Finite Group Databasebeta

?

← Prev (#7705485) Next (#7705487) →

C₂×#49558 #7705486

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

Aliases

Subgroups

9054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7612682);