Finite Group Databasebeta

?

← Prev (#7625338) Next (#7625340) →

C₂²×#2356 #7625339

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

Aliases

Subgroups

9314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

(1,2);(3,4);(5,6,7,8)(9,10,13,12)(11,14,16,15)(19,23)(21,24);(10,12)(14,15)(17,18,20,22)(19,21,23,24);(9,11,13,16)(10,14,12,15)(17,19,20,23)(18,21,22,24);(9,12,13,10)(11,15,16,14)

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532535);