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