In this paper, we examined the results of fixed point set of symmetric groups Sn (n≤7) acting on X (3) and X . In order to find the fixed point set| fix (g) | of these permutation groups, we used the method developed by Higman (1970) to compute the number of orbits, ranks and sub degrees of these actions. The results were used to find the number of orbits as proposed by Harary (1969) in Cauchy-Frobenius Lemma and hence deduce transitivity.
Key words: Cycles, | Fix (g) |, Lemma.
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