How to represent a product of cycles in matrix form?

mat = {Sort @ #, #} & @ PermutationList[a];
MatrixForm @ mat // TeXForm

$ \left( \begin{array}{ccccccccccc} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ 9 & 11 & 7 & 8 & 10 & 2 & 1 & 5 & 3 & 4 & 6 \\ \end{array} \right)$

One idea is to overload MatrixForm so that it does this for you automatically:

Unprotect[MatrixForm];
MatrixForm /: MakeBoxes[MatrixForm[cyc_Cycles], StandardForm] := With[
    {list=PermutationList[cyc]},
    ToBoxes[MatrixForm[{Range@Length@list, list}], StandardForm]
]
Protect[MatrixForm];

Then:

Cycles[{{1, 9, 3, 7}, {2, 11, 6}, {4, 8, 5, 10}}] //MatrixForm