Finite Group Databasebeta

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C₁₉×#2446 #14560303

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 39 points:

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

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1178);