Finite Group Databasebeta

?

← Prev (#72292907) Next (#72292909) →

C₂²×#35232 #72292908

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

Aliases

Subgroups

110869 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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)(10,13)(11,15)(17,18,21,22)(19,24,20,23), (3,4), (5,6,7,8)(10,13)(14,16)(18,22)(19,20), (17,18)(19,23)(20,24)(21,22), (1,2)(3,4), (9,10)(11,14)(12,13)(15,16)(17,19,21,20)(18,23,22,24), (9,11,12,15)(10,14,13,16)(17,20,21,19)(18,24,22,23));