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C₂×#13034 #494552

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

Aliases

Subgroups

1286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401748);