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C₁₉×#3177 #14561034

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

338 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)(22,25)(23,24)(26,27)(28,29,33,37)(30,34,39,47)(31,41,44,56)(32,45,42,36)(35,49,50,43)(38,51,53,59)(40,55,52,48)(46,57,58,54);(21,24)(25,27)(28,30,33,39)(29,34,37,47)(31,38,44,53)(32,40,42,52)(35,46,50,58)(36,48,45,55)(41,51,56,59)(43,54,49,57);(28,31,42,49,33,44,32,43)(29,35,45,56,37,50,36,41)(30,38,52,57,39,53,40,54)(34,46,55,59,47,58,48,51);(20,22,23,26)(21,25,24,27)(30,39)(34,47)(38,53)(40,52)(46,58)(48,55)(51,59)(54,57)

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, 1909);