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C₂²×#41932 #72296530

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

Aliases

Subgroups

120305 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 24 points:

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

Conjugacy classes & character table

208 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((11,15)(14,16)(18,20)(22,23), (6,7)(17,18)(19,23)(20,21)(22,24), (5,6,8,7)(10,13)(11,15)(18,20)(22,23), (5,6,8,7)(9,10)(11,16)(12,13)(14,15)(17,19,21,24)(18,22,20,23), (5,7,8,6)(9,11,12,15)(10,14,13,16)(17,20,21,18)(19,23,24,22), (3,4), (1,2)(3,4));