Question: (5] In this problem, consider the group G = .93 acting on X = S4 by conjugation. In other words1 given an element 9 E

(5] In this problem, consider the group G = .93 acting on X = S4 by conjugation. In other words1 given an element 9 E 33 (thought of as a permutation of {1,2, 3}] and an element :5 E 54 (thought of as a permutation of {1, 2,3,4}), the action is dened by g -:r = 93:9'1- For example, (12) - (34) = (12)(34)(12)'1 = (34). Answer the following, being sure to carefully justify your answers. (a) Describe the orbit OrbG((l4)), and the stabiliser StabG((l4)). [5 marks] (b) Is the action faithful? [5 marks] (c) How many distinct orbits are there in X? [5 marks]

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