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Aliases
Subgroups
890 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)(38,39,43,41)(40,46,48,44)(42,49,50,45)(47,51,53,52)(54,55,59,63)(56,61,57,60)(58,66,67,62)(64,68,65,69);(38,40,43,48)(39,44,41,46)(42,47,50,53)(45,51,49,52)(54,55)(56,61)(57,60)(58,62)(59,63)(64,69)(65,68)(66,67);(54,56,59,57)(55,60,63,61)(58,64,67,65)(62,68,66,69);(38,41,43,39)(40,44,48,46)(42,49,50,45)(47,51,53,52)(54,57,59,56)(55,61,63,60)(58,65,67,64)(62,69,66,68);(38,42,43,50)(39,45,41,49)(40,47,48,53)(44,51,46,52)(54,58,59,67)(55,62,63,66)(56,64,57,65)(60,68,61,69)
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, 2288);
Finite Group Databasebeta