Its just the inverse transformation of the camera to the group*. You can do this by re jigging (instead of connecting to the matrix connect to inverse matrix) the connections in a parent constraint.
Then bake down the keys. As a result the keys will not make sense in graphs anymore tough, so you will loose the ease of use in the graph editor tough (no you cant just convert the individual keys, interpolation is affected im afraid). So you may want to keep the original.
- this rresults in stationary camera looking in -z direction
PS: by the way each and every time you refresh a viewport and render anything, something alonmg this gets done. So the computer is doing this multiple times each second anyway.