Summary: Boolean functions with symmetry have been the object of interest to the researchers. With their concise representation and ease of computation, they offer themselves as cut above the rest candidates for the filtering and exploration of optimal Boolean functions. Generalized Boolean functions have been explored as a number of trade-offs in usual Boolean hinder, the process of selecting good Boolean functions required for a specific application. Therefore, it would be interesting to investigate symmetry in Boolean functions in a generalized scenario. We look into three different symmetries in generalized Boolean function according to different parameter of symmetry and present enumeration formulae. We also present an exhaustive construction of bent and balanced symmetric generalized functions (in form of ANF) on smaller domains.