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Purpose and Scope of MathHub Data

Small Groups Library

In most situations, researchers will want to use the Small Groups Library through a computer algebra system (Gap or Magma), because it will let them perform complex calculations.

The web interface serves a different purpose: quick lookup of properties or looking for examples of groups satisfying certain properties.  For students, and sometimes for researchers, this is more helpful than running a computer algebra system. In particular, for such a purpose one is only really interested in groups of really small orders (smaller than the larger ones that appear in the library).  Partly this is because the structural description becomes less helpful as the group orders (and thus prime factorisations of orders) become more complex.