Finite Group Databasebeta

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C₁₉×#2827 #14560684

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

414 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)(21,24)(25,27)(28,29,32,33)(30,34,35,31)(37,40)(41,42);(22,26)(25,27)(30,35)(31,34)(36,37,39,40)(38,41,43,42);(20,21)(22,25)(23,24)(26,27)(28,30)(29,31)(32,35)(33,34)(36,37)(38,42)(39,40)(41,43);(20,22)(21,25)(23,26)(24,27)(28,31)(29,30)(32,34)(33,35)(36,38)(37,41)(39,43)(40,42)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1559);