finding conjugating element for two conjugate permutations
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?
I don't know of anything built in, but how large a group are you working with? If I use
G=SymmetricGroup(11), a naïve brute force search for a single elementxtakes 7µs on my machine, and a brute force search for all elementsxtakes about 30 seconds.