Finite Group Databasebeta

?

← Prev (#7633470) Next (#7633472) →

C₂²×#2715 #7633471

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

Aliases

Subgroups

10374 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)(18,21)(22,23);(6,8)(10,13)(14,16)(17,18,20,21)(19,23,24,22);(5,6)(7,8)(9,10,12,13)(11,14,15,16)(17,18)(19,22)(20,21)(23,24);(9,11)(10,14)(12,15)(13,16)(17,19,20,24)(18,22,21,23)

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, 7540667);