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C₁₉×#1537 #14559394

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

194 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)(20,21,23,27,24,26,32,34)(22,28,29,35,30,25,31,33)(36,37)(38,45,47,50)(39,48)(40,43)(41,44)(42,46,51,49);(20,22,24,30)(21,25,26,28)(23,31,32,29)(27,35,34,33)(36,38)(37,42)(39,46)(40,49)(41,47)(43,50)(44,51)(45,48);(36,39,41,40)(37,43,44,48)(38,46,47,49)(42,50,51,45)

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, 269);