Its possible. Can be a little tricky to master but heres the general lowdown:
On Admin->General there is a checkbox labelled along the lines of group homepages.
Under Admin->Groups you can setup homepages (Im not sure if these have to be wiki page names or can be urls i.e. tiki-articles etc)
Under Admin->Users (cant remember if its 1.8 or 1.9 this) there is a drop down box for the default group for a user, this will be the group homepage default.
Thats about it.
If the group homepages need to be wiki pagenames use the ARTICLES plugin to show the articles on a wiki page. like http://www.damosoft.co.uk does on its new front page.