Finite Group Databasebeta

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C₁₉×#2844 #14560701

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

356 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)(20,21,23,25)(22,24,26,27)(28,29,32,31)(30,33,34,35);(22,26)(24,27)(29,31)(33,35)(36,37,39,41)(38,42,43,40);(20,21)(22,24)(23,25)(26,27)(28,30)(29,33)(31,35)(32,34)(36,38,39,43)(37,40,41,42);(20,22)(21,24)(23,26)(25,27)(28,31,32,29)(30,33,34,35)

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, 1576);