Finite Group Databasebeta

?

← Prev (#6372652) Next (#6372654) →

C₄×#3012 #6372653

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

Aliases

Subgroups

4896 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)(11,16)(12,17)(13,22)(14,18)(15,19)(20,23)(21,24);(9,11)(10,15)(12,19)(13,21)(14,20)(16,22)(17,23)(18,24);(6,8)(9,11)(10,16)(12,21)(13,19)(14,20)(15,22)(17,24)(18,23);(9,12,14,13)(10,17,18,22)(11,19,20,21)(15,23,24,16)

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, 6279849);