Finite Group Databasebeta

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C₁₉×#3377 #14561234

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

332 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)(28,29,33,36)(30,37,38,43)(31,35,32,40)(34,41,42,39);(20,21,23,24)(22,26,27,25)(30,38)(34,42)(37,43)(39,41);(28,30,33,38)(29,34,36,42)(31,39,32,41)(35,43,40,37);(20,22,23,27)(21,25,24,26)(28,31,33,32)(29,35,36,40)(30,39,38,41)(34,43,42,37)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2109);