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Aliases
Splittings
Subgroups
6694 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 6 generators on 81 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)(51,57)(55,58)(56,63)(62,64)(66,69,70,76)(67,73,72,79)(68,75,74,80)(71,78,77,81);(52,60)(55,58)(59,65)(62,64)(67,72)(71,77)(73,79)(78,81);(50,53,54,61)(51,56,57,63)(52,59,60,65)(55,62,58,64)(67,72)(68,74)(73,79)(75,80);(50,52)(51,55)(53,59)(54,60)(56,62)(57,58)(61,65)(63,64)(66,68)(67,71)(69,75)(70,74)(72,77)(73,78)(76,80)(79,81);(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)(50,51)(52,58)(53,56)(54,57)(55,60)(59,64)(61,63)(62,65)(66,67)(68,71)(69,73)(70,72)(74,77)(75,78)(76,79)(80,81);(48,49)
Conjugacy classes & character table
1364 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1077104);
Finite Group Databasebeta