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C₁₉×#3545 #14561402

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1060 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)(30,36)(31,33)(32,39)(34,37)(35,40)(38,41)(42,43);(21,24)(25,27)(29,31)(30,37)(35,39)(38,43);(20,21,23,24)(22,25,26,27)(28,30)(29,34)(31,36)(32,38)(33,37)(35,41)(39,42)(40,43);(20,22)(21,25)(23,26)(24,27)(28,31,33,29)(30,36,37,34)(32,39,40,35)(38,42,43,41);(28,32)(29,35)(30,38)(31,39)(33,40)(34,41)(36,42)(37,43)

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, 2277);