From The Gauntlet Blog:-

Just like Circles¹⁾, the Faction Roll represents how connected the crew is and how well they can leverage those connections to get what they want. It allows for players to do world building and presents trade offs between resource consumption, faction potency, and complication of relationships. The Faction Roll costs 1 downtime activity. A successful Faction Roll creates a new faction in the game, sets a status for the crew with the faction, and grants temporary access to their resources.

To create the faction, name who you’re looking for and what you want from them. The GM sets a minimum Tier for the faction you want resources from and you roll your crew’s Tier.

The result grants a budget of points to be spent on the tier of the faction and the status of the relationship. Using the crew’s Tier as the base, the number of points is as follows:

  1-3: Tier -1
  4/5: Tier
  6: Tier +1
  critical: Tier +2. ​

You can spend coin to raise the result of this roll beyond critical by spending 2 coin per additional Tier level added.

The faction begins at Tier 1 and their status with the crew begins at -2. Spend result points 1 for 1 to raise these values. The player must narrate how the resulting faction relationship makes sense in the fiction according to the following guidelines, and declare if the faction is weird, establishment, or criminal. The quality of the resource temporarily provided to the crew is equal to the faction’s Tier. As long as the created faction meets the minimum Tier, the player gets the resource, even if the relationship is negative.

​How powerful are they?

  Tier 1: Strong locally or weak on a few planets
  Tier 2: Strong in one system or weak in a few
  Tier 3: Strong in a few systems or weak throughout the sector
  Tier 4: Strong in multiple systems
  Tier 5 has reach and dominance beyond Tier 4 in some way

What is their status with the crew?

  +3: Allies. This faction will help you even if it’s not in their best interest to do so. 
      They expect you to do the same for them.
  +2: Friendly. This faction will help you if it doesn’t create serious problems for them. 
      They expect you to do the same.
  +1: Helpful. This faction will help you if it causes no problems or significant cost for them. 
      They expect the same from you.
  0: Neutral
  -1: Interfering. This faction will look for opportunities to cause trouble for you 
      (or profit from your misfortune) as long as it causes no problems or significant cost for them. 
      They expect the same from you.
  -2: Hostile. This faction will look for opportunities to hurt you as long as it doesn’t create 
      serious problems for them. They expect you to do the same, and take precautions against you.