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C₁₉×#3043 #14560900

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

490 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)(21,23)(26,32)(27,34)(29,36)(31,38)(33,35)(37,39);(20,21,22,23)(24,25)(26,29)(27,31)(28,30)(32,36)(33,37)(34,38)(35,39);(24,26,28,33)(25,29,30,37)(27,35,34,32)(31,39,38,36);(25,30)(29,37)(31,38)(36,39)

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, 1775);