Finite Group Databasebeta

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C₂²×#35367 #72296005

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

Aliases

Subgroups

202845 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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