Finite Group Databasebeta

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C₁₉×#2566 #14560423

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

548 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)(21,23)(24,25)(26,30)(27,29)(28,31)(32,33,35,37)(34,38,39,36);(24,25,27,29)(26,28,31,30)(32,33)(34,36)(35,37)(38,39);(20,21,22,23)(24,25)(26,28)(27,29)(30,31);(24,26,27,31)(25,28,29,30)(32,34,35,39)(33,36,37,38)

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, 1298);