Finite Group Databasebeta

?

← Prev (#6444422) Next (#6444424) →

C₂×#26230 #6444423

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

Aliases

Subgroups

3226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6351619);