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C₂×#12613 #492969

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

Aliases

Subgroups

1080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400165);