11. The outer automorphism group of Q is then S 4 / V which is isomorphic to S 3. 12. For the automorphism group is Z 2, with trivial inner automorphism group and outer automorphism group Z 2. 13. Equivalently the symmetric group } } is the only symmetric group with a non-trivial outer automorphism group. 14. An automorphism of a group which is not inner is called an "'outer automorphism " '. 15. This yields the outer automorphism of S 6, discussed below, and corresponds to the resolvent sextic of a quintic. 16. Its outer automorphism group, for } }, is, while the outer automorphism group of is the trivial group. 17. Its outer automorphism group, for } }, is, while the outer automorphism group of is the trivial group. 18. "S " 6, with 720 elements, is the only finite symmetric group which has an outer automorphism . 19. It has three 8-dimensional representations over the field " L ", permuted by the outer automorphism ? of order 3. 20. It has order 211341312 = 2 12 ?" 3 4 ?" 7 2 ?" 13 and outer automorphism group of order 3.
