this problem, consider the group G = S3 acting on X = S4 by conjugation. other words, given an element gE S3 (thought of as a permutation of {1,2,3}) d an element x E S4 (thought of as a permutation of {1, 2, 3, 4}), the action is efined by g •x = gxg¯'. or example, (12) · (34) = (12)(34)(12)-1 = (34). nswer the following, being sure to carefully justify your answers. a) Describe the orbit Orbg((14)), and the stabiliser Stabg((14)). b) Is the action faithful? c) How many distinct orbits are there in X?

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