Mutua, Felix MutindaKamaku, Peter WaweruKimani, Patrick Mwangi2022-10-282022-10-282020https://doi.org/10.12988/ija.2020.91273https://doi.org/10.12988/ija.2020.91273http://repository.embuni.ac.ke/handle/123456789/4198In this paper, transitivity, ranks and subdegrees of the action of ex- ternal direct product of Cyclic and Dihedral group on Cartesian Product of two sets are determined. The action is proved to be transitive. Also, it's established that the rank associated with the action is n( r+1 2 ) and subdegrees are [1][n] and [2][n( r􀀀1 2 )] when r is old. Additionally, the rank of the action for the case where r is even is proved to be n( r+2 2 ) and subdegrees are [1][2n] and [2][n( r􀀀2 2 )].enActionCyclic groupDihedral groupExternal direct prod- uctCartesian productRankSubdegreesArticle