You should read the sentence with meaningful breaks like this:
The first century or so | of the industrial revolution | increased productivity...
- or so means "approximately" and modifies "first century".
- of is a preposition that introduces "industrial revolution" and helps defining the term: we are talking about the first century of the industrial revolution (and not of the Christian era for instance).
As a historical period The Industrial Revolution started in the 18th century and lasted for about a century. But when we read the IELTS paper you are referring to we must understand they are not referring to the historical period as such :
- because the terms are not capitalized,
- because it would not make sense to talk about the first century of a period that lasted for about a century,
- because of the context that deals with the economy of the 20th and 21st centuries.
So here "industrial revolution" is to be understood as the period that started at the beginning of the historical period known as "The Industrial Revolution" with a process that is still active. What is really meant is "the first century of the industrial era that is known as the Industrial Revolution". Personally I would have written this sentence as:
During the Industrial Revolution increased productivity led...
or
During the first century of our industrial era...