Finite Group Databasebeta

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C₂²×#14926 #72321291

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

Aliases

Subgroups

117237 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

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