If we have the following permutation: $\sigma = (2,1,4)(4,5,1,6) \in S_7$
Am I right in assuming it will permute in the following way?
$ \begin{array}{clcr} 1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \\ 6 \ 1 \ 3 \ 5 \ 2 \ 4 \ 7 \end{array}$
And, is there a quick way of finding a $\tau \in S_7$ such that $\tau^{-1} \sigma \tau = (1,2)(3,4,5)$, i.e. not having to write out all the permutations and checking which one fits? I've tried solving it with the cancellation law but screwed up somewhere.
Thanks.