Click "Reports" on the left sidebar
Click "+ Report"
Select "Group Message History" report type
Select the start and end dates for the data you'd like to export
Check "Send Email" box if you'd like to receive email about your report
Click “Save” and close the modal
If you chose to receive an email, you'll get an email with the report
Othewise, the report will be listed at the top of the reports page
Just click "Actions" and then "Download" to download the file