If its a device group then it’s the Inventory API rather than Group API.
https://cumulocity.com/api/10.13.0/#operation/postManagedObjectCollectionResource
You can create a group with POST to …/inventory/managedObjects
Payload…
{type: “c8y_DeviceGroup”, c8y_IsDeviceGroup: {}, name: “aaaaaaaaaa”, c8y_Notes: “”}
Then add a device to it.
POST to …inventory/managedObjects//childAssets
Payload…
{references: [{managedObject: {id: “”}}]}