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C₁₉×SD₁₂₈ #14559287

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

Aliases

Subgroups

38 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)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(21,51)(22,82)(23,49)(24,80)(25,47)(26,78)(27,45)(28,76)(29,43)(30,74)(31,41)(32,72)(33,39)(34,70)(35,37)(36,68)(38,66)(40,64)(42,62)(44,60)(46,58)(48,56)(50,54)(53,83)(55,81)(57,79)(59,77)(61,75)(63,73)(65,71)(67,69)

Conjugacy classes & character table

665 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 162);