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C₂×#23174 #6382726

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

Aliases

Subgroups

3482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6289922);