Auto URL Aliasing for Custom Menu Paths with Term Id
I am not sure whether we should take this way or not but I found this:

We can save new path alias using path_save() function. 

Here is how I managed it:

I called the function after submission of node or group node.

Then I called a custom function and fetch the real URL of the node i.e in your case it will be group/tid.

Now I retrived term name from term id and created new alias with term name.

Called path_save() function with necessary information.