Finite Group Databasebeta

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C₁₉×#2951 #14560808

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

484 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)(20,21,23,22)(24,25)(26,31)(27,33)(28,32)(29,34)(30,35)(36,39)(37,38);(24,26)(25,30)(27,35)(28,37)(29,36)(31,32)(33,39)(34,38);(20,22,23,21)(24,26)(25,31)(27,37)(28,35)(29,36)(30,32)(33,38)(34,39);(24,27,29,28)(25,32,34,33)(26,35,36,37)(30,31,38,39)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1683);