Finite Group Databasebeta

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C₁₉×#3388 #14561245

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

334 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)(28,29,31,35)(30,37,38,33)(32,34,40,36)(39,41,43,42);(20,22,24,27)(21,25,23,26)(28,30,31,38)(29,33,35,37)(32,39,40,43)(34,42,36,41);(29,34)(30,38)(32,40)(33,41)(35,36)(37,42);(20,23,24,21)(22,25,27,26)(30,38)(33,37)(39,43)(41,42)

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, 2120);