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C₂²×#15227 #72334747

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

Aliases

Subgroups

120373 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)(13,14,15,16)(19,23)(22,24);(6,7)(14,16)(18,21)(19,23);(10,11)(13,14,15,16)(17,18,20,21)(19,24,23,22);(5,7,8,6)(9,11,12,10)(13,14)(15,16)(17,19,20,23)(18,22,21,24);(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((5,6)(7,8)(9,10,12,11)(13,14,15,16)(19,23)(22,24), (6,7)(14,16)(18,21)(19,23), (10,11)(13,14,15,16)(17,18,20,21)(19,24,23,22), (5,7,8,6)(9,11,12,10)(13,14)(15,16)(17,19,20,23)(18,22,21,24), (3,4), (1,2)(3,4));