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C₂²×#14366 #72296848

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

Aliases

Subgroups

141253 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

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