Finite Group Databasebeta

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C₂²×#46364 #72295935

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

Aliases

Subgroups

111429 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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