Kamuti, I.N.Kibet, S. K.Kerich, G.Kimutai, A.2014-01-212014-01-212012-08African Journal of Mathematics and Computer Science Research Vol.5(10) , pp. 173-175 , August 20122006-9731http://ir-library.ku.ac.ke/handle/123456789/8773DOI: 10.5897/AJMCSR12.008In this paper, we investigated some properties associated with the action of symmetric group Sn (n≤7) acting on X(3). If Gx is the stabilizer of the lengths of the orbits of Gx on X are called sub-degrees and the numbers of orbits are called ranks. Ranks and sub-degrees of symmetric groups Sn (n=1, 2, ----) acting on 2-elements subsets from the set X= (1, 2, ---, n) have been calculated by Higman (1970). He showed that the rank is 3 and the sub-degrees are. Therefore, we extend these calculations to the specific symmetric groups Sn (n≤7) acting on X (3).enRankssub-degreessuborbitsprimitivityArticle