Can you add a contact group to a location through glog xml?

I am trying to post xml and update a location with a contract group.  But I get this error: "exists in database as type GROUP and must be modified with ContactGroup element".  Does anyone know if this is possible?  I can add it through the UI and when I query the location xml it shows up.  Part of XML listed Below:

<TransmissionBody>
            <GLogXMLElement>
            <Location>
                  <TransactionCode>U</TransactionCode>
                  <LocationGid>
                     <Gid>
                        <DomainName>MENLO/A370</DomainName>
                        <Xid>000074</Xid>
                     </Gid>
                  </LocationGid>
                  <Contact>  <!- This is a contact group -->
                     <ContactGid>
                        <Gid>
                           <DomainName>MENLO/A370</DomainName>
                           <Xid>LOC800820DL</Xid>
                        </Gid>
                     </ContactGid>
                    ...
                  </Contact>
               </Location>

            </GLogXMLElement>