III. The structure of $1,1,2,2-$tetraiododisilane is shown here. $($Reference: T$.$ H$.$ Johansen, K$.$ Hassler, G$.$ Tekautz, K$.$ Hagen, J$.$ Mol. Struct $.,2001,598,171.)$

a$.$ What is the point group of this molecule?

b$.$ Predict the number of IR$-$active $Si-$ I stretching vibrations.

Assign unit vectors on each atom and determine houthey transform based on the operations. The basis set is $1$ if unchanged, $0$ if they go somewhere else and $-1$ of the sign changes.

Once you generate the reducible representation, determine the rotational motions and translational motions so that the only remaining motions are vibrational.

c$.$ Predict the number of Raman$-$active $Si-$ I stretching vibrations.