Finite Group Databasebeta

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C₂²×#35226 #72295693

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

Aliases

Subgroups

114933 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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