Finite Group Databasebeta

?

← Prev (#6458780) Next (#6458782) →

C₂×#27585 #6458781

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

Aliases

Subgroups

3634 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6365977);