Finite Group Databasebeta

?

← Prev (#11927408) Next (#11927410) →

C₂²×C₆₁⋊C₅ #11927409

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 65 points:

(1,2)(6,7,9,13,21)(8,11,17,29,39)(10,15,25,42,36)(12,19,32,52,30)(14,23,38,22,37)(16,27,44,33,53)(18,31,50,20,34)(24,40,47,48,56)(26,43,59,58,55)(28,46,61,65,49)(35,54,45,60,62)(41,57,64,63,51);(3,4)(5,6,8,12,20,35,23,39,53,7,10,16,28,47,50,40,56,25,11,18,9,14,24,41,57,65,43,19,33,15,26,42,58,64,21,36,34,44,27,45,17,30,49,37,55,54,60,46,62,31,51,59,52,63,38,29,48,61,13,22,32)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1220, 9);