Finite Group Databasebeta

?

← Prev (#6437654) Next (#6437656) →

C₂×#24376 #6437655

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

Aliases

Subgroups

4876 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344851);