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.