Finite Group Databasebeta

?

← Prev (#608423) Next (#608425) →

C₂×#15167 #608424

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

Aliases

Subgroups

5990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(8,9)(13,17)(16,18)(19,20)(21,22)(23,24)(25,26);(7,8,10,9)(12,15)(16,18)(20,24)(21,25);(7,8,10,9)(11,12)(13,16)(14,15)(17,18)(19,21,23,25)(20,22,24,26);(3,4,5,6)(7,9,10,8)(11,13)(12,16)(14,17)(15,18)(19,22)(20,25)(21,24)(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, 515620);