Finite Group Databasebeta

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C₁₉×#3013 #14560870

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

712 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)(24,25)(26,33)(27,31)(28,36)(29,32)(30,34)(35,38)(37,39);(24,26,29,35)(25,30,32,39)(27,34,28,37)(31,38,36,33);(21,23)(24,25)(26,30)(27,36)(28,31)(29,32)(33,34)(35,39)(37,38);(24,27,29,28)(25,31,32,36)(26,34,35,37)(30,38,39,33)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1745);