Finite Group Databasebeta

?

← Prev (#13051181) Next (#13051183) →

C₃×#89317 #13051182

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 74 points:

(1,2,3)(4,5,7,9,10,8,6)(11,13,17,27)(12,18,22,43)(14,29,33,63)(15,35,37,69)(16,39,36,26)(19,45,47,72)(20,49,50,74)(21,51,38,42)(23,52,54,28)(24,44,40,31)(25,48,57,30)(32,67,65,62)(34,41,68,70)(46,73,59,56)(53,60,58,66)(55,64,61,71);(5,6)(7,8)(9,10)(11,12,17,22)(13,23,27,54)(14,28,33,52)(15,34,37,68)(16,38,36,21)(18,40,43,24)(19,44,47,31)(20,48,50,30)(25,56,57,73)(26,58,39,53)(29,49,63,74)(32,66,65,60)(35,45,69,72)(41,67,70,62)(42,55,51,61)(46,64,59,71)

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 471);