Finite Group Databasebeta

?

← Prev (#608542) Next (#608544) →

C₂×#15224 #608543

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

Aliases

Subgroups

5430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 515739);