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C₂²×#13886 #72337051

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

Aliases

Subgroups

80477 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

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