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This paper studies the joint design of user grouping, scheduling (or admission control) and precoding to optimize energy efficiency (EE) for multigroup multicast scenarios in single-cell multiuser MISO downlink channels. Noticing that the existing definition of EE fails to account for group sizes, a new metric called multicast energy efficiency (MEE) is proposed. In this context, the joint design is considered for the maximization of MEE, EE, and scheduled users. Firstly, with the help of binary variables (associated with grouping and scheduling) the joint design problem is formulated as a mixed-Boolean fractional programming problem such that it facilitates the joint update of grouping, scheduling and precoding variables. Further, several novel optimization formulations are proposed to reveal the hidden difference of convex/ concave structure in the objective and associated constraints. Thereafter, we propose a convex-concave procedure framework based iterative algorithm for each optimization criteria where grouping, scheduling, and precoding variables are updated jointly in each iteration. Finally, we compare the performance of the three design criteria concerning three performance metrics namely MEE, EE, and scheduled users through Monte-Carlo simulations. These simulations establish the need for MEE and the improvement from the system optimization.