How to create a distribution list for sending eMail?
You can use the Rules module for this, simply by using Rules Action "Send mail to all users of a role". So all you'd have to do is to create a role that corresponds to your "user group", and grant access to the role you created for it.

However, if your user group consists of many, many users, then you might want to use a more granular approach as details in my answer to "How to delay sending emails using Rules to avoid being considered as a spammer?".