This question already has an answer here:
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?
This question already has an answer here: 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? 

marked as duplicate by Ian Agol, Theo JohnsonFreyd, Andrey Rekalo, Carlo Beenakker, Derek Holt Jul 8 '13 at 9:02This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question. 


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. 

