Finite Group Databasebeta

?

← Prev (#7633484) Next (#7633486) →

C₂²×#2712 #7633485

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

Aliases

Subgroups

12058 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540681);