Finite Group Databasebeta

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C₁₉×#2447 #14560304

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

540 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)(25,28)(26,30)(33,37)(35,38);(21,23)(24,25,27,28)(26,29,30,31)(32,33)(34,38)(35,39)(36,37);(20,21)(22,23)(24,25)(26,29)(27,28)(30,31)(32,34,36,39)(33,38,37,35);(24,26,27,30)(25,29,28,31)(32,35,36,38)(33,39,37,34)

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, 1179);