Finite Group Databasebeta

?

← Prev (#72296077) Next (#72296079) →

C₂²×#7642244 #72296078

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

Aliases

Subgroups

3503928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 24 points:

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

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