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Aliases
Subgroups
912 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)(40,47)(41,44)(42,50)(43,46)(45,51)(48,52)(49,53)(54,55,60,63)(56,58,61,57)(59,67,68,62)(64,65,69,66);(38,40,43,41)(39,44,46,47)(42,48,51,49)(45,52,50,53)(54,56,60,61)(55,57,63,58)(59,64,68,69)(62,65,67,66);(38,41,43,40)(39,44,46,47)(42,49,51,48)(45,52,50,53)(54,57,60,58)(55,61,63,56)(59,65,68,66)(62,69,67,64);(38,39)(40,47)(41,44)(42,45)(43,46)(48,53)(49,52)(50,51)(54,58,60,57)(55,56,63,61)(59,66,68,65)(62,64,67,69);(38,42)(39,45)(40,48)(41,49)(43,51)(44,52)(46,50)(47,53)(54,59)(55,62)(56,64)(57,65)(58,66)(60,68)(61,69)(63,67)
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, 2295);
Finite Group Databasebeta