Finite Group Databasebeta

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C₁₉×#2955 #14560812

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

456 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)(20,21,25,30,26,29,24,38)(22,31,33,27,34,42,39,41)(23,28,36,44,37,43,35,48)(32,45,46,40,47,51,49,50);(20,22)(21,27)(23,32)(24,39)(25,33)(26,34)(28,40)(29,41)(30,42)(31,38)(35,49)(36,46)(37,47)(43,50)(44,51)(45,48);(20,23,25,36,26,37,24,35)(21,28,30,44,29,43,38,48)(22,32,33,46,34,47,39,49)(27,40,42,51,41,50,31,45);(21,29)(27,41)(28,43)(30,38)(31,42)(40,50)(44,48)(45,51)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1687);