Finite Group Databasebeta

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C₁₉×#3344 #14561201

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

344 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)(20,21,24,23)(22,26,27,25)(28,29,32,36)(30,33,37,41)(31,34,39,35)(38,42,43,40);(20,22)(21,25)(23,26)(24,27)(28,30)(29,33)(31,38)(32,37)(34,42)(35,40)(36,41)(39,43);(20,23,24,21)(22,26,27,25)(29,34)(30,37)(31,39)(33,40)(35,36)(41,42);(22,27)(25,26)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2076);