Finite Group Databasebeta

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C₁₉×#2759 #14560616

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

394 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)(21,24)(22,26)(28,29,31,33)(30,34,35,32)(37,40)(41,42);(30,35)(32,34)(36,37,39,40)(38,42,43,41);(20,21,23,24)(22,25,26,27)(28,30,31,35)(29,32,33,34)(36,37)(38,41)(39,40)(42,43);(20,22)(21,25)(23,26)(24,27)(28,29)(30,32)(31,33)(34,35)(36,38,39,43)(37,41,40,42)

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, 1491);