Finite Group Databasebeta

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C₁₉×#3069 #14560926

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

446 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)(20,21,26,31)(22,32,34,43)(23,37,39,45)(24,30,25,29)(27,36,42,35)(28,40,44,38)(33,47,48,41)(46,50,51,49);(20,22,24,35,26,34,25,36)(21,27,29,32,31,42,30,43)(23,33,38,49,39,48,40,50)(28,41,37,46,44,47,45,51);(20,23)(21,28)(22,33)(24,38)(25,40)(26,39)(27,41)(29,37)(30,45)(31,44)(32,46)(34,48)(35,49)(36,50)(42,47)(43,51);(22,34)(27,42)(32,43)(33,48)(35,36)(41,47)(46,51)(49,50)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1801);