In many ways, influencing a whole group in your organization is parallel to influencing individuals:
First, you must not demonize them by characterizing them with all sorts of negative stereotypes, tempting as it might be.
Second, you need to understand their world, what they value, how they are rewarded, what pressures they are under, and so forth.
With that information, you now have a sense of the types of currencies you might be able to trade in return for what you want from others.
But, even more than when you are dealing interpersonally, it is important to pay attention to the nature of your relationship. Just as you may have stereotyped other people, they have probably done the same in return.
Any good diagnosis has many facets, but there are some particular issues that are important to pay attention to in dealing across groups, departments, and divisions. Are the dominant currencies of the group true for all members? How much latitude will individuals have to trade for different currencies? Do you need total compliance with your request from everybody in that unit or just some people to go along?
As organizations grow more complex, there is hardly any group that doesn't need cooperation from other units. Furthermore, often the other group does not have to follow your requests. If you are part of a central staff function such as purchasing, information technology, quality control, finance, auditing, or human ...