Finite Group Databasebeta

?

← Prev (#72326015) Next (#72326017) →

C₂²×#45443 #72326016

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

Aliases

Subgroups

110613 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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