# 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 element`x`

takes 7µs on my machine, and a brute force search for all elements`x`

takes about 30 seconds.