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C₂×#21394 #6372388

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

Aliases

Subgroups

4034 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2);(4,6)(7,8)(9,12)(10,11)(13,14)(15,16,19,20,18,21,17,22);(3,4,5,6)(16,20)(17,19)(21,22);(8,11)(12,14)(16,21)(20,22);(7,9,10,13)(8,12,11,14)(16,21)(20,22)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279584);