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C₂×#12841 #493823

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

Aliases

Subgroups

944 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401019);