Finite Group Databasebeta

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C₁₉×#2772 #14560629

• 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)(20,21)(22,26)(23,24)(25,27)(29,30)(33,34)(36,37,40,43)(38,41,42,39);(21,24)(22,27)(28,29,32,30)(31,34,35,33)(36,38,40,42)(37,41,43,39);(20,21)(22,25)(23,24)(26,27)(28,30,32,29)(31,34,35,33)(36,39,40,41)(37,42,43,38);(20,22,23,27)(21,25,24,26)(28,31,32,35)(29,33,30,34)(36,37)(38,41)(39,42)(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, 1504);