When you say "sending FROM a group email account" it sounds like you are confusing a few things. I think you are more likely to be wanting to send TO the email group?
You already have your iPhone connected to a user account on the Exchange server, and within that account you have a number of email groups defined (which you see in Outlook).
You will need to get those groups from Exchange to the iPhone address book, then you will be able to send email to the group using "MailShot Pro" (which imports address book groups to create special group contacts you can use from many different apps, including Mail) or another third party app (which typically send email from their own app)
It is quite tricky to get iTunes to synch groups from Exchange into your address book, and hard to find information on it, but it can be done. We have posted what information we have on it on our website at
http://solubleapps.com/mailshot-support/#GROUPS as a public service.
As we don't use Outlook currently ourselves, we can't offer support on this aspect (though we are well-known for our level of technical support within MailShot itself, so please do get in touch if you have any problem once you have the groups on your device.)
If you cannot synchronise those groups across its not the end of the world, as it is quite quick to rebuild the groups again using a checklist, which the better group email apps should include.
I hope this helps. Best of luck.