Creating application groups requires the delegated administration permission of the Delivery Group Administration built-in role. This is stated in the following web pages from Citrix:
Create application groups | Citrix DaaS: "Creating application groups requires the delegated administration permission of the Delivery Group Administrator built-in role. See Delegated administration for details." Create application groups | Citrix Virtual Apps and Desktops 7 2212: "To create application groups, you need permissions on the Application Groups object. The permissions for most administrative operations are the same as on applications." The Application Groups object is under the Delivery Groups node in the Studio navigation pane.