Finite Group Databasebeta

?

← Prev (#34833) Next (#34835) →

C₂×#2585 #34834

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

Aliases

Subgroups

983 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27822);