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C₂×#13643 #512735

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

Aliases

Subgroups

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 419931);