Finite Group Databasebeta

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C₁₉×#2828 #14560685

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

508 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)(25,27)(28,29,31,32)(30,33,35,34)(36,37,40,41)(38,42,43,39);(22,26)(25,27)(29,32)(33,34)(38,43)(39,42);(20,21)(22,25)(23,24)(26,27)(28,29)(30,34)(31,32)(33,35)(36,38)(37,39)(40,43)(41,42);(20,22)(21,25)(23,26)(24,27)(28,30,31,35)(29,33,32,34)(36,39)(37,38)(40,42)(41,43)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1560);