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Suppose a and b are elements of a symmetric group that are conjugate, how to find a conjugating element in sage?

For example,

G=SymmetricGroup(3); a=G((1,2)) b=G((2,3))

Then

G.conjugacy_class(a) == G.conjugacy_class(b)

is true, but is there a function to give x such that xa=bx?

Suppose a and b are elements of a symmetric group that are conjugate, how to find a conjugating element in sage?

For example,

G=SymmetricGroup(3);
a=G((1,2))
b=G((2,3))
b=G((2,3))

G.conjugacy_class(a) == G.conjugacy_class(b)
G.conjugacy_class(b)