Finite Group Databasebeta

?

← Prev (#72296101) Next (#72296103) →

C₂²×#845309 #72296102

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

Aliases

Subgroups

2854348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

368 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)(17,18)(19,21)(20,23)(22,24), (5,6,7,8)(9,10,11,12)(13,14)(15,16)(17,19,20,24)(18,21,23,22), (6,8)(10,12)(17,19,20,24)(18,21,23,22), (9,10)(11,12)(17,19)(18,22)(20,24)(21,23), (5,6)(7,8)(9,10)(11,12)(17,18)(19,22)(20,23)(21,24), (3,4), (1,2)(3,4));