Finite Group Databasebeta

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C₁₉×#3238 #14561095

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

362 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)(22,25)(23,26)(24,27)(28,29)(30,36)(31,34)(32,35)(33,38)(37,42)(39,41)(40,43);(20,22,24,23)(21,25,27,26)(28,30,32,38)(29,33,35,36)(31,39,40,37)(34,42,43,41);(21,26)(22,23)(25,27)(28,31,32,40)(29,34,35,43)(30,37,38,39)(33,41,36,42);(29,35)(33,36)(34,43)(41,42)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1970);