Finite Group Databasebeta

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C₂²×#35062 #72326043

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

Aliases

Subgroups

117421 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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((6,8)(18,21)(19,23), (9,10)(11,15)(12,13)(14,16)(17,18)(19,22)(20,21)(23,24), (5,6)(7,8)(10,12)(11,16)(17,18)(19,24)(20,21)(22,23), (3,4), (5,6)(7,8)(9,11)(10,14)(12,15)(13,16)(17,19,20,23)(18,22,21,24), (1,2)(3,4), (5,6)(7,8)(9,12,13,10)(11,15,16,14)(17,18)(19,24)(20,21)(22,23));