Finite Group Databasebeta

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C₁₉×#2774 #14560631

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

368 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)(20,21,24,23)(22,26,27,25)(28,29)(30,34)(31,33)(32,35)(36,37,40,42)(38,39,43,41);(21,23)(22,27)(28,29,31,33)(30,34,35,32)(36,38,40,43)(37,41,42,39);(20,22,24,27)(21,25,23,26)(28,29)(30,32)(31,33)(34,35);(20,23,24,21)(22,26,27,25)(28,30,31,35)(29,32,33,34)(36,39,40,41)(37,38,42,43)

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, 1506);