If SCG is a subset of a group. What is the subgroup (S) < G called? Give the definition of the subgroup (S) Consider the following equilateral triangle Consider the permutations Po = f1 = 2 2 2 3 2 3 32 1 P1 = H2 = 3 2 2 3 23 32 P2 = 1 3 1 1 2 - (73) 2 1 43 = 2. Describe what the transformations p; and , represent as symmetries of the triangles. 3. Show that the subsets {p2, 1} and {1, 2} both generate S3, and draw the Cayley graphs of S3 with respect to these generating sets.