Finite Group Databasebeta

?

← Prev (#72326044) Next (#72326046) →

C₂²×#37185 #72326045

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

Aliases

Subgroups

111301 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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((6,8)(9,10)(11,15)(12,13)(14,16)(17,18)(19,23)(20,21)(22,24), (6,8)(11,16)(14,15)(18,20)(19,24), (5,6)(7,8)(10,12)(11,16)(17,19)(18,22)(20,23)(21,24), (3,4), (5,6)(7,8)(9,11)(10,14)(12,15)(13,16)(17,20,21,18)(19,22,24,23), (1,2)(3,4), (5,6)(7,8)(9,12,13,10)(11,15,16,14)(17,19)(18,22)(20,23)(21,24));