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C₂²×#37660 #72236633

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

Aliases

Subgroups

203701 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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