Finite Group Databasebeta

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C₁₉×#2810 #14560667

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

344 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)(29,32)(30,34)(36,37,41,38)(39,43,40,42);(21,24)(22,27)(28,29,31,32)(30,35,34,33)(36,38,41,37)(39,43,40,42);(20,22)(21,25)(23,27)(24,26)(36,39,41,40)(37,42,38,43);(20,21)(22,25)(23,24)(26,27)(28,30,31,34)(29,33,32,35)(36,40,41,39)(37,43,38,42)

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, 1542);