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C₁₉×#3156 #14561013

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

532 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)(21,23)(24,25,29,33)(26,34,38,48)(27,31,39,45)(28,41,35,32)(30,42,44,37)(36,47,50,55)(40,52,49,46)(43,53,54,51);(24,26,35,42,29,38,28,37)(25,30,41,48,33,44,32,34)(27,36,49,53,39,50,40,51)(31,43,52,55,45,54,46,47);(20,21,22,23)(24,27)(25,31)(26,36)(28,40)(29,39)(30,43)(32,46)(33,45)(34,47)(35,49)(37,51)(38,50)(41,52)(42,53)(44,54)(48,55);(27,39)(31,45)(36,50)(40,49)(43,54)(46,52)(47,55)(51,53)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1888);