Finite Group Databasebeta

?

← Prev (#72296522) Next (#72296524) →

C₂²×#39412 #72296523

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

Aliases

Subgroups

111897 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

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