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C₁₉×#2166 #14560023

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 51 points:

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

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, 898);