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C₂×#1425 #13635

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

Aliases

Subgroups

91 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 66 points:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6623);