In a workflow, do the following:
GetUsersInGroup component - this actually fetches all the emails of the persons in the group. Pass in the GroupId of the Group you want. If you don't know the ID, but know the name, just use the Get Group By Name to get the ID.
Pass this output to the Send email component. You can specify the entire array; you don't have to loop nthrough all the users.
Pretty simple. In the event the email doesn't get sent, check the logs for information. Usually it's a bad setup to connect to the email server.