Finite Group Databasebeta

?

← Prev (#6373302) Next (#6373304) →

C₄×#3115 #6373303

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

Aliases

Subgroups

2592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6280499);