We want to start a Google Group of women academics to share relevant information. Some administrative costs are involved and we need to have an income to meet these costs. Is it permissible to charge a fee to members of the Google Group?
This would seem to be something that is covered in the Google Groups Terms of Service. On a quick browse I didn't see anything about paid groups.
That said, Google Groups does offer the ability to have private, closed groups. How you determine who can be on the list of participants is up to you.
That also said, even private groups are subject to Google's Content Policy.
Google won't manage the (paid) membership for you, so you'd need to work that out some other way.