Exercise

Let B = {(1,2,3)(4,5), (2,3)(3,4), (1,4)(6,7)} be a generating set for the subgroup G of S₇. What are the G-orbits on {1, ..., 7}?

{1, ..., 7}

{1,2,3}, {4,5}, {2,3}, {3,4}, {1,4} and {6,7}

{1,2,3,4,5} and {6,7}

False, there is no g G with g(1) = 6.