on a group of the form 211:m24

The conway group co1 is one of the 26 sporadic simple groups. it is the largest of the three conway groups with order 4157776806543360000 = 2^21 .3⁹ .5⁴ .7² .11.13.23 and has 22 conjugacy classes of maximal subgroups. in this paper, we discuss a group of the form g = n : g, where n = 211 and g = m24. this group g = n : g = 2^11 : m24 is a split extension of an elementary abelian group n = 2^11 by a mathieu group g = m24. using the computed fischer matrices for each class representative g of g and ordinary character tables of the inertia factor groups of g, we obtain the full character table of g. the complete fusion of g into its mother group co1 is also determined using the permutation character of co1.