Finite Group Databasebeta

?

← Prev (#72296094) Next (#72296096) →

C₂²×#4307938 #72296095

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

Aliases

Subgroups

2911056 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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