Finite Group Databasebeta

?

← Prev (#72296789) Next (#72296791) →

C₂²×#43102 #72296790

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

Aliases

Subgroups

116357 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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