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C₁₉×#3564 #14561421

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 51 points:

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

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, 2296);