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C₁₉×#3011 #14560868

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

700 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,29,33)(26,34,37,47)(27,31,38,45)(28,40,42,32)(30,41,44,36)(35,48,49,55)(39,52,51,46)(43,53,54,50);(24,26,29,37)(25,30,33,44)(27,35,38,49)(28,41,42,36)(31,43,45,54)(32,47,40,34)(39,53,51,50)(46,55,52,48);(21,23)(24,27)(25,31)(26,35)(28,39)(29,38)(30,43)(32,46)(33,45)(34,48)(36,50)(37,49)(40,52)(41,53)(42,51)(44,54)(47,55);(27,38)(31,45)(35,49)(39,51)(43,54)(46,52)(48,55)(50,53)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1743);