Finite Group Databasebeta

?

← Prev (#52211) Next (#52213) →

C₂×#2772 #52212

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

Aliases

Subgroups

981 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,9)(6,7)(8,10)(12,13)(16,17)(19,20,23,26)(21,24,25,22);(4,7)(5,10)(11,12,15,13)(14,17,18,16)(19,21,23,25)(20,24,26,22);(3,4)(5,8)(6,7)(9,10)(11,13,15,12)(14,17,18,16)(19,22,23,24)(20,25,26,21);(3,5,6,10)(4,8,7,9)(11,14,15,18)(12,16,13,17)(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, 45200);