Finite Group Databasebeta

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C₁₉×#3175 #14561032

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

362 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)(22,25)(23,24)(26,27)(30,36)(31,37)(33,39)(35,40)(38,42)(41,43);(21,24)(25,27)(28,29)(30,33)(31,35)(32,34)(36,39)(37,40)(38,41)(42,43);(28,30,37,42,32,38,31,36)(29,33,40,43,34,41,35,39);(20,22,23,26)(21,25,24,27)(29,34)(33,41)(35,40)(39,43)

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, 1907);