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C₂²×#9659 #72319919

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

Aliases

Subgroups

11813 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

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