Finite Group Databasebeta

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C₂²×#37692 #72326241

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

Aliases

Subgroups

110921 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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)(9,10,12,13)(11,15,16,14)(17,18,20,22)(19,23,24,21), (5,6)(7,8)(17,19)(18,21)(20,24)(22,23), (3,4), (5,6,7,8)(10,13)(11,16)(19,24)(21,23), (1,2)(3,4), (5,6)(7,8)(9,10)(11,15)(12,13)(14,16)(17,19)(18,21)(20,24)(22,23), (5,6)(7,8)(9,11)(10,14)(12,16)(13,15)(17,18)(19,21)(20,22)(23,24));