Gikunju, David MuriukiNyaga, Lewis NamuRimberia, Jane Kagwiria2023-07-252023-07-252017-02Gikunju David Muriuki, Nyaga Lewis Namu, Rimberia Jane Kagwiria. Ranks, Subdegrees and Suborbital Graphs of Direct Product of the Symmetric Group Acting on the Cartesian Product of Three Sets. Pure and Applied Mathematics Journal. Vol. 6, No. 1, 2017, pp. 1-4. doi: 10.11648/j.pamj.20170601.11doi: 10.11648/j.pamj.20170601.11http://ir-library.ku.ac.ke/handle/123456789/26394articleTransitivity and Primitivity of the action of the direct product of the symmetric group on Cartesian product of three sets are investigated in this paper. We prove that this action is both transitive and imprimitive for all n ³ 2 . In addition, we establish that the rank associated with the action is a constant 3 2 . Further; we calculate the subdegrees associated with the action and arrange them according to their increasing magnitude.enDirect ProductSymmetric GroupActionRankSubdegreesCartesian ProductSuborbitArticle