Reading this document:
https://communities.ca.com/docs/DOC-231158020
it states the same:
“Exchange Server Administrator role”
However your question is interesting. Some customers have found it easier to not use default group names in their enterprise.
To find out if your group name is a default group name or not see this list:
https://technet.microsoft.com/en-us/library/Dd638105%28v=EXCHG.150%29.aspx
I found this link by typing this into google:
exchange 2013 management groups
it looks like the OOTB role in exchange 2013 is:
Organization Management
Thanks,
Bill Patton