Finite Group Databasebeta

?

← Prev (#72291313) Next (#72291315) →

C₂⁴×#2404 #72291314

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

Aliases

Subgroups

8085096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

608 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((17,18)(19,21)(20,22)(23,24), (13,14)(15,16)(17,18,20,22)(19,23,24,21), (10,12)(14,16)(17,18)(19,23)(20,22)(21,24), (3,4), (9,10)(11,12)(13,14)(15,16)(17,19,20,24)(18,21,22,23), (5,6), (7,8), (1,2)(3,4)(5,6)(7,8));