Finite Group Databasebeta

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C₁₉×#2811 #14560668

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

432 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)(20,21,24,22)(23,26,27,25)(28,29)(30,34)(31,32)(33,35)(37,38)(41,42);(21,22)(23,27)(29,32)(30,35)(36,37,40,38)(39,42,43,41);(20,22,24,21)(23,26,27,25)(28,30)(29,33)(31,35)(32,34)(36,38,40,37)(39,42,43,41);(20,23,24,27)(21,25,22,26)(28,29)(30,33)(31,32)(34,35)(36,39)(37,41)(38,42)(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, 1543);