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C₁₉×#3567 #14561424

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

950 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)(21,25)(22,28)(27,32)(29,34)(36,37)(38,41)(39,44)(40,45)(42,46)(43,48)(47,49)(50,51);(21,25)(26,31)(27,32)(33,35)(37,38)(39,46)(43,45)(47,51);(20,21)(22,26)(23,27)(24,25)(28,31)(29,33)(30,32)(34,35)(36,38,41,37)(39,44,46,42)(40,45,48,43)(47,50,51,49);(20,22,24,28)(21,26,25,31)(23,29,30,34)(27,33,32,35)(36,39)(37,42)(38,44)(40,47)(41,46)(43,49)(45,50)(48,51);(20,23,24,30)(21,27,25,32)(22,29,28,34)(26,33,31,35)(36,40)(37,43)(38,45)(39,47)(41,48)(42,49)(44,50)(46,51)

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, 2299);