Finite Group Databasebeta

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C₁₉×#3369 #14561226

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

338 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)(21,24)(25,26)(28,29)(30,34)(31,38)(32,41)(33,36)(35,37)(39,43)(40,42);(20,21,23,24)(22,26,27,25)(28,30,33,32)(29,34,36,41)(31,39,40,37)(35,38,43,42);(28,31,33,40)(29,35,36,43)(30,37,32,39)(34,42,41,38);(20,22,23,27)(21,25,24,26)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2101);