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C₁₉×#3540 #14561397

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1058 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)(22,26)(28,29)(30,37)(31,34)(32,40)(33,36)(35,41)(38,42)(39,43);(21,24)(25,27)(28,30,33,31)(29,34,36,37)(32,38,41,39)(35,42,40,43);(20,21)(22,25)(23,24)(26,27)(28,31,33,30)(29,34,36,37)(32,39,41,38)(35,42,40,43);(20,22)(21,25)(23,26)(24,27)(28,29)(30,37)(31,34)(32,35)(33,36)(38,43)(39,42)(40,41);(28,32,33,41)(29,35,36,40)(30,38,31,39)(34,42,37,43)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2272);