Finite Group Databasebeta

?

← Prev (#61428) Next (#61430) →

Q₁₆×#41 #61429

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

Aliases

Subgroups

913 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54417);