Kimani, patrickAdicka, Daniel2024-06-062024-06-062021ISSN: 2456-9968http://repository.embuni.ac.ke/handle/embuni/4343ArticleMost researchers consider the action of projective general group on the cosets of its maximal subgroups leaving out non-maximal subgroupsCq+1. In this paper, we consider the action ofPGL (2, ) centralizer of an elliptic element which is a non maximal subgroup . In particular, we determine the subdegrees, rank and properties of the suborbital graphs of the action. We achieve this through the application of the action of a group by conjugation. We have proved that the rank is and the subdegrees are [1][ ] and [ + 1][ ] .enRanksubdegreescentralizersuborbital graphsArticle