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C₁₉×#2833 #14560690

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

332 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)(21,24)(25,27)(28,29,32,33)(30,34,35,31)(37,41)(42,44)(43,47)(50,51);(22,26)(25,27)(30,35)(31,34)(36,37,40,41)(38,44,46,42)(39,47,49,43)(45,50,48,51);(20,21)(22,25)(23,24)(26,27)(28,30)(29,31)(32,35)(33,34)(36,38,40,46)(37,42,41,44)(39,48,49,45)(43,51,47,50);(20,22)(21,25)(23,26)(24,27)(28,31)(29,30)(32,34)(33,35)(36,39,40,49)(37,43,41,47)(38,45,46,48)(42,50,44,51)

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, 1565);