MaxDim of some simple groups

MaxDim, along with it relatives m and i, are group invariants analogous to the concept of dimension in vector spaces. In this paper we give the following result on the MaxDim of sporadic groups: 1. An inductive argument for the lower bounds of the MaxDim of those groups in the Suzuki tower, utilizing the fact that those groups act on strongly regular graphs. 2. A detailed computation of the MaxDim of Mathieu 24 group, utilizing the fact that it acts as automorphisms of Steiner system. 3. Estimations of the MaxDim for McLaughlin and Higmann-Sims Group.