Finite Group Databasebeta

?

← Prev (#608058) Next (#608060) →

C₂×#15007 #608059

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

Aliases

Subgroups

7402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 515255);