Finite Group Databasebeta

?

← Prev (#607711) Next (#607713) →

C₂×#14776 #607712

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

Aliases

Subgroups

8570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 514908);