Finite Group Databasebeta

?

← Prev (#7633462) Next (#7633464) →

C₂²×#2706 #7633463

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

Aliases

Subgroups

11942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540659);