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C₁₉×#3547 #14561404

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 43 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2279);