The Omicron system was an inhabited planetary system with at least four planets. The fourth planet, Omicron IV, was the homeworld for the Omicron IV natives. (TOS: "Assignment: Earth")

Crew members aboard Federation starships used the system as a reliable point when computing distances between astronomical locations. Lieutenant Commander Data often told an "amusing" anecdote concerning how he computed the distance between the Omicron system and the Crab Nebula "by using the square root of pi and multiplying it by nine to the third power,". In 2365, he recounted the story to Jean-Luc Picard and Lwaxana Troi, much to their boredom. (TNG: "Manhunt")

This system was only mentioned in dialogue.
In the script, Data calculated the distance between the Omicron galaxy and the Crab Nebula. [1]