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C₂×#3353 #61246

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

Aliases

Subgroups

1041 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

(1,2);(3,4,7,6)(5,9,10,8)(11,12)(13,16)(14,17)(15,18);(3,5)(4,8)(6,9)(7,10)(11,13,15,14)(12,16,18,17);(3,6,7,4)(5,9,10,8)(12,17)(13,14)(16,18);(5,10)(8,9)(12,18)(16,17)

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54234);