Finite Group Databasebeta

?

← Prev (#52180) Next (#52182) →

C₂×#2745 #52181

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

Aliases

Subgroups

1067 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,7)(6,8)(9,10)(11,12)(13,16)(14,18)(15,17)(19,20,23,21)(22,25,26,24);(4,5)(6,10)(11,13,15,18)(12,16,17,14)(19,21,23,20)(22,25,26,24);(3,5,7,4)(6,9,10,8)(11,13)(12,14)(15,18)(16,17)(19,22)(20,24)(21,25)(23,26);(3,6)(4,8)(5,9)(7,10)(11,14)(12,13)(15,16)(17,18)(19,22)(20,24)(21,25)(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, 45169);