Filter content by group
Using the modules you described: 


Create a index containing all the nodes that are group content
Edit the fields of this index and add a relationship to 'Groups' (at the bottom of the page)
You will get additional (group)fields available 
Check the one named "Groups » title" and change the type to "string" (instead of default fulltext)
In the Facet tab, make the facet available, and place the block.


This should do the trick!