Finite Group Databasebeta

?

← Prev (#7628029) Next (#7628031) →

C₂²×#2599 #7628030

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

Aliases

Subgroups

10362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535226);