Finite Group Databasebeta

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C₁₉×#2995 #14560852

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

346 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)(22,26)(28,29,31,35,32,34,38,41)(30,33,37,40,36,39,42,43);(20,21)(22,25)(23,24)(26,27)(28,30)(29,33)(31,37)(32,36)(34,39)(35,40)(38,42)(41,43);(21,24)(25,27)(29,34)(30,36)(35,41)(37,42);(20,22,23,26)(21,25,24,27)(30,36)(33,39)(37,42)(40,43)

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, 1727);