Finite Group Databasebeta

?

← Prev (#608099) Next (#608101) →

C₂×#15020 #608100

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

Aliases

Subgroups

4626 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(4,5)(8,9)(11,12,15,16)(13,17,18,14)(21,24)(22,26);(3,4,6,5)(7,8,10,9)(12,16)(13,18)(19,20,23,25)(21,22,24,26);(7,8,10,9)(11,13)(12,17)(14,16)(15,18)(19,21,23,24)(20,22,25,26);(3,5,6,4)(7,9,10,8)(11,14,15,17)(12,13,16,18)(19,22)(20,24)(21,25)(23,26)

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, 515296);