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C₁₉×#2719 #14560576

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(26,29)(27,31)(32,33,35,37)(34,38,39,36);(21,23)(24,25,28,30)(26,27,29,31)(32,33)(34,38)(35,37)(36,39);(20,21)(22,23)(24,26,28,29)(25,27,30,31);(24,27)(25,29)(26,30)(28,31)(32,34,35,39)(33,36,37,38)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1451);