Finite Group Databasebeta

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C₂²×#47853 #72295948

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

Aliases

Subgroups

111109 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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((3,4), (5,6)(7,8)(17,18)(19,24)(20,22)(21,23), (9,10,13,14)(11,15,16,12)(17,18,21,23)(19,22,20,24), (6,8)(10,14)(12,15)(17,19,21,20)(18,22,23,24), (9,11)(10,12)(13,16)(14,15)(17,20,21,19)(18,22,23,24), (5,6)(7,8)(9,12)(10,11)(13,15)(14,16)(17,18)(19,22)(20,24)(21,23), (1,2)(3,4));