This exercise asks you to verify the class equation outside of the usual situation where the group action is conjugation. Consider the example of the automorphism group of the path on 11 vertices. First construct the list of orbits. From each orbit, grab the first element of the orbit as a representative. Compute the size of the orbit as the index of the stabilizer of the representative in the group via Theorem 14.1.11. (Yes, you could just compute the size of the full orbit, but the idea of the exercise is to use more group-theoretic results.) Then sum these orbit-sizes, which should equal the size of the whole vertex set since the orbits form a partition.