Finite Group Databasebeta

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C₁₉×#3380 #14561237

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

352 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)(20,21,24,23)(22,26,27,25)(28,29)(30,33)(31,34)(32,36)(35,39)(37,40)(38,42)(41,43);(20,22,24,27)(21,25,23,26)(28,30,32,38)(29,33,36,42)(31,37,39,43)(34,40,35,41);(29,34)(31,39)(33,40)(35,36)(37,43)(41,42);(20,23,24,21)(22,25,27,26)

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, 2112);