Finite Group Databasebeta

?

← Prev (#607672) Next (#607674) →

C₂×#14741 #607673

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

Aliases

Subgroups

6290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 514869);