The title says it all: is there a table that sums up the parameters, the assumptions/symmetries, and the (most important) predictions of the standard model?
Yes, indeed. There is a working group called the 'particle data group' operating
Where they sum up all experimental results, have short reviews about the physics behind it, also explaining the implicit assumptions made and give bounds on the most popular extensions of the standard model.
This link might be helpful: http://einstein-schrodinger.com/Standard_Model.pdf
It has a fairly detailed description of the SM Lagrangian.
For a less-technical summary you should examine the posters etc. produced by the Contemporary Physics Education Project.