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C₁₉×#3054 #14560911

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

500 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)(28,37)(29,32)(30,36)(34,39)(35,38);(24,26,28,36,29,34,27,35)(25,30,31,33,32,38,37,39);(21,23)(26,34)(30,38)(33,39)(35,36);(24,27,29,28)(25,31,32,37)(26,35,34,36)(30,33,38,39)

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, 1786);