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C₁₉×#3223 #14561080

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

364 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,25)(24,27)(28,29,33,37)(30,34,39,48)(31,41,43,51)(32,44,46,36)(35,45,50,42)(38,52,53,59)(40,56,55,49)(47,57,58,54);(20,22,23,27)(21,24,25,26)(28,30)(29,34)(31,38)(32,40)(33,39)(35,47)(36,49)(37,48)(41,52)(42,54)(43,53)(44,56)(45,57)(46,55)(50,58)(51,59);(22,27)(24,26)(28,31,33,43)(29,35,37,50)(30,38,39,53)(32,45,46,42)(34,47,48,58)(36,51,44,41)(40,57,55,54)(49,59,56,52);(21,25)(24,26)(30,39)(34,48)(38,53)(40,55)(47,58)(49,56)(52,59)(54,57)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1955);