Finite Group Databasebeta

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C₁₉×#2474 #14560331

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

526 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)(26,28)(27,30)(29,31)(32,33)(34,35)(36,38)(37,39);(21,23)(25,26)(29,30)(32,34,36,39)(33,35,38,37);(20,21)(22,23)(24,26,28,25)(27,30,31,29)(32,34)(33,37)(35,38)(36,39);(24,27,28,31)(25,29,26,30)(32,35,36,37)(33,34,38,39)

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, 1206);