You cannot get the selected row as a Group because you didn't set the itemsSource as a collection of Group (a List< Group> for example).
So in your case the .SelectedItem gives a DataRowView, you shoud write
DataRowView drv = (DataRowView)dg_unassigned.SelectedItem;
Then you can get a Group object this way:
Group group = new Group { Name = drv["Name"].ToString() };
I don't know how your table looks like, but you can access any field in your table with
drv["nameOfTheField"].ToString();
After that this code should work!
MessageBox.Show(group.Name);