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C₁₉×#2070 #14559927

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 51 points:

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

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 802);