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C₂²×#11006 #72315061

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

Aliases

Subgroups

49237 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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((9,10,12,17)(11,16,13,22)(14,19,21,24)(15,23,18,20), (6,8)(10,15)(11,20)(13,23)(16,19)(17,18)(22,24), (1,2), (5,6)(7,8)(10,15)(11,20)(12,21)(16,19)(17,22)(18,24), (3,4));