82,82,83,83,84,84,85,85]);
ALF("2.RuN2","2.Ru",[1,2,4,3,4,3,3,4,4,3,3,4,4,3,4,3,3,4,3,4,4,3,5,5,5,3,
4,3,4,12,13,13,8,9,13,13,8,9,13,12,12,9,8,8,9,9,8,12,13,12,13,13,13,13,8,
9,12,10,11,11,10,10,11,13,10,11,10,11,13,12,11,10,11,10,13,12,13,13,13,8,
9,13,13,12,9,8,12,12,8,9,13,13,13,13,12,13,13,12,12,8,9,13,12,12,25,24,26,
26,26,26,26,23,22,22,23,23,22,24,25,25,24,22,23,23,22,26,26,41,42,43,44]);

MOT("5^(1+2):(4x4):4",
[
"origin: Dixon's Algorithm"
],
[8000,8000,200,200,2000,2000,160,160,160,160,160,160,160,160,320,320,100,100,
40,40,80,80,40,40,40,40,40,40,16,16,16,16,64,64,64,64,80,80,20,20,32,32,32,32,
80,80,40,40,40,40],
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,9,10,11,12,13,14,15,16,1,2,13,14,15,16,7,8,9,10,11,12,29,30,31,32,33,34,35,36
,37,38,37,38,41,42,43,44,45,46,45,46,45,46]],
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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),-1,-1,1,1,1,1,1,1,
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[TENSOR,[2,2]],
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-E(4),E(4)],
[TENSOR,[26,7]],
[TENSOR,[5,27]],
[TENSOR,[5,26]],
[TENSOR,[2,29]],
[TENSOR,[2,26]],
[TENSOR,[2,27]],
[TENSOR,[2,28]],
[TENSOR,[9,26]],
[TENSOR,[9,30]],
[TENSOR,[11,27]],
[TENSOR,[11,30]],
[TENSOR,[11,32]],
[TENSOR,[11,26]],
[TENSOR,[15,30]],
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[TENSOR,[19,27]],
[TENSOR,[19,26]],
[TENSOR,[21,26]],
[TENSOR,[21,27]],
[TENSOR,[23,26]],
[TENSOR,[23,27]],
[TENSOR,[25,26]]],
[(47,49)(48,50),(29,30)(31,32)(37,38)(39,40)(45,46)(47,48)(49,50),
( 7, 8)( 9,10)(23,24)(25,26)(29,30)(31,32)(41,42)(43,44),
( 7, 9)( 8,10)(23,25)(24,26)(29,32)(30,31)(33,35)(34,36)(41,43)(42,44)]);
ALF("5^(1+2):(4x4):4","5^1+2:(2^5)",[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]);
ALF("5^(1+2):(4x4):4","2.Ru",[1,2,14,15,14,15,8,9,8,9,4,3,8,9,3,4,16,17,
45,46,27,28,45,46,45,46,28,27,26,26,26,26,13,13,13,13,5,5,29,29,13,13,13,
13,10,11,47,48,49,50]);
ALN("5^(1+2):(4x4):4",["2.RuN5"]);

MOT("3.F3+N5",
[
"origin: Dixon's Algorithm"
],
[86400,3600,3456,28800,2880,1152,960,86400,86400,3600,144,36,36,3456,3456,1152
,1152,576,480,480,480,480,192,96,96,96,96,28800,28800,3456,3456,2880,2880,1152
,1152,960,960,360,360,360,144,144,144,144,144,144,144,144,36,36,48,48,48,48,
1200,720,240,3456,3456,3456,3456,1152,1152,1152,1152,576,576,480,480,480,480,
480,480,480,480,192,192,144,144,144,144,144,144,144,144,144,144,96,96,96,96,96
,96,96,96,72,72,72,36,36,36,36,3600,3600,450,450,450,120,120,120,120,48,48,48,
48,48,48,48,48,1200,1200,720,720,240,240,90,90,90,120,120,120,120,120,120,120,
120],
[,[1,2,1,1,1,1,1,9,8,10,11,12,13,3,3,3,3,3,7,7,5,5,3,7,7,5,5,9,8,9,8,9,8,9,8,9
,8,10,10,10,10,11,11,11,11,11,11,11,12,13,14,15,16,17,2,2,2,31,30,31,30,31,30,
31,30,31,30,37,36,37,36,33,32,33,32,31,30,41,41,42,42,42,42,42,42,42,42,37,36,
37,36,33,32,33,32,41,41,41,49,49,50,50,104,103,105,107,106,57,57,56,56,59,58,
61,60,63,62,65,64,104,103,104,103,104,103,105,106,107,125,124,125,124,123,122,
123,122],[1,2,3,4,5,6,7,1,1,1,1,1,1,15,14,17,16,18,20,19,22,21,23,25,24,27,26,
4,4,3,3,5,5,6,6,7,7,5,5,5,3,3,4,6,4,4,6,6,3,3,52,51,54,53,55,56,57,15,15,14,14
,17,17,16,16,18,18,20,20,19,19,22,22,21,21,23,23,15,14,16,17,16,16,17,17,14,15
,25,25,24,24,27,27,26,26,18,18,18,14,15,15,14,2,2,2,2,2,109,108,111,110,52,52,
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41,41,42,42,19,19,14,15,31,32,31,31,32,32,29,30,47,47,48,48,45,45,46,46,
23,23,23,37,38,39,40,4,4,6,6,6,55,56,53,54,49,49,50,50,51,51,52,52,5,5,20,
20,21,21,24,24,24,55,55,56,56,53,53,54,54]);
ALF("3.F3+N5","3.F3+",[1,28,7,4,4,7,7,2,3,10,17,18,18,19,19,25,25,19,19,
19,22,22,25,25,25,22,22,5,6,8,9,5,6,8,9,8,9,31,33,32,40,56,47,50,49,48,52,
51,57,57,64,64,70,70,83,83,86,20,21,20,21,26,27,26,27,20,21,20,21,20,21,
23,24,23,24,26,27,96,96,118,118,119,120,119,120,103,103,26,27,26,27,23,24,
23,24,96,96,96,110,110,111,111,29,30,130,131,132,166,166,163,163,65,66,65,
66,71,72,71,72,84,85,84,85,87,88,214,216,215,167,168,167,168,164,165,164,
165]);
ALF("3.F3+N5","3.F3+.2N5",[1,2,3,4,5,6,7,8,8,9,10,11,11,12,13,14,15,16,17,
18,19,20,21,22,23,24,25,26,26,27,27,28,28,29,29,30,30,31,32,32,33,34,35,
36,37,37,38,38,39,39,40,41,42,43,44,45,46,47,47,48,48,49,49,50,50,51,51,
52,52,53,53,54,54,55,55,56,56,57,58,59,60,61,61,62,62,63,64,65,65,66,66,
67,67,68,68,69,70,70,71,72,72,71,73,73,74,75,75,76,77,78,79,80,80,81,81,
82,82,83,83,84,84,85,85,86,86,87,88,88,89,89,90,90,91,91,92,92]);

MOT("3.F3+.2N5",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[172800,7200,6912,57600,5760,2304,1920,86400,7200,288,36,6912,6912,2304,2304,
1152,960,960,960,960,384,192,192,192,192,28800,3456,2880,1152,960,720,360,288,
288,288,288,144,144,36,96,96,96,96,2400,1440,480,3456,3456,1152,1152,576,480,
480,480,480,192,288,288,288,288,144,144,288,288,96,96,96,96,144,72,36,36,3600,
900,450,240,240,240,240,48,48,48,48,1200,720,240,180,90,120,120,120,120,1920,
1920,384,384,192,192,480,480,640,640,128,128,64,64,160,160,240,240,48,48,24,24
,60,60,9600,384,320,48,384,384,64,400,48,80,48,48,9600,384,320,48,384,384,64,
400,48,80,48,48],
[,[1,2,1,1,1,1,1,8,9,10,11,3,3,3,3,3,7,7,5,5,3,7,7,5,5,8,8,8,8,8,9,9,9,10,10,
10,10,10,11,12,13,14,15,2,2,2,27,27,27,27,27,30,30,28,28,27,33,33,34,34,34,34,
34,34,30,30,28,28,33,33,39,39,73,74,75,46,46,45,45,47,48,49,50,73,73,73,74,75,
86,86,85,85,5,5,5,5,13,12,45,45,5,5,5,5,13,12,45,45,31,31,31,31,58,57,87,87,1,
1,1,10,3,3,3,2,10,2,34,34,4,4,4,35,6,6,6,44,35,44,36,36],[1,2,3,4,5,6,7,1,1,1,
1,13,12,15,14,16,18,17,20,19,21,23,22,25,24,4,3,5,6,7,5,5,3,3,4,6,4,6,3,41,40,
43,42,44,45,46,13,12,15,14,16,18,17,20,19,21,13,12,14,15,14,15,12,13,23,22,25,
24,16,16,12,13,2,2,2,77,76,79,78,41,40,43,42,44,45,46,45,45,77,76,79,78,94,93,
96,95,98,97,100,99,102,101,104,103,106,105,108,107,94,93,96,95,98,97,100,99,
117,118,119,117,122,121,123,124,118,126,122,121,129,130,131,129,134,133,135,
136,130,138,134,133],,[1,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,
22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,4,5,7,47,48,
49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,8,9,9,
17,18,19,20,80,81,82,83,26,28,30,31,32,52,53,54,55,93,94,95,96,97,98,93,94,101
,102,103,104,105,106,101,102,109,110,111,112,113,114,109,110,117,118,119,120,
121,122,123,117,125,119,127,128,129,130,131,132,133,134,135,129,137,131,139,
140]],
0,
[
( 12, 13)( 14, 15)( 17, 18)( 19, 20)( 22, 23)( 24, 25)( 40, 41)( 42, 43)
( 47, 48)( 49, 50)( 52, 53)( 54, 55)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 71, 72)( 76, 77)( 78, 79)( 80, 81)( 82, 83)( 89, 90)
( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)
(107,108)(109,110)(111,112)(113,114)(115,116)(121,122)(127,128)(133,134)
(139,140)
],
["ConstructMGA","3.F3+N5","S4x5^2:4S4",[[17,19],[18,20],[21,22],[23,24],[29,30
],[31,32],[33,35],[34,36],[37,39],[38,40],[41,42],[43,44],[49,50],[51,52],[53,
54],[55,56],[61,63],[62,64],[65,66],[67,68],[81,83],[82,84],[85,87],[86,88],[
93,95],[94,96],[97,99],[98,100],[103,105],[104,106],[111,113],[112,114],[115,
116],[117,118],[121,122],[123,124],[129,130],[131,132],[133,135],[134,136]],()
]);
ALF("3.F3+.2N5","S4x5^2:4S4",[1,12,2,21,3,22,23,1,41,4,44,5,6,25,26,11,87,
88,67,68,31,89,90,69,70,21,2,3,22,23,43,43,42,13,24,33,24,33,53,75,74,95,
94,32,16,36,5,6,25,26,11,87,88,67,68,31,45,46,38,37,38,37,18,17,89,90,69,
70,51,51,58,57,12,52,52,99,100,79,80,75,74,95,94,32,16,36,56,56,99,100,79,
80,7,8,9,10,14,15,19,20,27,28,29,30,34,35,39,40,47,48,49,50,54,55,59,60,
61,62,63,64,65,66,71,72,73,76,77,78,81,82,83,84,85,86,91,92,93,96,97,98]);

MOT("3xF3+N7",
[
"Sylow 7 normalizer in 3.F3+"
],
0,
0,
0,
[(31,34)(32,35)(33,36)(88,91)(89,92)(90,93),
( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(16,19)(17,21)(18,20)(23,24)(26,27)(29,30)
(31,34)(32,36)(33,35)(37,40)(38,42)(39,41)(43,46)(44,48)(45,47)(49,52)(50,54)
(51,53)(56,57)(59,60)(62,63)(64,67)(65,69)(66,68)(70,73)(71,75)(72,74)(76,79)
(77,81)(78,80)(83,84)(86,87)(88,91)(89,93)(90,92)
,
(16,17,18)(19,21,20)(37,38,39)(40,42,41)(43,44,45)(46,48,47)(49,50,51)
(52,54,53)(64,66,65)(67,68,69)(70,72,71)(73,74,75)(76,78,77)(79,80,81)
,
(16,19)(17,20)(18,21)(37,40)(38,41)(39,42)(43,46)(44,47)(45,48)(49,52)(50,53)
(51,54)(64,67)(65,68)(66,69)(70,73)(71,74)(72,75)(76,79)(77,80)(78,81)
,
(10,13)(11,14)(12,15)(22,58)(23,59)(24,60)(28,85)(29,86)(30,87)(43,79)(44,80)
(45,81)(46,76)(47,77)(48,78)
],
["ConstructDirectProduct",[["F3+N7"],["Cyclic",3]]]);
ALF("3xF3+N7","3.F3+",[1,2,3,61,62,63,58,59,60,61,62,63,61,62,63,18,18,18,
18,18,18,7,8,9,14,15,16,127,128,129,171,172,173,174,175,176,18,18,18,18,
18,18,57,57,57,57,57,57,170,170,170,170,170,170,7,8,9,7,8,9,34,35,36,57,
57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,127,128,129,127,128,
129,245,246,247,242,243,244]);
ALF("3xF3+N7","3.F3+.2N7",[1,2,2,3,4,4,5,6,6,7,8,9,7,9,8,10,11,11,12,13,
13,14,15,16,17,18,18,19,20,21,22,23,24,22,24,23,25,26,26,27,28,28,29,30,
31,32,33,34,35,36,36,37,38,38,39,40,40,14,16,15,41,42,42,43,44,44,45,46,
46,47,48,48,49,50,50,32,34,33,29,31,30,51,52,52,19,21,20,53,54,55,53,55,
54]);
ALN("3xF3+N7",["3.F3+N7"]);

MOT("3.F3+.2N7",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[74088,37044,12348,6174,882,441,294,294,294,216,108,216,108,252,252,252,756,
378,42,42,42,126,126,126,756,378,756,378,36,36,36,36,36,36,126,63,126,63,1512,
756,756,378,216,108,216,108,108,54,108,54,252,126,126,126,126,252,84,252,252,
36,36,36,36,36,36,12,12,42,28,28,42,42],
[,[1,2,3,4,5,6,7,9,8,12,13,10,11,1,2,2,17,18,7,8,9,22,23,24,27,28,25,26,12,13,
13,10,11,11,37,38,35,36,1,2,17,18,10,11,12,13,25,26,27,28,3,4,22,24,23,1,39,27
,25,17,17,25,27,12,10,45,43,5,51,51,37,35],[1,1,3,3,5,5,7,7,7,1,1,1,1,14,14,14
,1,1,19,19,19,3,3,3,1,1,1,1,14,14,14,14,14,14,5,5,5,5,39,39,39,39,39,39,39,39,
39,39,39,39,51,51,51,51,51,56,57,56,56,56,56,56,56,56,56,57,57,68,69,70,68,68]
,,,,[1,2,1,2,1,2,1,2,2,10,11,12,13,14,15,16,17,18,14,15,16,17,18,18,25,26,27,
28,29,30,31,32,33,34,25,26,27,28,39,40,41,42,43,44,45,46,47,48,49,50,39,40,41,
42,42,56,57,58,59,60,61,62,63,64,65,66,67,56,57,57,58,59]],
0,
[(69,70),(23,24)(54,55)(69,70),
(10,12)(11,13)(25,27)(26,28)(29,32)(30,33)(31,34)(35,37)(36,38)(43,45)(44,46)
(47,49)(48,50)(58,59)(60,61)(62,63)(64,65)(66,67)(69,70)(71,72)
,
( 8, 9)(10,12)(11,13)(15,16)(20,21)(25,27)(26,28)(29,32)(30,34)(31,33)(35,37)
(36,38)(43,45)(44,46)(47,49)(48,50)(58,59)(60,61)(62,63)(64,65)(66,67)(69,70)
(71,72)
],
["ConstructMGA","3xF3+N7","7^(1+2)_+:(6xS3).2",[[2,3],[5,9],[6,8],[11,12],[14,
15],[17,18],[20,21],[23,24],[26,33],[27,32],[29,36],[30,35],[38,39],[41,42],[
44,45],[47,48],[50,51],[53,54],[56,57],[59,60],[62,63],[65,75],[66,74],[68,72]
,[69,71],[77,78],[80,81],[83,87],[84,86],[89,93],[90,92]],()]);
ALF("3.F3+.2N7","7^(1+2)_+:(6xS3).2",[1,1,2,2,3,3,4,4,4,5,5,6,6,11,11,11,
12,12,14,14,14,15,15,15,17,17,18,18,22,22,22,21,21,21,23,23,24,24,7,7,13,
13,9,9,8,8,20,20,19,19,10,10,16,16,16,25,26,27,28,29,30,31,32,33,34,35,36,
37,38,39,40,41]);
ALF("3.F3+.2N7","3.F3+.2",[1,2,43,44,41,42,43,44,44,13,13,13,13,5,6,6,10,
11,89,90,90,119,120,121,13,13,13,13,40,40,40,40,40,40,118,118,118,118,5,6,
24,25,40,40,40,40,40,40,40,40,89,90,164,166,165,173,177,188,188,186,186,
188,188,188,188,208,208,210,233,234,247,247]);

MOT("(A4x11:5).2",
[
"constructed using `CharacterTableOfIndexTwoSubdirectProduct'"
],
[1320,132,120,120,120,120,440,44,40,40,40,40,165,33,33,15,15,15,15,20,20,20,20
,20,20,20,20,20,20],
[,[1,2,4,6,3,5,1,2,4,6,3,5,13,14,15,17,19,16,18,3,5,1,4,6,9,11,7,10,12],[1,2,5
,3,6,4,7,8,11,9,12,10,1,2,2,5,3,6,4,21,24,22,20,23,26,29,27,25,28],,[1,2,1,1,1
,1,7,8,7,7,7,7,13,15,14,13,13,13,13,22,22,22,22,22,27,27,27,27,27],,,,,,[1,1,3
,4,5,6,7,7,9,10,11,12,13,13,13,16,17,18,19,20,21,22,23,24,25,26,27,28,29]],
0,
[(14,15),( 3, 4, 6, 5)( 9,10,12,11)(16,17,19,18)(20,23,24,21)(25,28,29,26)],
["ConstructIndexTwoSubdirectProduct","a4","s4","11:5","11:10",[36,38,40,42,44,
47,49,51,53,55],(),()]);
ALF("(A4x11:5).2","s4",[1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,5,
5,5,5,5]);
ALF("(A4x11:5).2","11:10",[1,2,4,6,8,10,1,2,4,6,8,10,1,2,2,4,6,8,10,3,5,7,
9,11,3,5,7,9,11]);
ALF("(A4x11:5).2","F3+",[1,37,12,12,12,12,2,73,35,35,35,35,5,92,93,55,55,
55,55,36,36,3,36,36,67,67,10,67,67],[
"fusion map is unique up to table aut."
]);
ALN("(A4x11:5).2",["F3+N11"]);

MOT("3x(A4x11:5).2",
[
"Sylow 11 normalizer in 3.F3+"
],
0,
0,
0,
[(40,43)(41,44)(42,45),
( 7,10,16,13)( 8,11,17,14)( 9,12,18,15)(25,28,34,31)(26,29,35,32)(27,30,36,33)
(46,49,55,52)(47,50,56,53)(48,51,57,54)(58,67,70,61)(59,68,71,62)(60,69,72,63)
(73,82,85,76)(74,83,86,77)(75,84,87,78)
,
( 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)(40,43)(41,45)(42,44)(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)
],
["ConstructDirectProduct",[["(A4x11:5).2"],["Cyclic",3]]]);
ALN("3x(A4x11:5).2",["3.F3+N11"]);

MOT("(3^(1+2)_+:2x13:6).2",
[
"constructed using `CharacterTableOfIndexTwoSubdirectProduct'"
],
[8424,702,648,648,648,648,648,8424,702,648,648,648,648,648,8424,702,648,648,
648,648,648,702,117,117,54,54,54,54,54,702,117,117,54,54,54,54,54,936,78,72,72
,72,72,72,936,78,72,72,72,72,72,936,78,72,72,72,72,72,72,72,72,72,72,72,72,72,
72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,72,
72,72],
[,[1,2,4,6,1,4,6,15,16,18,20,15,18,20,8,9,11,13,8,11,13,22,24,23,26,28,22,26,
28,30,32,31,34,36,30,34,36,1,2,4,6,1,4,6,15,16,18,20,15,18,20,8,9,11,13,8,11,
13,40,42,44,40,42,44,54,56,58,54,56,58,47,49,51,47,49,51,40,42,44,40,42,44,54,
56,58,54,56,58,47,49,51,47,49,51],[1,2,5,1,5,1,5,1,2,5,1,5,1,5,1,2,5,1,5,1,5,1
,2,2,5,1,5,1,5,1,2,2,5,1,5,1,5,38,39,42,38,42,38,42,38,39,42,38,42,38,42,38,39
,42,38,42,38,42,78,81,78,81,78,81,78,81,78,81,78,81,78,81,78,81,78,81,60,63,60
,63,60,63,60,63,60,63,60,63,60,63,60,63,60,63],,,,,,,,,,[1,1,3,4,5,6,7,8,8,10,
11,12,13,14,15,15,17,18,19,20,21,22,22,22,25,26,27,28,29,30,30,30,33,34,35,36,
37,38,38,40,41,42,43,44,45,45,47,48,49,50,51,52,52,54,55,56,57,58,59,60,61,62,
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,
89,90,91,92,93,94]],
0,
[
(59,62)(60,63)(61,64)(65,68)(66,69)(67,70)(71,74)(72,75)(73,76)(77,80)(78,81)
(79,82)(83,86)(84,87)(85,88)(89,92)(90,93)(91,94)
,(31,32),(23,24),(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(29,37),
(59,77)(60,78)(61,79)(62,80)(63,81)(64,82)(65,83)(66,84)(67,85)(68,86)(69,87)
(70,88)(71,89)(72,90)(73,91)(74,92)(75,93)(76,94)
,
( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21)(45,52)(46,53)(47,54)(48,55)
(49,56)(50,57)(51,58)(65,71)(66,72)(67,73)(68,74)(69,75)(70,76)(83,89)(84,90)
(85,91)(86,92)(87,93)(88,94)
,
( 3, 7)( 4, 6)(10,14)(11,13)(17,21)(18,20)(25,29)(26,28)(33,37)(34,36)(40,44)
(41,43)(47,51)(48,50)(54,58)(55,57)(59,61)(62,64)(65,67)(68,70)(71,73)(74,76)
(77,79)(80,82)(83,85)(86,88)(89,91)(92,94)
,
( 3,10,17)( 4,18,11)( 6,13,20)( 7,21,14)(40,47,54)(41,55,48)(43,50,57)
(44,58,51)(59,71,65)(61,67,73)(62,74,68)(64,70,76)(77,89,83)(79,85,91)
(80,92,86)(82,88,94)
],
["ConstructIndexTwoSubdirectProduct","3^(1+2)_+:2","3^(1+2):4","13:6","13:12",
[107,109,111,113,115,117,120,122,124,126,128,130,133,135,137,139,141,143,146,
148,150,152,154,156,159,161,163,165,167,169,172,174,176,178,180,182],(),()]);
ALF("(3^(1+2)_+:2x13:6).2","3^(1+2):4",[1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,
3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,
8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,11,11,11,12,12,12,12,12,12,
13,13,13,13,13,13,14,14,14,14,14,14]);
ALF("(3^(1+2)_+:2x13:6).2","13:12",[1,2,4,6,8,10,12,1,2,4,6,8,10,12,1,2,4,
6,8,10,12,1,2,2,4,6,8,10,12,1,2,2,4,6,8,10,12,1,2,4,6,8,10,12,1,2,4,6,8,
10,12,1,2,4,6,8,10,12,3,5,7,9,11,13,3,5,7,9,11,13,3,5,7,9,11,13,3,5,7,9,
11,13,3,5,7,9,11,13,3,5,7,9,11,13]);
ALF("(3^(1+2)_+:2x13:6).2","(3^2:2x13:6).2",[1,2,3,4,5,6,7,1,2,3,4,5,6,7,
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,
28,29,30,24,25,26,27,28,29,30,24,25,26,27,28,29,30,31,32,33,34,35,36,31,
32,33,34,35,36,31,32,33,34,35,36,37,38,39,40,41,42,37,38,39,40,41,42,37,
38,39,40,41,42]);
ALF("(3^(1+2)_+:2x13:6).2","3.F3+",[1,121,50,17,7,17,50,2,122,51,17,8,17,
51,3,123,52,17,9,17,52,10,235,236,56,17,40,17,56,18,237,238,57,18,57,18,
57,4,199,56,47,7,47,56,5,200,56,48,8,48,56,6,201,56,49,9,49,56,119,25,120,
120,25,119,120,26,118,118,26,120,118,27,119,119,27,118,120,25,119,119,25,
120,118,26,120,120,26,118,119,27,118,118,27,119],[
"determined using the fusion (3^2:2x13:6).2 -> F3+"
]);

MOT("3x17:16",
[
"Sylow 17 normalizer in 3.F3+"
],
0,
0,
0,
[
( 7,19,31,43)( 8,20,32,44)( 9,21,33,45)(10,34)(11,35)(12,36)(13,49,37,25)
(14,50,38,26)(15,51,39,27)(22,46)(23,47)(24,48)
,
( 7,49)( 8,50)( 9,51)(10,46)(11,47)(12,48)(13,43)(14,44)(15,45)(16,40)(17,41)
(18,42)(19,37)(20,38)(21,39)(22,34)(23,35)(24,36)(25,31)(26,32)(27,33)
,
( 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)
],
["ConstructDirectProduct",[["17:16"],["Cyclic",3]]]);
ALN("3x17:16",["3.F3+N17"]);

MOT("3x23:11",
[
"Sylow 23 normalizer in 3.F3+"
],
0,
0,
0,
[
(10,13,19,31,22,37,34,28,16,25)(11,14,20,32,23,38,35,29,17,26)(12,15,21,33,24,
 39,36,30,18,27)
,( 4, 7)( 5, 8)( 6, 9),
( 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)
],
["ConstructDirectProduct",[["23:11"],["Cyclic",3]]]);
ALN("3x23:11",["3.F3+N23"]);

MOT("3x29:14",
[
"Sylow 29 normalizer in 3.F3+"
],
0,
0,
0,
[
(10,16,34,46,40,22)(11,17,35,47,41,23)(12,18,36,48,42,24)(13,25,19,43,31,37)
(14,26,20,44,32,38)(15,27,21,45,33,39)
,( 4, 7)( 5, 8)( 6, 9),
( 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)
],
["ConstructDirectProduct",[["29:14"],["Cyclic",3]]]);
ALN("3x29:14",["3.F3+N29"]);

MOT("3x(D10xA9).2",
[
"defect normalizer in 3.F3+",
],
0,
0,
0,
[
(151,193)(152,194)(153,195)(154,196)(155,197)(156,198)(157,199)(158,200)
(159,201)(160,202)(161,203)(162,204)(163,205)(164,206)(165,207)(166,208)
(167,209)(168,210)(169,211)(170,212)(171,213)(172,214)(173,215)(174,216)
(175,217)(176,218)(177,219)(178,220)(179,221)(180,222)(181,223)(182,224)
(183,225)(184,226)(185,227)(186,228)(187,229)(188,230)(189,231)(190,232)
(191,233)(192,234)
,( 97,100)( 98,101)( 99,102),( 85, 88)( 86, 89)( 87, 90),
(  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)( 95, 96)
( 97,100)( 98,102)( 99,101)(104,105)(107,108)(110,111)(113,114)(116,117)
(119,120)(122,123)(125,126)(128,129)(131,132)(134,135)(137,138)(140,141)
(143,144)(146,147)(149,150)(152,153)(155,156)(158,159)(161,162)(164,165)
(167,168)(170,171)(173,174)(176,177)(179,180)(182,183)(185,186)(188,189)
(191,192)(194,195)(197,198)(200,201)(203,204)(206,207)(209,210)(212,213)
(215,216)(218,219)(221,222)(224,225)(227,228)(230,231)(233,234)
],
["ConstructDirectProduct",[["(D10xA9).2"],["Cyclic",3]]]);
ALF("3x(D10xA9).2","3.F3+",[1,2,3,4,5,6,7,8,9,10,10,10,11,12,13,14,15,16,
22,23,24,19,20,21,28,29,30,31,32,33,34,35,36,58,59,60,74,75,76,83,84,85,
97,98,99,130,131,132,28,29,30,83,84,85,86,87,88,130,131,132,133,134,135,
136,137,138,163,164,165,166,167,168,28,29,30,214,215,216,217,218,219,226,
227,228,248,249,250,251,252,253,83,84,85,254,255,256,131,132,130,132,130,
131,4,5,6,7,8,9,7,8,9,31,32,33,37,38,39,44,45,46,22,23,24,25,26,27,83,84,
85,40,40,40,53,54,55,124,125,126,150,151,152,86,87,88,97,98,99,214,215,
216,22,23,24,22,23,24,19,20,21,25,26,27,97,98,99,97,98,99,115,116,117,115,
116,117,104,105,106,70,71,72,163,164,165,96,96,96,205,206,207,166,167,168,
22,23,24,22,23,24,19,20,21,25,26,27,97,98,99,97,98,99,115,116,117,115,116,
117,104,105,106,70,71,72,163,164,165,96,96,96,205,206,207,166,167,168]);

MOT("3x(3xA6):2_2",
[
"6th maximal subgroup in 3.J3"
],
0,
0,
0,
[(43,46)(44,47)(45,48),(16,19)(17,20)(18,21),(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),(28,31)(29,32)(30,33)(34,37)(35,38)(36,39)(49,52)(50,53)(51,54)],
["ConstructDirectProduct",[["j3m6"],["Cyclic",3]]]);
ALF("3x(3xA6):2_2","j3m6",[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]);
ALF("3x(3xA6):2_2","3.(3xM10):2",[1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,
13,11,13,12,14,15,15,16,17,17,18,19,20,18,20,19,21,23,22,21,22,23,27,28,
28,29,30,31,29,31,30,32,33,34,32,34,33]);
ALF("3x(3xA6):2_2","3.J3",[1,2,3,7,8,9,4,5,6,20,21,22,10,10,10,8,9,7,9,7,
8,11,12,13,35,36,37,14,15,16,17,18,19,38,39,40,41,42,43,4,5,6,23,24,25,23,
24,25,32,33,34,29,30,31]);
ALN("3x(3xA6):2_2",["NDG(3.J3,3^2)"]);

MOT("3.(3xM10):2",
[
"origin: Dixon's Algorithm"
],
[12960,6480,6480,3240,288,144,144,72,162,81,81,81,81,144,72,72,36,90,90,90,45,
45,45,48,16,6,120,60,24,24,24,30,30,30,24,12,24,24,24],
[,[1,2,3,4,1,2,3,4,9,10,11,12,13,5,6,7,8,18,19,20,21,22,23,1,5,9,1,2,14,15,15,
18,20,19,5,7,14,16,16],[1,1,1,1,5,5,5,5,1,1,1,1,1,14,14,14,14,18,18,18,18,18,
18,24,25,24,27,27,29,29,29,32,32,32,35,35,37,37,37],,[1,2,3,4,5,6,7,8,9,10,11,
12,13,14,15,16,17,1,2,2,3,4,4,24,25,26,27,28,29,30,31,27,28,28,35,36,37,38,39]
],
0,
[(38,39),(30,31),(12,13),(19,20)(22,23)(33,34)],
["ConstructIndexTwoSubdirectProduct","C3","S3","j3m6","(3xM10):2",[53,54,55,
59,60,61,62,63],(2,3,5,9,18,10,21,15,4,7,14)(6,11,27,28,30,34,26,23,20,13,32,
24,19,12,29,31,33,25,22,17,8,16),(2,3)(5,14,20,11,16,8,6,15,7)(9,18,12,17,10,
21,13,19)(25,31,39,34,30,38,35,29,37,27,33,28,36)(26,32)]);
ALF("3.(3xM10):2","(3xM10):2",[1,1,2,2,3,3,4,4,5,5,6,6,6,7,7,8,8,9,9,9,10,
10,10,11,12,13,14,14,15,15,15,16,16,16,17,18,19,20,21]);
ALF("3.(3xM10):2","3.J3.2",[1,2,5,6,3,4,13,14,7,7,6,6,5,8,9,23,24,10,11,
12,25,27,26,35,36,37,3,4,15,16,16,20,22,21,36,40,38,44,45],[
"compatible with 3x(3xA6):2_2 -> 3.J3"
]);
ALN("3.(3xM10):2",["3.J3.2M5","NDG(3.J3.2,3^2)"]);

MOT("3xJ3N2",
[
"Sylow 2 normalizer in 3.J3"
],
0,
0,
0,
[
( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(16,19)(17,21)(18,20)(23,24)(26,27)(29,30)
(31,34)(32,36)(33,35)(37,40)(38,42)(39,41)(43,46)(44,48)(45,47)(50,51)(52,55)
(53,57)(54,56)
,
(16,17,18)(19,21,20)(31,33,32)(34,35,36)(37,38,39)(40,42,41)(43,45,44)
(46,47,48)(52,54,53)(55,56,57)
,
(16,19)(17,20)(18,21)(31,34)(32,35)(33,36)(37,40)(38,41)(39,42)(43,46)(44,47)
(45,48)(52,55)(53,56)(54,57)
],
["ConstructDirectProduct",[["J3N2"],["Cyclic",3]]]);
ALF("3xJ3N2","3.J3",[1,2,3,4,5,6,4,5,6,4,5,6,4,5,6,7,8,9,7,8,9,11,12,13,
11,12,13,11,12,13,20,21,22,20,21,22,20,21,22,20,21,22,20,21,22,20,21,22,
23,24,25,35,36,37,35,36,37]);
ALN("3xJ3N2",["3.J3N2"]);

MOT("3^3.3^(1+2):8",
[
"origin: Dixon's Algorithm"
],
[5832,5832,5832,243,324,324,324,27,27,27,72,72,72,36,36,36,72,72,72,36,36,36,
72,72,72,36,36,36,24,24,24,24,24,24,24,24,24,24,24,24],
[,[1,3,2,4,5,7,6,9,10,8,1,2,3,5,7,6,11,12,13,15,16,14,11,12,13,15,16,14,17,19,
18,23,24,25,17,19,18,23,24,25],[1,1,1,1,1,1,1,4,4,4,11,11,11,11,11,11,23,23,23
,23,23,23,17,17,17,17,17,17,32,32,32,29,29,29,38,38,38,35,35,35]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,
-1,-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-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)
],
[TENSOR,[2,3]],[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(8),E(8),E(8),E(8)^3,E(8)^3,
E(8)^3,-E(8),-E(8),-E(8),-E(8)^3,-E(8)^3,-E(8)^3],
[TENSOR,[5,4]],
[TENSOR,[2,5]],
[TENSOR,[2,6]],[6,6,6,6,-3,-3,-3,0,0,0,-2,-2,-2,1,1,1,2,2,2,-1,-1,-1,2,2,2,-1
,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[9,3]],
[TENSOR,[9,5]],
[TENSOR,[9,6]],[8,8,8,8,8,8,8,-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],[24,24,24,-3,0,0,0,-2*E(9)^2-E(9)^4-E(9)^5-2*E(9)^7,
E(9)^2-E(9)^4-E(9)^5+E(9)^7,E(9)^2+2*E(9)^4+2*E(9)^5+E(9)^7,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[GALOIS,[14,4]],
[GALOIS,[14,2]],[9,9*E(3)^2,9*E(3),0,-3,-3*E(3),-3*E(3)^2,0,0,0,-1,-E(3),
-E(3)^2,-1,-E(3),-E(3)^2,-E(4),-E(12)^11,-E(12)^7,-E(12)^11,-E(12)^7,-E(4),
E(4),E(12)^11,E(12)^7,E(12)^11,E(12)^7,E(4),-E(8)^3,-E(24),-E(24)^17,-E(8),
-E(24)^11,-E(24)^19,E(8)^3,E(24),E(24)^17,E(8),E(24)^11,E(24)^19],
[TENSOR,[17,2]],
[TENSOR,[17,4]],
[TENSOR,[17,3]],
[GALOIS,[17,17]],
[TENSOR,[21,2]],
[TENSOR,[21,4]],
[TENSOR,[21,3]],
[TENSOR,[17,6]],
[TENSOR,[17,8]],
[TENSOR,[21,6]],
[TENSOR,[21,8]],
[TENSOR,[17,7]],
[TENSOR,[21,7]],
[TENSOR,[17,5]],
[TENSOR,[21,5]],[18,18*E(3)^2,18*E(3),0,3,3*E(3),3*E(3)^2,0,0,0,-2,-2*E(3),
-2*E(3)^2,1,E(3),E(3)^2,2*E(4),2*E(12)^11,2*E(12)^7,-E(12)^11,-E(12)^7,-E(4),
-2*E(4),-2*E(12)^11,-2*E(12)^7,E(12)^11,E(12)^7,E(4),0,0,0,0,0,0,0,0,0,0,0,0],
[TENSOR,[33,3]],
[GALOIS,[33,5]],
[TENSOR,[35,3]],
[TENSOR,[33,6]],
[TENSOR,[35,6]],
[TENSOR,[33,5]],
[TENSOR,[35,5]]],
[( 8, 9,10),(29,35)(30,36)(31,37)(32,38)(33,39)(34,40),
(17,23)(18,24)(19,25)(20,26)(21,27)(22,28)(29,32)(30,34)(31,33)(35,38)(36,40)
(37,39)
,
( 2, 3)( 6, 7)(12,13)(15,16)(18,19)(20,21)(24,25)(26,27)(30,31)(33,34)(36,37)
(39,40)
]);
ALF("3^3.3^(1+2):8","3^2.3^(1+2):8",[1,1,1,2,3,3,3,4,5,6,7,7,7,8,8,8,9,9,
9,10,10,10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16]);
ALF("3^3.3^(1+2):8","3^3.3^(1+2):8.2",[1,2,2,3,4,5,5,6,7,8,9,10,10,11,12,
12,13,14,15,18,17,16,13,15,14,17,18,16,19,21,20,19,21,20,22,23,24,22,23,
24]);
ALF("3^3.3^(1+2):8","3.J3",[1,2,3,10,7,9,8,26,27,28,4,6,5,20,22,21,11,12,
13,36,37,35,11,12,13,36,37,35,23,24,25,23,25,24,23,24,25,23,25,24],[
"fusion map is unique up to table automorphisms"
]);
ALN("3^3.3^(1+2):8",["3.J3N3"]);

MOT("3^3.3^(1+2):8.2",
[
"origin: Dixon's Algorithm"
],
[11664,5832,486,648,324,54,54,54,144,72,72,36,72,72,72,36,36,36,24,24,24,24,24
,24,36,12,18,12,12,18,18,18],
[,[1,2,3,4,5,7,8,6,1,2,4,5,9,10,10,11,12,12,13,14,15,13,15,14,1,9,3,11,11,7,8,
6],[1,1,1,1,1,3,3,3,9,9,9,9,13,13,13,13,13,13,19,19,19,22,22,22,25,26,25,26,26
,27,27,27]],
[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1],
[TENSOR,[1,1]],[2,2,2,2,2,2,2,2,-2,-2,-2,-2,0,0,0,0,0,0,-E(8)-E(8)^3,
-E(8)-E(8)^3,-E(8)-E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,E(8)+E(8)^3,0,0,0,0,0,0,0,0]
,
[GALOIS,[3,5]],[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],[12,12,12,-6,-6,0,0,0,4,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,
-1],
[TENSOR,[1,7]],[6,6,6,-3,-3,0,0,0,-2,-2,1,1,2,2,2,-1,-1,-1,0,0,0,0,0,0,0,2,0,
-1,-1,0,0,0],
[TENSOR,[9,1]],[6,6,6,-3,-3,0,0,0,-2,-2,1,1,-2,-2,-2,1,1,1,0,0,0,0,0,0,0,0,0,
-E(3)+E(3)^2,E(3)-E(3)^2,0,0,0],
[TENSOR,[11,1]],[24,24,-3,0,0,E(9)^2+2*E(9)^4+2*E(9)^5+E(9)^7,
-2*E(9)^2-E(9)^4-E(9)^5-2*E(9)^7,E(9)^2-E(9)^4-E(9)^5+E(9)^7,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,2,0,-1,0,0,E(9)^2+E(9)^7,E(9)^4+E(9)^5,
-E(9)^2-E(9)^4-E(9)^5-E(9)^7],
[TENSOR,[13,1]],
[GALOIS,[13,4]],
[TENSOR,[15,1]],[8,8,8,8,8,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,0,-2,0
,0,1,1,1],
[TENSOR,[17,1]],
[GALOIS,[14,2]],
[TENSOR,[19,1]],[18,-9,0,-6,3,0,0,0,2,-1,2,-1,2,-1,-1,2,-1,-1,2,-1,-1,2,-1,-1
,0,0,0,0,0,0,0,0],
[TENSOR,[21,7]],[18,-9,0,-6,3,0,0,0,-2,1,-2,1,0,E(12)^7-E(12)^11,
-E(12)^7+E(12)^11,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,-E(8)-E(8)^3,
-E(24)^17-E(24)^19,-E(24)-E(24)^11,E(8)+E(8)^3,E(24)+E(24)^11,
E(24)^17+E(24)^19,0,0,0,0,0,0,0,0],
[TENSOR,[23,7]],
[GALOIS,[23,17]],
[TENSOR,[25,7]],[18,-9,0,-6,3,0,0,0,2,-1,2,-1,-2,1,1,-2,1,1,0,
-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,E(12)^7-E(12)^11,-E(12)^7+E(12)^11,0,0,0,
0,0,0,0,0],
[TENSOR,[27,7]],[36,-18,0,6,-3,0,0,0,4,-2,-2,1,-4,2,2,2,-1,-1,0,0,0,0,0,0,0,0
,0,0,0,0,0,0],[36,-18,0,6,-3,0,0,0,4,-2,-2,1,4,-2,-2,-2,1,1,0,0,0,0,0,0,0,0,0,
0,0,0,0,0],[36,-18,0,6,-3,0,0,0,-4,2,2,-1,0,-2*E(12)^7+2*E(12)^11,
2*E(12)^7-2*E(12)^11,0,-E(12)^7+E(12)^11,E(12)^7-E(12)^11,0,0,0,0,0,0,0,0,0,0,
0,0,0,0],
[GALOIS,[31,5]]],
[(28,29),( 6, 7, 8)(30,31,32),(19,22)(20,24)(21,23),
(14,15)(17,18)(20,21)(23,24)]);
ALF("3^3.3^(1+2):8.2","3^2.3^(1+2):8.2",[1,1,2,3,3,4,5,6,7,7,8,8,9,9,9,
10,10,10,11,11,11,12,12,12,13,14,15,16,17,18,19,20]);
ALF("3^3.3^(1+2):8.2","3.J3.2",[1,2,7,5,6,17,18,19,3,4,13,14,8,9,9,23,
24,24,15,16,16,15,16,16,35,36,37,40,40,41,42,43]);
ALN("3^3.3^(1+2):8.2",["3.J3.2M6","3.J3.2N3"]);

MOT("3.McL.2N5",
[
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[18000,9000,720,360,360,180,144,72,144,72,4500,2250,150,75,360,180,24,24,24,24
,24,24,180,90,72,36,72,36,90,90,90,90,90,90,40,40,24,24,10,20,20,24,24,24,24],
[,[1,2,1,2,5,6,3,4,3,4,11,12,13,14,5,6,7,8,8,9,10,10,11,12,15,16,15,16,29,31,
30,29,31,30,1,3,9,7,13,23,23,25,27,25,27],[1,1,3,3,1,1,9,9,7,7,11,11,13,13,3,3
,20,20,20,17,17,17,23,23,9,9,7,7,11,11,11,23,23,23,35,36,38,37,39,40,41,37,38,
37,38],,[1,2,3,4,5,6,7,8,9,10,1,2,1,2,15,16,17,18,19,20,21,22,3,4,25,26,27,28,
5,6,6,15,16,16,35,36,37,38,35,36,36,42,43,44,45]],
0,
[(40,41),(30,31)(33,34),(18,19)(21,22),(42,44)(43,45),
( 7, 9)( 8,10)(17,20)(18,21)(19,22)(25,27)(26,28)(37,38)(42,45)(43,44)],
["ConstructMGA","3x5^(1+2):3:8","5^(1+2):(24:2)",[[2,6],[3,5],[8,9],[11,12],
[14,15],[17,18],[20,24],[21,23],[26,27],[29,30],[32,33],[35,36],[38,42],[39,
41],[44,45],[47,51],[48,50],[53,54],[56,57]],()]);
ALF("3.McL.2N5","5^(1+2):(24:2)",[1,1,2,2,4,4,5,5,6,6,8,8,9,9,10,10,13,13,
13,14,14,14,15,15,18,18,17,17,19,19,19,26,26,26,3,7,11,12,16,20,21,22,23,
24,25]);
ALF("3.McL.2N5","3.McL.2",[1,2,3,4,5,6,8,9,8,9,10,11,12,13,14,15,21,22,22,
21,22,22,24,25,30,31,30,31,35,36,37,38,39,40,41,42,44,44,46,49,50,53,53,
54,54]);

MOT("3xMcLN2",
[
"Sylow 2 normalizer in 3.McL"
],
0,
0,
0,
[
(10,13)(11,14)(12,15)(16,22)(17,23)(18,24)(28,37)(29,38)(30,39)(43,46)(44,47)
(45,48)
,
( 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)
],
["ConstructDirectProduct",[["McLN2"],["Cyclic",3]]]);
ALF("3xMcLN2","3.McL",[1,2,3,4,5,6,4,5,6,4,5,6,4,5,6,4,5,6,4,5,6,4,5,6,11,
12,13,11,12,13,11,12,13,11,12,13,11,12,13,11,12,13,11,12,13,11,12,13,32,
33,34],[
"fusion map is unique up to table automorphisms"
]);
ALF("3xMcLN2","(3xMcLN2).2",[1,2,2,3,4,4,5,6,6,7,8,9,7,9,8,10,11,12,13,14,
14,10,12,11,15,16,16,17,18,19,20,21,21,22,23,23,17,19,18,24,25,25,26,27,
28,26,28,27,29,30,30]);
ALF("3xMcLN2","2^4:D8",[1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,8,8,8,6,6,6,7,7,7,9,
9,9,12,12,12,10,10,10,13,13,13,11,11,11,14,14,14,16,16,16,15,15,15,17,17,
17]);
ALF("3xMcLN2","3.M22",[1,2,3,4,5,6,4,5,6,4,5,6,4,5,6,4,5,6,4,5,6,4,5,6,8,
9,10,11,12,13,8,9,10,11,12,13,11,12,13,8,9,10,11,12,13,8,9,10,26,27,28],[
"determined using the fusion 2^4:D8 -> M22"
]);
ALN("3xMcLN2",["3.M22N2","3.McLN2"]);

MOT("(3xMcLN2).2",
[
"normalizer of a 2-defect group of order 2^7 in Ly,\n",
"constructed using `PossibleCharacterTablesOfTypeMGA'"
],
[768,384,768,384,384,192,96,96,96,48,48,48,96,48,192,96,48,48,48,96,48,96,48,
96,48,24,24,24,48,24,16,32,32,16,32,32,16,16,8],
[,[1,2,1,2,1,2,1,2,2,1,2,2,1,2,3,4,5,6,6,3,4,3,4,5,6,7,8,9,15,16,15,1,3,1,15,
15,24,24,22],[1,1,3,3,5,5,7,7,7,10,10,10,13,13,15,15,17,17,17,20,20,22,22,24,
24,26,26,26,29,29,31,32,33,34,35,36,37,38,39]],
0,
[(37,38),( 8, 9)(11,12)(18,19)(27,28)(37,38)],
["ConstructMGA","3xMcLN2","LyN2",[[2,21],[3,20],[5,6],[8,15],[9,14],[11,12],
--> --------------------

--> maximum size reached

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