There are a couple ways you can send email to a group in HomeSwingCORE. The easiest way, assuming you already have a group and contacts in it. If not, you can view this article to review how to create a group: https://helpdesk.homeswing.com/hc/en-us/articles/203130569-How-do-I-create-a-Contact-Group-and-add-Contacts-
The easiest way is to go to your CORE E-mail menu and select "New E-mail".
This will open the Mail Composer. In the Recipient/To text box, type the name of a group.
Your groups should appear as a drop down. Select your group and compose your mail. Once you send, you can see data as to who has read the message.