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C₂×#12916 #494226

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

Aliases

Subgroups

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401422);