Finite Group Databasebeta

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C₁₉×#3183 #14561040

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

370 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)(22,25)(23,24)(26,27)(28,29)(30,34)(31,38)(32,41)(33,36)(35,39)(37,43)(40,42);(21,24)(25,27)(28,30,33,32)(29,34,36,41)(31,39,40,37)(35,42,43,38);(28,31,32,39,33,40,30,37)(29,35,34,38,36,43,41,42);(20,22,23,26)(21,25,24,27)(31,40)(35,43)(37,39)(38,42)

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, 1915);