Adding IAM IdC Group to Sagemaker Studio

I am using aws_sagemaker_domain to create a Sagemaker domain. I can also use aws_safemaker_user_profile to add individual users to the user profile list.

That is part is not really valuable because if we assign a group under the "Groups" tab in the Management Console, any user within that group has a user profile created at run time. Documentation followed to add the group via the Management Console

The problem: I can't find any way to add the group to the Sagemaker Domain other than through the Management Console. I need to use Terraform, but I cannot even find any of the documentation within CloudFormation.