Finite Group Databasebeta

?

← Prev (#72325920) Next (#72325922) →

C₂²×#34991 #72325921

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

Aliases

Subgroups

110341 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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