Finite Group Databasebeta

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C₁₉×#3120 #14560977

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

372 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)(20,21)(22,25)(23,24)(26,27)(28,29,32,36)(30,33,37,41)(31,34,39,35)(38,40,43,42);(21,24)(25,27)(28,30,32,37)(29,33,36,41)(31,38,39,43)(34,40,35,42);(29,34)(31,39)(33,40)(35,36)(38,43)(41,42);(20,22,23,26)(21,25,24,27)(30,37)(33,41)(38,43)(40,42)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1852);