2
Anything's possible
You'll need to edit include/checklogin.php page for the login script. At the end, just before you redirect, you'd need some code to check the groups and then change the page based on whether or not they user is in a particular group.
However, recognize that most pages will redirect back to the page you were trying reach after logging in by default, but if you want to over-ride it, then you can, and that would be the place.
AFAIK, there is no module that does this for you.