If a user is already subscribed to a group and blocked a member of the same group, the user that blocked a member will not be receiving any notification or updates from that user. 

For example, User A blocked User B and both were part of the same group. Then, User B posted on the group. User A will not receive any notification and will not even see that post on that group. 

However, if User A posted in the group, User B was still able to receive the notification and even see User A's posts.