Finite Group Databasebeta

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C₂²×#38358 #72278445

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

Aliases

Subgroups

119929 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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