Clinked allows you to subscribe to your group's calendar via an RSS feed. Clicking the link beneath your calendar monthly view should prompt your calendar setup to begin within your default calendar client.
If this doesn't work, copy the URL to the RSS feed and use it to set up your calendar manually.
Invitees will receive invitations in their email inbox. If sent to Gmail, they can add the event to their Google Calendar. Alternatively, they can download the .ics file.