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C₂²×#14731 #72337050

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

Aliases

Subgroups

78181 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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