You don't need to solve (c). This is question from 'Group theorey and Quantum chemistry'

3-7 (a) Form a representation of D3, the rotational symmetry group of the equilateral triangle, which has F = xzg(') as part of its basis. The z axis is the three-fold axis, and g() is such as to assure radial convergence in the normalization integral. What are the other basis functions ? (6) If this representation is reducible, into what irreducible representations does it reduce ? (c) If your basis functions are not orthonormal, choose a new set of linear combinations of them that are. (You need orthonormalize only the angular part.) By applying the corresponding similarity transformation to the matrices of your representation, transform it into a unitary representation. If you have chosen your orthonormal functions wisely, the matrices will now be in block form. If not, reduce them to block form by a suitable unitary transformation to a new ortho- normal basis. (d) Express F = xzg(r) explicitly as a sum of parts "), each of which transforms according to a particular row of one of the irreducible representations. 1