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C₁₉×#2950 #14560807

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

456 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)(20,21,23,22)(24,25)(26,34)(27,31)(28,40)(29,32)(30,36)(33,42)(35,48)(37,47)(38,46)(39,52)(41,44)(43,50)(45,51)(49,55)(53,54);(24,26,29,37)(25,30,32,44)(27,35,38,49)(28,41,42,36)(31,43,46,54)(33,47,40,34)(39,53,51,50)(45,55,52,48);(20,22,23,21)(24,27,29,38)(25,31,32,46)(26,35,37,49)(28,39,42,51)(30,43,44,54)(33,45,40,52)(34,48,47,55)(36,50,41,53);(25,32)(27,38)(30,44)(33,40)(34,47)(35,49)(39,51)(50,53)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1682);