Finite Group Databasebeta

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C₁₉×#3045 #14560902

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

504 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)(24,25)(26,30)(27,32)(28,37)(29,33)(31,34)(35,39)(36,38);(20,21,22,23)(24,26)(25,30)(27,36)(28,34)(29,35)(31,37)(32,38)(33,39);(24,26)(25,31)(27,34)(28,36)(29,35)(30,37)(32,39)(33,38);(24,27,29,28)(25,32,33,37)(26,34,35,36)(30,31,39,38)

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, 1777);