Finite Group Databasebeta

?

← Prev (#7633460) Next (#7633462) →

C₂²×#2700 #7633461

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

Aliases

Subgroups

10694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540657);