Is it possible to integrate the media module to social groups? 

We drop the module on the group activity page and on each group activity page, there will be a video of its own. Is this possible?

So for example, I have two groups:

localhost/test/Groups/GroupActivity/tabid/89/groupid/9/Default.aspx

localhost/test/Groups/GroupActivity/tabid/89/groupid/8/Default.aspx

Each of these two groups will have different videos. So, anytime I create a new group, I should be able to add its own video on its group activity page, is that possible?

:( oh ok... any approximate date atleast?

The module has never functioned in a gallery way and there are no plans to do that for this module at this time.  The social integration is persona-based, but it leads you to the appropriate area, whether it's another DNN page, or a group page.