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C₂×#20837 #6371254

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

Aliases

Subgroups

5750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278450);