Enlisting a player corporation into Factional Warfare takes effect after the next downtime. As with solo players, the player corporate standing must be 0.0 or greater towards the empire they wish to fight for.
Player corporate standing is an average of it’s members individual standings. Player corporate standings are calculated with the unmodified standings of each member, not standings modified by Social skills. A character with no standing, for example towards Caldari State, is not calculated as “0” but is completely removed from the equation. The player corporate standings will gradually increase or decrease over the course of 7 down-times until they reflect the average of all members.
The player corporate standing is determined by adding all members base/unmodified Faction standing and then dividing that total by the amount of members who actually have Faction standing. Let’s say there are 5 members in your corporation, you have Caldari standing of 5.0, Petey has 3.22, Jim Bob has 7.3 and everybody else has neutral/0.00 Faction standing. Your corporate standing total would be (5.0 + 3.22 + 7.3)/3 = 5.17 standing with Caldari Faction.
Player standings are basically recalculated almost immediately after they change. Player corporate standings are recalculated at each downtime.
Hope that helps, good luck and may you have much success.
This old thread has some more info available: