Finite Group Databasebeta

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C₁₉×#2380 #14560237

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

648 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)(25,28)(26,30)(32,33,36,34)(35,38,39,37);(25,28)(29,31)(33,34)(35,39);(24,25,27,28)(26,29,30,31)(32,34,36,33)(35,38,39,37);(24,26)(25,29)(27,30)(28,31)(32,35,36,39)(33,37,34,38)

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, 1112);