Finite Group Databasebeta

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C₂²×#43038 #72301096

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

Aliases

Subgroups

101165 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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