The aim of the Modular Atlas Project, begun some 15 years ago and still being under progress, is to compute the Brauer character tables of all the almost quasi-simple groups whose ordinary character tables can be found in the Atlas Of Finite Groups. Work of several people has so far led to the following explicit results, all of which are available in the database of GAP and in the InterNet via http://www.math.rwth-aachen.de/LDFM.
Almost everything is known for 16 of the 26 sporadic groups, i. e. up to the second Conway group Co2, which is of order ~ 4 . 1013, including the alternating and Lie type groups occurring in the Atlas and having order less than that. For the symmetric groups Sn everything is known up to n = 17.
To obtain these results a whole bunch of computational techniques has been developed, e. g. to handle ordinary and Brauer characters as class functions and as elements of Grothendieck groups, for the construction of matrix representations, for the structural analysis of modules, and for so-called ‘condensation’, i. e. explicit computation of images of modules under a certain Schur functor.