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C₁₉×#3521 #14561378

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1042 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)(28,29)(30,36)(31,39)(32,33)(34,38)(35,40)(37,41)(42,43);(29,33)(34,36)(35,39)(41,42);(20,21)(22,25)(23,24)(26,27)(28,30,32,38)(29,34,33,36)(31,37,40,43)(35,41,39,42);(28,29)(30,34)(31,35)(32,33)(36,38)(37,41)(39,40)(42,43);(20,22,23,26)(21,25,24,27)(28,31)(29,35)(30,37)(32,40)(33,39)(34,41)(36,42)(38,43)

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, 2253);