the paging group is used by the BTS to know when to schedule the tx of this particular paging message.
The MS is only listening to the messages scheduled during its own paging group scheduling.
In other words, the paging group defines the occurences of the BCCH-multiframe in which its pagings are sent.
Since both BTS and MS knows about it, there is no need to indicate it in the paging message. (i didn’t verify if it is actually written in the message or not, I’m taking your word for it)