$\displaystyle \alpha=\left( {\begin{array}{cccccccccccc}

1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\

5 & 6 & 7 & 8 & 3 & 11 & 9 & 12 & 1 & 10 & 2 & 4 \\

\end{array} } \right)$

$\displaystyle \beta=\left( {\begin{array}{cccccccccccc}

1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\

6 & 7 & 4 & 5 & 12 & 1 & 11 & 9 & 2 & 3 & 10 & 8 \\

\end{array} } \right)$

$\displaystyle \beta^{-1}*\pi^{2006}*\beta=\alpha$

I dont know how to get cyclic structure of $\displaystyle \pi$ permutation and how to solve upper equation.

Any help would be apriciated.