Finite Group Databasebeta

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C₁₉×#2832 #14560689

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

416 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)(21,24)(25,27)(28,29)(30,32)(31,33)(34,35)(36,37,40,39)(38,41,42,43);(22,26)(25,27)(29,30)(33,34)(37,39)(41,43);(20,21)(22,25)(23,24)(26,27)(28,30,32,29)(31,33,35,34)(36,38,40,42)(37,41,39,43);(20,22)(21,25)(23,26)(24,27)(28,31,32,35)(29,33,30,34)(36,39,40,37)(38,41,42,43)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1564);