Finite Group Databasebeta

?

← Prev (#72300980) Next (#72300982) →

C₂²×#38026 #72300981

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

Aliases

Subgroups

115469 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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