Question: Math problem Problem 5: The following rigid structure can be rotated or reflected. 8 7 6 3 5 4 (a) Find the group of symmetries

Math problem

Problem 5: The following rigid structure can be rotated or reflected. 8 7 6 3 5 4 (a) Find the group of symmetries acting on the eight circles. (b) Find the cycle index of this group of permutations. (c) Hence find the number of inequivalent ways to colour the eight circles using (i) up to two colours; (ii) up to three colours; (iii) exactly three colours

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