Finite Group Databasebeta

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C₁₉×#3364 #14561221

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

336 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)(25,26)(28,29)(30,34)(31,38)(32,40)(33,36)(35,37)(39,42)(41,43);(20,21,23,24)(22,26,27,25)(28,30,33,32)(29,34,36,40)(31,37,39,41)(35,42,43,38);(28,31,33,39)(29,35,36,43)(30,37,32,41)(34,42,40,38);(20,22,23,27)(21,25,24,26)

Conjugacy classes & character table

665 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2096);