It seems in GR the symmetry group for transformations is GL(R,4) or Diff(M) depending on who you ask: http://physics.stackexchange.com/questions/65688/group-theory-in-general-relativity

However (I might have missed it) the answers in the above link don't mention if there is an explicit formula akin to [itex]\Lambda^{T}\eta\Lambda=\eta[/itex] for allowed transformations, or a formula for a conserved quantity like [itex]ds'^{2}=ds^2[/itex]?