Finite Group Databasebeta

?

← Prev (#72320847) Next (#72320849) →

C₂²×#4307962 #72320848

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

Aliases

Subgroups

848648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

416 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((3,4), (9,10,11,12)(17,18,21,23)(19,20,24,22), (5,6)(7,8)(13,14,15,16)(17,19)(18,22)(20,23)(21,24), (6,8)(9,10)(11,12)(13,14)(15,16)(17,20,21,22)(18,19,23,24), (1,2)(3,4), (17,19)(18,20)(21,24)(22,23), (5,6)(7,8)(17,19)(18,20)(21,24)(22,23));