How to send an SMS to a group of users and the users receive the sms but within a group

[erck]

I know we can send out sms to users/groups , but I have a requirement that we need the receivers of the SMS to all be in a group together so they can stay in that group and talk to each other. 

Is there a way to implement this?

[erck]

When they receive the SMS, they should receive it looking something like this: 
(Screenshot is from an iOS device)