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C₂×#13648 #512748

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

Aliases

Subgroups

422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 419944);