On a Maximal Subgroup 2^6:(3 . S6) of M24

The Mathieu group M24 has a maximal subgroup of the form G ̅=N:G, where N=2^6 and G=3. S6 ≅ 3. PGL2 (9). Using Atlas, we can see that M24 has only one maximal subgroup of type 2^6:(3. S6). The group is a split extension of an elementary abelian group, N=26 by a non-split extensionmgroup, G=3. S6. The Fischer matrices for each class representative of G are computed which together with character tables of inertia factor groups of G lead to the full character table of G ̅. The complete fusion of G ̅ into the parent group M24 has been determined using the technique of set intersections of characters.