Finite Group Databasebeta

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C₁₉×#3229 #14561086

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

360 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)(20,21,23,26)(22,24,27,25)(28,29)(30,36)(31,34)(32,35)(33,38)(37,42)(39,41)(40,43);(28,30,32,38)(29,33,35,36)(31,39,40,37)(34,42,43,41);(21,24)(22,27)(25,26)(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

608 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1961);