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C₁₉×#3244 #14561101

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(22,28)(23,26)(24,27)(25,30)(29,34)(31,33)(32,35)(36,37)(38,45)(39,43)(40,42)(41,46)(44,48)(47,49)(50,51);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33)(36,38)(37,41)(39,46)(40,47)(42,50)(43,45)(44,49)(48,51);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(37,42)(38,46)(40,48)(41,49)(43,44)(45,50);(21,27)(25,28)(26,35)(33,34)(37,43)(38,46)(42,44)(47,51)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1976);