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C₂×#13620 #512694

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

Aliases

Subgroups

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 419890);