Finite Group Databasebeta

?

← Prev (#72326006) Next (#72326008) →

C₂²×#43005 #72326007

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

Aliases

Subgroups

111493 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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