Thanks for responding. When I tested this, I was in a group with two iphones, and all three of us had 4G LTE with mobile data enabled, but we were also connected to a Wi-Fi network (I suppose the Wi-Fi connection would have priority over the mobile data by default to reduce unnecessary mobile data usage?). The messages were just text (and pretty short too). I called them "MMS messages" because I had the setting to "use MMS for group messages" enabled. Do you think it would be helpful to try turning off the Wi-Fi connection and see what effect that has?