Finite Group Databasebeta

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C₂²×#35395 #72291828

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

Aliases

Subgroups

118677 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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