Finite Group Databasebeta

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C₁₉×#3137 #14560994

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

372 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)(28,29,33,35)(30,36,37,43)(31,32,39,40)(34,41,42,38);(21,24)(25,27)(28,30,32,38,33,37,40,41)(29,34,31,36,35,42,39,43);(20,22,23,26)(21,25,24,27)(28,31,32,35,33,39,40,29)(30,36,38,42,37,43,41,34);(30,37)(34,42)(36,43)(38,41)

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, 1869);