Finite Group Databasebeta

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C₂²×#14257 #72337037

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

Aliases

Subgroups

97285 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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