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C₁₉×#3553 #14561410

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

932 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)(22,27)(23,28)(24,32)(25,26)(29,33)(30,31)(34,35)(37,41)(38,44)(39,47)(49,51);(21,26)(23,27)(29,32)(31,34)(36,37,40,41)(38,45,44,42)(39,43,47,48)(46,51,50,49);(20,22,25,28)(21,27,26,23)(24,30,33,35)(29,34,32,31)(36,37)(38,42)(39,43)(40,41)(44,45)(46,49)(47,48)(50,51);(20,23,25,27)(21,28,26,22)(24,31,33,34)(29,35,32,30)(36,38,40,44)(37,42,41,45)(39,46,47,50)(43,49,48,51);(20,24)(21,29)(22,30)(23,31)(25,33)(26,32)(27,34)(28,35)(36,39)(37,43)(38,46)(40,47)(41,48)(42,49)(44,50)(45,51)

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, 2285);