This talk is a survey article on the classification of groups. The classification of prime power groups of order at most p6 was done using the notion of isoclinism and invoking a fundamental instrument, namely the capability of groups. Since the basic concepts of this classification i.e., isoclinism and capability were generalized to any variety of groups, therefore this talk intends to propound a basic question whether it is possible to define some suitable varieties that could play the key role for classifying some other families of groups.

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