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C₁₉×#2161 #14560018

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

140 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)(20,21,24,29,26,30,25,40)(22,31,35,47,33,45,36,50)(23,37,38,44,39,51,32,28)(27,41,43,49,42,48,46,34);(20,22,32,48,25,36,39,49,26,33,38,41,24,35,23,34)(21,27,37,47,29,43,44,45,30,42,51,50,40,46,28,31);(22,33)(27,42)(31,45)(34,49)(35,36)(41,48)(43,46)(47,50)

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, 893);