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C₂×#12878 #493926

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

Aliases

Subgroups

978 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401122);