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C₂×#13556 #512554

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

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, 419750);