Finite Group Databasebeta

?

← Prev (#493231) Next (#493233) →

C₄×#2177 #493232

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

Aliases

Subgroups

876 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400428);