Finite Group Databasebeta

?

← Prev (#72300972) Next (#72300974) →

C₂²×#37722 #72300973

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

Aliases

Subgroups

115833 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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