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C₁₉×#2493 #14560350

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 43 points:

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

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, 1225);