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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 68 points:
(1,2,3)(4,5)(6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68);(4,6,5,7)(9,68)(10,67)(11,66)(12,65)(13,64)(14,63)(15,62)(16,61)(17,60)(18,59)(19,58)(20,57)(21,56)(22,55)(23,54)(24,53)(25,52)(26,51)(27,50)(28,49)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,39)
Conjugacy classes & character table
192 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(732, 4);
Finite Group Databasebeta