7.69 ConjugacyClass

ConjugacyClass( G, g )

ConjugacyClass returns the conjugacy class of the element g in the group G. Signals an error if g is not an element in G. The conjugacy class is returned as a domain, so that all set theoretic functions are applicable (see Domains).

    gap> a5 := Group( (1,2,3), (3,4,5) );;  a5.name := "a5";;
    gap> c := ConjugacyClass( a5, (1,2,3,4,5) );
    ConjugacyClass( a5, (1,2,3,4,5) )
    gap> Size( c );
    12
    gap> Representative( c );
    (1,2,3,4,5)
    gap> Elements( c );
    [ (1,2,3,4,5), (1,2,4,5,3), (1,2,5,3,4), (1,3,5,4,2), (1,3,2,5,4), 
      (1,3,4,2,5), (1,4,3,5,2), (1,4,5,2,3), (1,4,2,3,5), (1,5,4,3,2), 
      (1,5,2,4,3), (1,5,3,2,4) ] 

ConjugacyClass calls G.operations.ConjugacyClass( G, g ) and returns that value.

The default function called this way is GroupOps.ConjugacyClass, which creates a conjugacy class record (see Conjugacy Class Records) with the Set Functions for Conjugacy Classes). Look in the index under ConjugacyClass to see for which groups this function is overlaid.

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