Finite Group Databasebeta

?

← Prev (#34785) Next (#34787) →

C₂×#2509 #34786

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

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, 27774);