Permutation question. $qpq^{-1}$, $q,p,r,s \in S_{8}$. Let $p,r,s,q \in S_{8}$ be the permutation given by the following products of cycles:
$$p=(1,4,3,8,2)(1,2)(1,5)$$
$$q=(1,2,3)(4,5,6,8)$$
$$r=(1,2,3,8,7,4,3)(5,6)$$
$$s=(1,3,4)(2,3,5,7)(1,8,4,6)$$
Compute $qpq^{-1}$ and $r^{-2}sr^{2}.$
thanks for your help. 
I want to write the following permutations like : 
$p=\begin{pmatrix}
1 & 2&3&4&5&6&7&8\\4&1&8&3&?&?&?&2\end{pmatrix}$
$q=\begin{pmatrix}
1 & 2&3&4&5&6&7&8\\2&3&1&5&6&8&7&4\end{pmatrix}$
$r=\begin{pmatrix}
1 & 2&3&4&5&6&7&8\\ 2&3&8&3&6&5&4&7\end{pmatrix}$
$s=\begin{pmatrix}
1 & 2&3&4&5&6&7&8\\ 3&?&4&1&?&?&?&?\end{pmatrix}$
can you help me plese to fill the $?$ mark. Is there another method to compute $qpq^{-1}$? 
thanks:) 

There is a quick way to compute both of your permutations, and it is by using this fact:
Suppose $\tau, \sigma \in S_n$ and in cycle notation, $\sigma = (a_1, a_2, \cdots a_p) (b_1, b_2, \cdots, b_q) \cdots (z_1, z_2, \cdots, z_l)$ say. Then $$ \tau \sigma \tau^{-1} = (\tau(a_1), \tau(a_2), \cdots \tau(a_p)) (\tau(b_1), \tau(b_2), \cdots, \tau(b_q)) \cdots (\tau(z_1), \tau(z_2), \cdots, \tau(z_l))$$
That is, to conjugate by $\tau$, replace the elements in the cycles of $\sigma$ by their images under $\tau.$ Exercise: Prove this.
