Finite Group Databasebeta

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C₁₉×#2777 #14560634

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,24)(22,25,26,27)(28,29)(30,31)(32,33)(34,35)(36,37,41,43)(38,40,39,42);(21,24)(22,26)(29,33)(31,34)(36,38,41,39)(37,42,43,40);(20,21)(22,25)(23,24)(26,27)(28,30)(29,34)(31,33)(32,35)(36,39,41,38)(37,42,43,40);(20,22,23,26)(21,25,24,27)(28,31,32,34)(29,30,33,35)(36,40,41,42)(37,38,43,39)

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, 1509);