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C₁₉×#3008 #14560865

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

784 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)(26,30)(27,29)(28,32)(31,35)(33,37)(34,36)(38,39);(25,29)(27,35)(30,36)(31,32)(34,39)(37,38);(21,23)(24,26)(25,30)(27,34)(28,33)(29,36)(31,38)(32,37)(35,39);(26,33)(30,37)(34,39)(36,38)

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, 1740);