Finite Group Databasebeta

?

← Prev (#358225) Next (#358227) →

C₂×#11258 #358226

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

Aliases

Subgroups

1854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 265422);