Finite Group Databasebeta

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C₁₉×#3396 #14561253

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

384 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)(21,25)(26,27)(28,29,33,36)(30,34,32,40)(31,38,39,42)(35,41,43,37);(20,21,24,25)(22,26,23,27)(28,30,33,32)(29,34,36,40)(31,37,39,41)(35,42,43,38);(20,22,24,23)(21,26,25,27)(28,31,33,39)(29,35,36,43)(30,37,32,41)(34,42,40,38);(20,23,24,22)(21,26,25,27)

Conjugacy classes & character table

665 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2128);