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C₂²×#38900 #72279209

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

Aliases

Subgroups

112133 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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