You can't create Outlook Contact Groups when connected to an EAS account
Original KB number: 2811596
When you use to connect to an EAS account, you can't create Contact Groups. Additionally, the New Contact Group button is unavailable.
Contact Groups aren't supported in Exchange ActiveSync (EAS). Outlook uses EAS to connect to @outlook.com, @hotmail.com, @live.com, and @msn.com email accounts.
If you are upgrading from Outlook 2007 or Outlook 2010, you can export your Contacts and Contact Groups to an Outlook Data (.pst) file, and then import them to a new .pst file in Outlook 2019, Outlook 2016, or Outlook 2013. For more information about importing Contact Groups in Outlook, see Import and export Outlook email, contacts, and calendar.