How can I stop obscene group messages?

If you are getting the same ones I am they are SMS text messages (green bubble) coming in from an email address listing several sequential phone numbers. These are all under the purview of your cell service provider so you need to notify them. On several carriers you can forward them to a number such as 7726 (I'm on AT&T and send them there) and it does eventually bring about a reduction.

Granny- wrote:

How can I stop obscene group messages?

block everyone phone number.

That won't work, the phone numbers listed are not sending the material and there are at least 20 in each text. Eventually since they are blasting to the prefix you will be blocking your neighbors.