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C₁₉×#2176 #14560033

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25)(26,34)(27,38)(28,43)(29,31)(30,35)(32,41)(33,40)(36,54)(37,51)(39,49)(42,50)(44,48)(45,53)(46,55)(47,52);(24,26,29,37)(25,30,31,45)(27,39,42,55)(28,44,40,36)(32,48,47,54)(33,49,43,46)(34,50,51,38)(35,52,53,41);(20,22,23,21)(25,31)(30,45)(32,47)(33,43)(34,51)(38,50)(46,49)(48,54)

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, 908);