Finite Group Databasebeta

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C₁₉×#3082 #14560939

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

362 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)(20,21,23,25)(22,26,27,24)(30,36)(31,38)(33,40)(35,42)(37,39)(41,43);(20,22,23,27)(21,24,25,26)(28,29)(30,33)(31,35)(32,34)(36,40)(37,41)(38,42)(39,43);(28,30,32,37)(29,33,34,41)(31,39,38,36)(35,43,42,40);(29,34)(33,41)(35,42)(40,43)

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, 1814);