My account has two iPhones and a Galaxy S5, and none of them can send group texts in MMS. Switching to SMS works, but each recipient can see only his or her name, and not the names of the others on the text. My understanding is that MMS allows the recipients to see all the names.
Also, would MMS be billed against my data? I turned off iMessage on the iPhones so as not to use data for messaging.