yeah you are correct, the core concept of the OOPS concept is to minimum input maximum throughput. So if it seems to you that the functions are unnecessary to the class, you need to define in another class or in some general functions list.
It also depends upon the how each function is carryout the functionality if its a file handling then it is advisable to use all the related file handling functionalities within one class rather then putting into two, Same applies for the webservices & the database related operations.
So its more dependent on the type of application you are using rather then any specific rule for a class size.
Hope this helps