Finite Group Databasebeta

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C₁₉×#2377 #14560234

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

576 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)(34,38)(35,36)(37,39);(25,28)(29,31)(33,36)(34,39);(24,25)(26,29)(27,28)(30,31)(32,33)(34,37)(35,36)(38,39);(24,26)(25,29)(27,30)(28,31)(32,34,35,39)(33,37,36,38)

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, 1109);