Equation with a permutation composition Is there any method to solving such an equation:
$$f_1\circ f = f_2$$
Where $f_1, f, f_2 \in S_7$ and:
$f_1 = (1234)(5)(6)(7)$
$f_2 = (172536)(4)$

So to my mind that would be the solution:
1) first we are to find $f_1^{-1}$:
$$f_1^{-1}\circ f = id \rightarrow f_1^{-1} = (13421)(5)(6)(7)$$
2) now we are to solve:
$$f_1^{-1} \circ f_2 = (17)(254)(36)$$
And that is our permutation $f$ we were looking for.
