No, the Default Group cannot be deleted, and you won't see a Delete option for it in the Genius billing page.
The Default Group holds every billing item that isn't assigned to one of your custom billing groups, including:
- Taxes and certain regulatory fees
- Organization-level subscriptions
- TrueLocal usage
- AVOXI outbound trunk charges
- Cloud Service Plan fees
Because these charges have to live somewhere, the Default Group always remains on your invoice alongside any custom billing groups you've created.