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C₁₉×#2916 #14560773

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 51 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1648);