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C₂²×#16516 #72321593

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

Aliases

Subgroups

63301 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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), (5,6,8,7)(10,12)(14,16)(19,23)(22,24), (5,6,8,7)(10,12)(13,14)(15,16)(18,21)(22,24), (6,7)(9,10)(11,12)(17,18)(19,22)(20,21)(23,24), (1,2)(3,4), (5,7,8,6)(9,10)(11,12)(17,19,20,23)(18,22,21,24));