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C₂×#12746 #493544

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 66 points:

(1,2);(3,4,8,15,10,14,9,32)(5,16,20,45,19,46,33,41)(6,21,23,40,24,12,31,39)(7,25,28,43,30,57,29,13)(11,26,35,52,37,59,36,18)(17,44,49,66,48,62,50,65)(22,54,56,42,27,60,61,38)(34,55,63,47,53,58,64,51);(3,5)(4,11)(6,17)(7,26)(8,20)(9,33)(10,19)(12,34)(13,41)(14,37)(15,35)(16,25)(18,29)(21,53)(22,55)(23,49)(24,48)(27,58)(28,52)(30,59)(31,50)(32,36)(38,65)(39,63)(40,64)(42,66)(43,45)(44,54)(46,57)(47,56)(51,61)(60,62);(3,6)(4,12)(5,17)(7,27)(8,31)(9,23)(10,24)(11,34)(13,42)(14,21)(15,40)(16,44)(18,51)(19,48)(20,50)(22,30)(25,54)(26,58)(28,56)(29,61)(32,39)(33,49)(35,64)(36,63)(37,53)(38,43)(41,66)(45,65)(46,62)(47,52)(55,59)(57,60)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400740);