Finite Group Databasebeta

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C₁₉×#2569 #14560426

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

456 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)(22,24)(23,26)(25,27)(28,29,32,33)(30,31,34,35)(36,37,40,43)(38,42,39,41);(21,22)(25,26)(29,33)(30,34)(36,38,40,39)(37,41,43,42);(20,22,24,21)(23,26,27,25)(28,30)(29,31)(32,34)(33,35)(36,39,40,38)(37,42,43,41);(20,23)(21,25)(22,26)(24,27)(28,31)(29,30)(32,35)(33,34)(36,37)(38,41)(39,42)(40,43)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1301);