If you can telnet to port 443, but not to ports 5228-5230, it is likely that connections to these ports are blocked by your network infrastructure / firewall. The best path to proceed would be to contact your network administrator and let them know you need to be able to open outbound connections to these ports.
Something else to keep in mind is that GCM is not necessarily using that specific host - in fact, it probably is not. You may potentially need to communicate on ports 5228-5230 to any IP address within Google's ASN 15169 in order to use GCM - it's not possible to verify connectivity to GCM by attempting to connect to any one specific IP address or hostname. The initial request (according to Google's documentation) connects to port 443 on gcm-http.googleapis.com (assuming you're using HTTP), but may use other IP addresses and ports later in the process. Google doesn't document any specific IP addresses that are used, and they may change over time - so it could be any IP address within ASN 15169.