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C₂×#13551 #512547

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

Aliases

Subgroups

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 419743);