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Have the conjugacy classes of the torsion subgroups of Gl(n, Z) been determined for small n (say, n<=6)? In general, can much be said about the torsion subgroup?
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There was a countably infinite series of papers by Pohst and Plesken doing dimensions five through 10 (lower dimensions were known before -- see the references in the first of the Pohst/Plesken series:
On Maximal Finite Irreducible Subgroups of GL(n, Z) I. The Five and Seven Dimensional Cases By Wilhelm Plesken and Michael Pohst* ) I don't know if anything is known about higher dimensions -- I doubt it, since it gets a bit tedious.