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We survey recent computational results concerning the Monster sporadic
simple group. The main results are: progress towards a complete
classification of the maximal subgroups, including showing that L2(27) is
not a subgroup; showing that the 196882-dimensional module over GF(2)
supports a quadratic form; a complete set of explicit conjugacy class representatives;
small representations of most of the maximal subgroups; and
a partial classification of the ‘nets’ (in the sense of Norton).