Finite Group Databasebeta

?

← Prev (#72325838) Next (#72325840) →

C₂²×#34185 #72325839

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

Aliases

Subgroups

111277 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

352 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((5,6,8,7)(9,10,12,13)(11,15,16,14)(18,21)(19,23), (5,7,8,6)(9,10,12,13)(11,15,16,14)(17,18)(19,24)(20,21)(22,23), (10,13)(14,15), (3,4), (1,2)(3,4), (9,11)(10,14)(12,16)(13,15), (9,10)(11,14)(12,13)(15,16)(17,19)(18,22)(20,23)(21,24));