Question 8. Let G be a nonabelian group of order 253 =23-11, let P
8. Let G be a nonabelian group of order 253 =23-11, let P P and Q? |P| = |2|= (b) (14 points) How many distinct conjugates of P and Q are there in G? Justify your answer (no credit without justification). 123 = the number of conjugates of P 711 = the number of conjugates of Q= (c) (7 points) Prove that G is isomorphic to a semidirect product P x Q.
P and Q? |P| = |2|= (b) (14 points) How many distinct conjugates of P and Q are there in G? Justify your answer (no credit without justification). 123 = the number of conjugates of P 711 = the number of conjugates of Q= (c) (7 points) Prove that G is isomorphic to a semidirect product P x Q.
