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C₁₉×#3563 #14561420

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

912 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)(22,29)(23,26)(24,32)(25,28)(27,33)(30,34)(31,35)(36,37,42,45)(38,40,43,39)(41,49,50,44)(46,47,51,48);(20,22,25,23)(21,26,28,29)(24,30,33,31)(27,34,32,35)(36,38,42,43)(37,39,45,40)(41,46,50,51)(44,47,49,48);(20,23,25,22)(21,26,28,29)(24,31,33,30)(27,34,32,35)(36,39,42,40)(37,43,45,38)(41,47,50,48)(44,51,49,46);(20,21)(22,29)(23,26)(24,27)(25,28)(30,35)(31,34)(32,33)(36,40,42,39)(37,38,45,43)(41,48,50,47)(44,46,49,51);(20,24)(21,27)(22,30)(23,31)(25,33)(26,34)(28,32)(29,35)(36,41)(37,44)(38,46)(39,47)(40,48)(42,50)(43,51)(45,49)

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, 2295);