Finite Group Databasebeta

?

← Prev (#7627699) Next (#7627701) →

C₂²×#2399 #7627700

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

Aliases

Subgroups

10434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7534896);