Finite Group Databasebeta

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C₁₉×#1822 #14559679

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 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)(22,25)(23,24)(26,27)(28,29,31,35,32,34,38,41)(30,33,36,40,37,39,42,43);(21,24)(25,27)(28,30,32,37)(29,33,34,39)(31,36,38,42)(35,40,41,43);(20,22,23,26)(21,25,24,27)(29,34)(31,38)(33,39)(36,42)

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, 554);