Finite Group Databasebeta

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C₁₉×#2484 #14560341

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

512 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)(25,26)(27,31)(32,33,35,37)(34,36,39,38);(24,25,28,26)(27,29,31,30)(32,34)(33,36)(35,39)(37,38);(20,21)(22,23)(24,26,28,25)(27,30,31,29)(32,33)(34,38)(35,37)(36,39);(24,27)(25,29)(26,30)(28,31)

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, 1216);