Finite Group Databasebeta

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C₁₉×#3096 #14560953

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

418 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)(30,33)(31,34)(32,36)(35,39)(37,41)(38,40)(42,43);(21,24)(25,27)(28,30)(29,33)(31,38)(32,37)(34,40)(35,42)(36,41)(39,43);(20,22,23,26)(21,25,24,27)(29,34)(31,39)(33,40)(35,36)(38,43)(41,42);(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, 1828);