Finite Group Databasebeta

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C₁₉×#2884 #14560741

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

716 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)(22,30,33,26)(23,27)(24,28)(25,29)(31,44,47,38)(32,45,49,39)(34,40)(35,41)(36,42)(37,43)(46,51,48,50);(20,22)(21,26)(23,31)(24,32)(25,33)(27,38)(28,39)(29,30)(34,46)(35,47)(36,48)(37,49)(40,50)(41,44)(42,51)(43,45);(20,23,25,35)(21,27,29,41)(22,31,33,47)(24,36,37,34)(26,38,30,44)(28,42,43,40)(32,48,49,46)(39,51,45,50);(20,24,25,37)(21,28,29,43)(22,32,33,49)(23,34,35,36)(26,39,30,45)(27,40,41,42)(31,46,47,48)(38,50,44,51)

Conjugacy classes & character table

779 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1616);