Finite Group Databasebeta

?

← Prev (#6372648) Next (#6372650) →

C₄×#3008 #6372649

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

Aliases

Subgroups

5000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279845);