Please I need solution for Q6. This question in representation theory.

gs = t and gu = v. Show the following. (a) The orbits of G's action partition S. (b) The multiplicity of the trivial representation in V = CS is the number of orbits. Thus if G is transitive, then the trivial represen- tation occurs exactly once. What does this say about the module Mu? (c) If G is doubly transitive and V has character x, then x - 1 is an irreducible character of G. Hint: Fix s E S and use Frobenius reciprocity on the stabilizer G s