Factory modules are modules that once constructed can create in game items; currently these items include: cloaking devices, hyperspace scanners, jump drives, docking bay modules, cloak disruptors, and exotic (codename) weapon and equipment foundries. In order to build those items you will have to provide the factory module with the required goods to construct the item. Constructing items is similar to construction modules: they consume commodities at the same rate, but their required commodities tends to be much higher or more expensive.
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As with base modules there are Hook commands that list what you can build.