Finite Group Databasebeta

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C₁₉×#2475 #14560332

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

476 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)(24,25)(26,27)(28,30)(29,31)(32,33,37,35)(34,36,39,38);(21,23)(24,26,28,31)(25,27,30,29)(32,34,37,39)(33,38,35,36);(20,21)(22,23)(24,26)(25,29)(27,30)(28,31)(32,35,37,33)(34,36,39,38);(24,27,28,29)(25,26,30,31)(32,36)(33,34)(35,39)(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, 1207);