Finite Group Databasebeta

?

← Prev (#72337201) Next (#72337203) →

C₂²×#7652921 #72337202

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

Aliases

Subgroups

1624424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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