I suspect in American English at least "faculty" is a poor translation here. I suspect this Ukrainian phrase means "a large academic department" (e.g. a biology department with many professors; in American English an academic department has a faculty: the professors and other instructional staff who are a part of it). Am I on the right track?
And if I am, how would one translate the American English meaning of "faculty" (the group of professors, lecturers, etc. of a college or university or teachers of a school) into Ukrainian?
Right you are, "great", "big", "large" are all translated to "великий" in Ukrainian. But the meanings are still not equal, so that a native Ukrainian can surely tell the difference when does it mean "great", and when "big/large". And I can hardly imagine the situation when "великий факультет" should be translated as "great university department". It's not common, not colloquial. Usually it's just big.