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C₂²×#51899 #72292884

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

Aliases

Subgroups

109017 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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