Finite Group Databasebeta

?

← Prev (#7627707) Next (#7627709) →

C₂²×#2613 #7627708

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

Aliases

Subgroups

38238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

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, 7534904);