Finite Group Databasebeta

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C₁₉×#3126 #14560983

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

382 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)(29,33)(30,36)(32,38)(34,42)(37,39)(40,43);(21,24)(25,27)(28,29)(30,34)(31,33)(32,35)(36,43)(37,40)(38,41)(39,42);(28,30,31,37)(29,34,33,40)(32,39,38,36)(35,42,41,43);(20,22,23,26)(21,25,24,27)(29,33)(34,40)(35,41)(42,43)

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, 1858);