The construction of perfect groups of a given order can be considered as the prototype of the construction of insoluble groups of a given order. I will describe a recent project to enumerate, up to isomorphism, the perfect groups of order up to 2⋅106. It crucially relies on new tools for calculating cohomology, as well as improved implementations for isomorphism test. This work extends results of Holt and Plesken from 1989 and illustrates the scope of algorithmic improvements over the past decades.
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