Finite Group Databasebeta

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C₁₉×#1835 #14559692

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,29)(27,28)(30,31)(32,33)(34,42)(35,38)(36,46)(37,41)(39,44)(40,43)(45,47);(25,28)(29,31)(32,34,43,45,37,44,36,35)(33,38,46,39,41,47,40,42);(24,26,27,30)(25,29,28,31)(32,35,36,44,37,45,43,34)(33,39,40,38,41,42,46,47)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 567);