Finite Group Databasebeta

?

← Prev (#72330072) Next (#72330074) →

C₂²×#1082743 #72330073

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

Aliases

Subgroups

At least 8565 conjugacy classes of subgroups; only the 44704 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 24 points:

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

Conjugacy classes & character table

344 conjugacy classes. The character table is too large to display.

Relationships

GAP

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

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