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Aliases
Subgroups
958 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 69 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,43,45)(40,49,53,51)(41,44,48,54)(42,56,57,47)(46,60,59,50)(52,65,66,63)(55,67,62,58)(61,64,68,69);(39,45)(40,50)(41,48)(46,51)(47,56)(49,59)(52,64)(53,60)(55,62)(61,65)(63,68)(66,69);(38,40,43,53)(39,46,45,59)(41,51,48,49)(42,52,57,66)(44,50,54,60)(47,61,56,68)(55,65,62,63)(58,64,67,69);(38,41,54,39)(40,51,60,46)(42,55,67,47)(43,48,44,45)(49,50,59,53)(52,65,69,61)(56,57,62,58)(63,64,68,66);(38,42,54,67)(39,47,41,55)(40,52,60,69)(43,57,44,58)(45,56,48,62)(46,61,51,65)(49,63,59,68)(50,64,53,66)
Conjugacy classes & character table
1406 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4736, 2300);
Finite Group Databasebeta