I cannot send messages in a group text or receive messages

What type of group is that?

Types of group text messages

There are three types of group messages that you might see: group iMessage, group MMS, and group SMS. The Messages app automatically chooses the type of group message to send based on settings, network connection, and carrier plan. For example:

• If you and your recipients are using Apple devices and iMessage is turned on, then the group message is sent as an iMessage. You need to activate iMessage
• If you send a group message to people who aren't using iMessage, then the message is sent as an MMS or SMS message. You need to contact your Carrier to enable SMS and/or MMS.

Send a group text message on your iPhone, iPad, or iPod touch - Apple Support (IN)