Finite Group Databasebeta

?

← Prev (#36659) Next (#36661) →

C₂×#2838 #36660

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

Aliases

Subgroups

957 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 29648);