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Aliases
Splittings
Subgroups
6566 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 6 generators on 81 points:
(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)(67,72)(71,74)(73,77)(80,81);(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)(51,57)(55,64)(56,60)(63,65)(66,69,70,79)(67,73,72,77)(68,76,75,78)(71,80,74,81);(50,53,54,62)(51,56,57,60)(52,58,59,61)(55,63,64,65)(67,72)(68,75)(73,77)(76,78);(50,52,54,59)(51,55,57,64)(53,61,62,58)(56,65,60,63)(66,68,70,75)(67,71,72,74)(69,78,79,76)(73,81,77,80);(50,51)(52,55)(53,60)(54,57)(56,62)(58,65)(59,64)(61,63)(66,67)(68,74)(69,77)(70,72)(71,75)(73,79)(76,80)(78,81);(48,49)
Conjugacy classes & character table
1226 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1077334);
Finite Group Databasebeta