This problem is designed to verify that the orbit-stabilizer theorem is true, and that the factors involved can vary. (a) (5 points) Compute orbç(3)

1. Let G be the group from our warmup that’s located on page 146: G = {e, (132)(456)(78),(132)(465), (123)(456) (123)(456)(78),(78)}. This problem is designed to verify that the orbit-stabilizer theorem is true, and that the factors involved can vary. (a) (5 points) Compute orbç(3). (b) (5 points) Compute stabc(3). (c) (5 points) Verify that lorbo(3). Istabo(3) = G). (d) (5 points) Compute orbG(8). (e) (5 points) Compute stabg(8) (1) (5 points) Verify that forbo(8)|- |stabo(8)| = GL. (8) (5 points) Stand in the mirror and take note of your interested face when you realize that the product of certain orbits and corresponding stabilizers still equates to the order of G, even though Jorba (3) Jorbo(8) and stabc(3) #staba(8).