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C₂²×#15283 #72291891

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

Aliases

Subgroups

172901 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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)(18,19)(22,23), (10,12)(14,15)(17,18,21,19)(20,22,24,23), (13,14,16,15)(17,19,21,18)(20,23,24,22), (5,6,7,8)(9,10,11,12)(13,15,16,14)(17,20,21,24)(18,22,19,23), (3,4), (1,2)(3,4));