Well, there are a couple possibilities here.
1. The group is truly hiding addresses either for privacy concerns, or to ensure that conversations go through the group. In this case, even if you look through the entire set of headers, you will not find the address.
2. There are ISP's that require that all e-mail sent with a from: of that ISP be certified as coming from an official SMTP server of the ISP. Therefore group mails have to change the from address to not have any remnants of the ISP.
For Google Groups, you can search the full headers for
x-original-from: and this will be the sender.
It might be that Outlook presents this because the from lines in Outlook are something like:
From Joe Smith on behalf of David Coperfield but I don't get any group mails on Outlook so I can't verify what Outlook is doing behind the scenes.