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Aliases
Subgroups
930 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)(40,45)(41,46)(42,50)(43,44)(47,51)(48,49)(52,53)(55,59)(56,62)(57,65)(67,69);(39,44)(41,45)(47,50)(49,52)(54,55,58,59)(56,63,62,60)(57,61,65,66)(64,69,68,67);(38,40,43,46)(39,45,44,41)(42,48,51,53)(47,52,50,49)(54,55)(56,60)(57,61)(58,59)(62,63)(64,67)(65,66)(68,69);(38,41,43,45)(39,46,44,40)(42,49,51,52)(47,53,50,48)(54,56,58,62)(55,60,59,63)(57,64,65,68)(61,67,66,69);(38,42,43,51)(39,47,44,50)(40,48,46,53)(41,49,45,52)(54,57,58,65)(55,61,59,66)(56,64,62,68)(60,67,63,69)
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, 2289);
Finite Group Databasebeta