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Aliases
Splittings
Subgroups
2286 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 81 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(58,60,61,64)(59,63,62,65)(69,77)(72,79)(75,81)(78,80);(55,57)(59,62)(63,65)(66,69,70,77)(67,72,73,79)(68,75,76,81)(71,78,74,80);(54,55)(56,57)(66,68,70,76)(67,71,73,74)(69,75,77,81)(72,78,79,80);(58,59)(60,63)(61,62)(64,65)(66,67,70,73)(68,74,76,71)(69,72,77,79)(75,80,81,78);(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)
Conjugacy classes & character table
896 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 336493);
Finite Group Databasebeta