Finite Group Databasebeta

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C₁₉×#2597 #14560454

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

454 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)(22,24)(23,26)(25,27)(28,29,32,31)(30,34,35,33)(37,39)(41,42);(21,22)(25,26)(30,35)(33,34)(36,37,40,39)(38,42,43,41);(20,22,24,21)(23,26,27,25)(28,30,32,35)(29,33,31,34)(36,38,40,43)(37,41,39,42);(20,23)(21,25)(22,26)(24,27)(28,31,32,29)(30,34,35,33)(36,39,40,37)(38,42,43,41)

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, 1329);