Finite Group Databasebeta

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C₂²×#35050 #72279234

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

Aliases

Subgroups

208989 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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