Finite Group Databasebeta

?

← Prev (#72254137) Next (#72254139) →

A₄×#2112 #72254138

• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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