Finite Group Databasebeta

?

← Prev (#14561422) Next (#14561424) →

C₁₉×#3566 #14561423

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,27)(22,32)(23,37)(24,40)(28,45)(29,35)(31,44)(33,43)(36,49)(38,46)(39,50)(41,51);(20,21)(22,33)(23,38)(24,30)(25,27)(26,31)(28,32)(29,39)(34,40)(35,37)(36,45)(41,47)(42,44)(43,49)(46,50)(48,51);(20,22,25,36)(21,28,27,43)(23,34,39,30)(24,35,40,46)(26,32,42,49)(29,41,38,51)(31,33,44,45)(37,48,50,47);(20,23)(21,29)(22,34)(24,33)(25,39)(26,37)(27,38)(28,41)(30,36)(31,46)(32,48)(35,44)(40,45)(42,50)(43,51)(47,49);(20,24,26,41)(21,30,31,47)(22,35,32,38)(23,33,37,28)(25,40,42,51)(27,34,44,48)(29,36,46,49)(39,45,50,43)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2298);