Finite Group Databasebeta

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C₂²×#11041 #72303207

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

Aliases

Subgroups

43749 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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