Finite Group Databasebeta

?

← Prev (#7622567) Next (#7622569) →

C₂²×#2169 #7622568

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

Aliases

Subgroups

2214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529764);