Finite Group Databasebeta

?

← Prev (#7625323) Next (#7625325) →

C₄×#3449 #7625324

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

Aliases

Subgroups

11494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532520);