Create report of group count
In the reports you can use the Filters tab to select on only the members who are in the group you are interested in. You can create a new report that has the filter so you can use this for the automatic mailing. This will send the whole list if group members (you can cut down the fields. It will have the number of group members at the bottom of the pdf, but will also list all the members (which you may not want).