Finite Group Databasebeta

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C₁₉×#2654 #14560511

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

378 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)(25,27)(28,29,32,31)(30,34,35,33)(37,38)(41,42);(30,35)(33,34)(36,37,40,38)(39,41,43,42);(20,21)(22,25)(23,24)(26,27)(28,30)(29,33)(31,34)(32,35)(36,38,40,37)(39,41,43,42);(20,22,23,26)(21,25,24,27)(28,31,32,29)(30,34,35,33)(36,39,40,43)(37,41,38,42)

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, 1386);