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Aliases
Splittings
Subgroups
2370 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)(60,64)(62,65)(66,69,70,76)(67,73,71,79)(68,74,75,77)(72,80,78,81);(55,57)(59,63)(62,65)(66,68,70,75)(67,72,71,78)(69,77,76,74)(73,81,79,80);(54,55)(56,57)(58,60)(59,62)(61,64)(63,65)(67,71)(69,76)(72,78)(74,77);(58,59,61,63)(60,62,64,65)(66,67)(68,72)(69,73)(70,71)(74,80)(75,78)(76,79)(77,81);(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)(48,49)(50,51)(52,53)
Conjugacy classes & character table
728 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 376127);
Finite Group Databasebeta