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C₁₉×#3242 #14561099

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

308 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)(36,37,40,44)(38,41,45,49)(39,42,47,43)(46,48,51,50);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33)(36,38)(37,41)(39,46)(40,45)(42,48)(43,50)(44,49)(47,51);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(37,42)(39,47)(41,48)(43,44)(46,51)(49,50);(21,27)(25,28)(26,35)(33,34)(38,45)(41,49)(46,51)(48,50)

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, 1974);