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C₁₉×#3516 #14561373

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(25,27)(29,32)(30,36)(35,39)(37,42);(28,29,33,32)(30,34,36,38)(31,39,40,35)(37,43,42,41);(20,21)(22,25)(23,24)(26,27)(28,30)(29,34)(31,37)(32,38)(33,36)(35,41)(39,43)(40,42);(28,31,33,40)(29,35,32,39)(30,37,36,42)(34,41,38,43);(20,22,23,26)(21,25,24,27)(28,32,33,29)(30,38,36,34)(31,39,40,35)(37,43,42,41)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2248);