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C₁₉×#3243 #14561100

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

320 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)(38,41)(39,42)(40,44)(43,47)(45,49)(46,48)(50,51);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33)(36,38,40,45)(37,41,44,49)(39,46,47,51)(42,48,43,50);(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, 1975);