Finite Group Databasebeta

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C₁₉×#3116 #14560973

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

386 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)(28,29,33,37)(30,34,40,43)(31,36,32,35)(38,42,39,41);(21,24)(25,27)(28,30,33,40)(29,34,37,43)(31,38,32,39)(35,41,36,42);(29,35)(31,32)(34,41)(36,37)(38,39)(42,43);(20,22,23,26)(21,25,24,27)(28,31,33,32)(29,36,37,35)(30,38,40,39)(34,42,43,41)

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, 1848);