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C₁₉×#1425 #14559282

• nilpotent
• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 83 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,30,27,32,26,48)(22,33,36,58,39,60,38,70)(23,40,42,71,44,73,43,74)(25,46,45,56,47,75,41,31)(28,49,50,66,52,65,76,35)(29,53,54,63,55,62,72,34)(37,68,67,80,69,83,64,59)(51,61,57,77,78,82,79,81);(20,22,34,61,25,37,42,49,24,36,53,77,45,67,44,66,27,39,63,82,47,69,43,65,26,38,62,81,41,64,23,35)(21,28,40,59,31,51,72,70,48,76,74,83,75,79,55,60,32,52,73,80,56,78,54,58,30,50,71,68,46,57,29,33)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 157);