Some factions are created by an environment.
So with Gaxton's Garrison, the soldiers that patrol Wintershold Castle in the coastal city of Blackcrag. Unusually for this part of the country, only about half are peasants fulfilling part of their duties to their lord by serving in the castle for a month. The other half are professional mercenaries who've traded in the uncertain life of pillaging for a smaller but more stable income.
Gaxton is a severe half-orc with a chip on his shoulder about his parentage. He's so hell-bent on convincing everyone around him that he inherited none of his father's savagery that he's devoted himself to looking as cultured and rational as possible (for a captain of the guard). Always impeccably dressed and sporting fabulous hair, his almost foppish habits belay an intelligent, driven man who's no slouch on the battlefield, either.
Gaxton's grim, resolute personality has rubbed off on the soldiers. They drill routinely, keep their weapons sharp, and when the gates shut for the night, they stay shut. Their behavior extends to off-hours, too; no soldier drinks before their turn on watch and they've even begun avoiding the intimate company of strangers.
As a result, garrison officers are often called on to deal with justice in the city or danger near it, whether it's quelling a riot or driving off wandering orc tribes that stray too close to the city walls.
They're also keenly aware of the crime that occurs not far from the castle walls. They're itching to do something about it, and if Gaxton could convince Blackcrag's noble family to extend their power, they'd be more than happy to kick down a few doors.
As a friendly faction, Gaxton's Garrison is an ideal quest-giver for good-aligned parties. Gaxton will be acutely aware of any nearby dangers and hire adventurers to stop them. The soldiers themselves can also provide quest hooks, as they're too dedicated to their duties to resolve problems with missing relatives. Soldiers can also accompany the party as combat-effective NPCs.
As a foe faction, Gaxton has turned the group intense, slightly paranoid, and a little like a cult. The soldiers drill incessantly and peer out over battlements that haven't seen a battle in decades. They don't trust anyone except those under Gaxton's orders.
Their impatience to address the crime problem makes them even more eager to jump into action when they do get involved in investigating one. This tends to create swift accusations and even swifter punishments, well before all the evidence has been gathered.
While Blackcrag is far from a police state, Gaxton's Garrison sure isn't calming the populace down.