Finite Group Databasebeta

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C₁₉×#2612 #14560469

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

388 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)(22,26)(23,24)(25,27)(36,37,40,43)(38,42,39,41);(21,24)(25,26)(28,29,31,33)(30,32,34,35)(36,38,40,39)(37,41,43,42);(20,21)(22,25)(23,24)(26,27)(28,29)(30,32)(31,33)(34,35)(36,39,40,38)(37,42,43,41);(20,22,23,27)(21,25,24,26)(28,30,31,34)(29,32,33,35)(36,37)(38,41)(39,42)(40,43)

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, 1344);