Finite Group Databasebeta

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C₁₉×#2766 #14560623

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

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, 1498);