You can only insert and update a group in a transaction with other sObjects. Other DML operations are not allowed.
You can only insert and update a group member in a transaction with other sObjects in Apex code that is saved using Salesforce API version 14.0 and earlier.
You can insert a user in a transaction with other sObjects in Apex code that is saved using Salesforce API version 14.0 and earlier.
You can insert a user in a transaction with other sObjects in Apex code that is saved using Salesforce API version 15.0 and later if UserRoleId is specified as null.
You can update a user in a transaction with other sObjects in Apex code that is saved using Salesforce API version 14.0 and earlier
For these sObjects, there are no restrictions on delete DML operations.
If you are using a Visualforce page with a custom controller, you can only perform DML operations on a single type of sObject within a single request or action. However, you can perform DML operations on different types of sObjects in subsequent requests, for example, you could create an account with a save button, then create a user with a submit button.