Finite Group Databasebeta

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C₁₉×#3309 #14561166

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

404 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)(20,21,23,25)(22,26,27,24)(28,29)(30,37)(31,35)(32,40)(33,36)(34,39)(38,43)(41,42);(20,22)(21,24)(23,27)(25,26)(30,38)(34,42)(37,43)(39,41);(28,30,33,38)(29,34,36,42)(31,39,32,41)(35,43,40,37);(22,27)(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, 2041);