Finite Group Databasebeta

?

← Prev (#72314761) Next (#72314763) →

C₂²×#11034 #72314762

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

Aliases

Subgroups

46837 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

184 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)(9,10)(11,19,22,24)(12,17)(13,15)(14,18)(16,21,23,20), (5,6)(7,8)(10,15)(11,20)(12,13)(16,23)(17,18)(21,22), (5,6)(7,8)(9,11,14,22)(10,16,18,23)(12,20,13,21)(15,19,17,24), (1,2), (3,4));