Finite Group Databasebeta

?

← Prev (#6343292) Next (#6343294) →

C₂²×#1504 #6343293

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

Aliases

Subgroups

6742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

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, 6250489);