For each family of finite classical groups, and their associated simple quotients, we provide an explicit presentation on a specific generating set of size at most 8. Since there exist efficient algorithms to construct this generating set in any copy of the group, our presentations can be used to verify claimed isomorphisms between representations of the classical group. The presentations are available in Magma.
 There is a constant such that all nonabelian finite simple groups of rank over , with the possible exception of the Ree groups , have presentations with at most generators and relations and total length at most . As a corollary, we deduce a conjecture of Holt: there is a constant such that for every finite simple group , every prime and every irreducible -module All nonabelian finite simple groups of rank @math over a field of size @math , with the possible exception of the Ree groups @math , have presentations with at most @math relations and bit-length @math . Moreover, @math and @math have presentations with 3 generators @math 7 relations and bit-length @math , while @math has a presentation with 7 generators, @math relations and bit-length @math