Finite Group Databasebeta

?

← Prev (#72284750) Next (#72284752) →

C₂²×#12966 #72284751

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

Aliases

Subgroups

11617 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

136 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((5,6,7,8)(10,14)(11,20)(16,23)(17,24)(18,19)(21,22), (1,2)(3,4)(9,10,15,18)(11,17,22,24)(12,19,13,14)(16,20,23,21), (1,2)(3,4)(10,16,18,24)(11,20,21,22)(12,15)(14,17,19,23), (1,2), (3,4));