Finite Group Databasebeta

?

← Prev (#61141) Next (#61143) →

C₂×#3322 #61142

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

Aliases

Subgroups

1159 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54130);