Finite Group Databasebeta

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C₁₉×#3111 #14560968

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

392 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)(23,24)(26,27)(28,29)(30,38)(31,36)(32,37)(33,35)(34,40)(39,42)(41,43);(21,24)(25,27)(28,30,32,40)(29,34,37,38)(31,39,33,41)(35,42,36,43);(29,35)(31,33)(34,42)(36,37)(38,43)(39,41);(20,22,23,26)(21,25,24,27)(28,31,32,33)(29,36,37,35)(30,39,40,41)(34,43,38,42)

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, 1843);