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Aliases
Splittings
Subgroups
7142 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 6 generators on 73 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(50,52,53,56)(51,55,54,57)(59,65)(63,66)(64,71)(70,72);(60,68)(63,66)(67,73)(70,72);(51,54)(55,57)(58,61,62,69)(59,64,65,71)(60,67,68,73)(63,70,66,72);(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)(58,60)(59,63)(61,67)(62,68)(64,70)(65,66)(69,73)(71,72);(50,51)(52,55)(53,54)(56,57)(58,59,62,65)(60,66,68,63)(61,64,69,71)(67,72,73,70);(48,49)
Conjugacy classes & character table
1376 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1077672);
Finite Group Databasebeta