Finite Group Databasebeta

?

← Prev (#6442575) Next (#6442577) →

C₂×#24281 #6442576

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

Aliases

Subgroups

5596 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6349772);