Finite Group Databasebeta

?

← Prev (#52252) Next (#52254) →

C₂×#2796 #52253

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

Aliases

Subgroups

1165 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45241);