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Aliases
Splittings
Subgroups
59186 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 7 generators on 87 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)(48,49)(50,51)(52,53)(57,65)(62,66)(63,77)(64,79)(74,80)(75,81)(76,78)(86,87);(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)(58,69)(62,66)(67,83)(68,85)(74,80)(75,81)(82,84)(86,87);(56,60,61,73)(57,64,65,79)(58,68,69,85)(59,70,71,72)(62,75,66,81)(63,76,77,78)(67,82,83,84)(74,86,80,87);(56,59,61,71)(57,63,65,77)(58,67,69,83)(60,72,73,70)(62,74,66,80)(64,78,79,76)(68,84,85,82)(75,87,81,86);(56,58)(57,62)(59,67)(60,68)(61,69)(63,74)(64,75)(65,66)(70,82)(71,83)(72,84)(73,85)(76,86)(77,80)(78,87)(79,81);(56,57)(58,66)(59,63)(60,64)(61,65)(62,69)(67,80)(68,81)(70,76)(71,77)(72,78)(73,79)(74,83)(75,85)(82,87)(84,86);(54,55)
Conjugacy classes & character table
1898 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1083467);
Finite Group Databasebeta