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C₁₉×#2957 #14560814

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

452 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)(20,21,25,30,26,29,24,38)(22,31,33,27,34,42,39,41)(23,28,37,43,35,44,36,48)(32,45,47,40,46,50,49,51);(20,22)(21,27)(23,32)(24,39)(25,33)(26,34)(28,40)(29,41)(30,42)(31,38)(35,46)(36,49)(37,47)(43,50)(44,51)(45,48);(20,23,25,37,26,35,24,36)(21,28,30,43,29,44,38,48)(22,32,33,47,34,46,39,49)(27,40,42,50,41,51,31,45);(21,29)(23,35)(27,41)(30,38)(31,42)(32,46)(36,37)(47,49)

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, 1689);