Finite Group Databasebeta

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C₁₉×#2450 #14560307

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

584 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)(24,25,28,29)(26,31,30,27)(32,33)(34,38)(35,37)(36,39);(21,23)(25,29)(26,30)(32,33,35,37)(34,36,39,38);(20,21)(22,23)(24,26,28,30)(25,27,29,31)(32,33)(34,36)(35,37)(38,39);(24,27)(25,30)(26,29)(28,31)(32,34)(33,36)(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, 1182);