Automorphism groups form a classical object of study in algebraic geometry. In recent years, a special focus has been put on automorphisms of K3 surface, the most famous example being Mukai’s classification of finite symplectic automorphism groups on complex K3 surfaces. Building on work of Dolgachev-Keum, I will discuss a joint project with Hisanori Ohashi (Tokyo) extending Mukai’s results to fields positive characteristic. Notably, we will retain the close connection to the Mathieu group M23 while realizing many larger groups compared to the complex setting.