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C₂²×#14812 #72337052

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

Aliases

Subgroups

79533 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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