Finite Group Databasebeta

?

← Prev (#14523801) Next (#14523803) →

C₂×C₃×C₇₁⋊C₅ #14523802

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 76 points:

(1,2)(3,4,5)(7,8,10,14,22)(9,12,18,29,44)(11,16,26,30,35)(13,20,33,50,21)(15,24,37,23,36)(17,28,43,62,63)(19,31,47,65,54)(25,39,58,45,64)(27,41,51,46,55)(32,49,68,53,72)(34,52,70,42,61)(38,57,40,48,56)(59,75,66,76,73)(60,71,69,67,74);(6,7,9,13,21,10,15,25,36,55,18,30,46,57,74,33,51,69,75,76,20,34,53,39,59,22,35,54,61,50,37,56,73,64,70,58,65,12,19,32,24,38,28,29,45,41,60,49,47,66,44,63,72,68,8,11,17,14,23,16,27,42,26,40,31,48,67,43,62,52,71)

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2130, 2);