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C₂×#20918 #6371395

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

Aliases

Subgroups

6222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(8,12,14,17)(9,15,16,18);(3,4,5,6)(7,8,10,17,11,14,19,12)(9,13,18,22,16,21,15,20);(7,9)(8,13)(10,18)(11,16)(12,20)(14,21)(15,19)(17,22);(8,14)(12,17)(13,21)(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, 6278591);