Finite Group Databasebeta

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C₁₉×#3136 #14560993

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

404 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)(29,33)(30,36)(31,38)(34,41)(35,40)(37,42);(21,24)(25,27)(28,29,31,33,32,35,38,40)(30,34,36,39,37,41,42,43);(20,22,23,26)(21,25,24,27)(28,30,31,36,32,37,38,42)(29,34,33,39,35,41,40,43);(29,35)(33,40)(34,41)(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, 1868);