Finite Group Databasebeta

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C₁₉×#3067 #14560924

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

452 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,32)(23,37)(24,29)(25,30)(26,31)(27,34)(28,38)(33,47)(35,43)(36,42)(39,44)(40,45)(41,49)(46,48)(50,51);(20,22,24,34,26,36,25,35)(21,27,30,32,31,43,29,42)(23,33,38,48,39,49,40,50)(28,41,37,46,45,47,44,51);(20,23)(21,28)(22,33)(24,38)(25,40)(26,39)(27,41)(29,44)(30,37)(31,45)(32,46)(34,48)(35,50)(36,49)(42,51)(43,47);(20,24,26,25)(21,29,31,30)(22,34,36,35)(23,38,39,40)(27,42,43,32)(28,44,45,37)(33,48,49,50)(41,51,47,46)

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, 1799);