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C₂×#13126 #494839

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

Aliases

Subgroups

742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402035);