Finite Group Databasebeta

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C₁₉×#2639 #14560496

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

576 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)(20,21,22,23)(24,25,28,29)(26,27,30,31)(32,33)(34,37)(35,38)(36,39);(20,21,22,23)(25,29)(26,30)(32,34)(33,36)(35,39)(37,38);(20,21)(22,23)(24,26)(25,27)(28,30)(29,31)(32,34)(33,37)(35,39)(36,38);(24,27)(25,30)(26,29)(28,31)(32,33)(34,36)(35,38)(37,39)

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, 1371);