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C₁₉×#3555 #14561412

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

910 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)(20,21,25,28)(22,23,30,26)(24,32,33,27)(29,34,35,31)(36,37,40,43)(38,41,46,44)(39,47,48,42)(45,50,51,49);(20,22,25,30)(21,26,28,23)(24,29,33,35)(27,34,32,31)(36,37)(38,44)(39,42)(40,43)(41,46)(45,50)(47,48)(49,51);(20,23,25,26)(21,22,28,30)(24,31,33,34)(27,29,32,35);(20,22)(21,26)(23,28)(24,29)(25,30)(27,34)(31,32)(33,35)(36,38)(37,41)(39,45)(40,46)(42,49)(43,44)(47,50)(48,51);(20,24,25,33)(21,27,28,32)(22,29,30,35)(23,31,26,34)(36,39,40,48)(37,42,43,47)(38,45,46,51)(41,49,44,50)

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, 2287);