Avikan Nomada

In short, they are the single largest spacefaring nation in the galaxy, with a size greater than the entire Elithian Alliance combined, and they generally aren't very friendly.

The Avikan Nomada has moved a lot closer to Elithian space by now - while the main fleet is still quite a ways off, Avikan scouting ships have already reached the Gar-Aeroix.

The Nomada is currently stationed nearby Kharmani, which is a desert planet with somewhat similar climate to Kadavan.

The Avikan didn't have any colonies at the time of the Exodus, so they've been forced to live as nomadic spacefarers since then. They establish smaller outposts on habitable planets occasionally, but those colonies are always small and often short-lived. The Avikan can't establish any larger, permanent settlements because the Theleans always find them.

The Theleans drove the Avikan from their homeworld in their pursuit of Centensian relics, and Thelean hunters (often called Errasmeyr) are still hunting down the Avikan now. The Nomada is always on the move, outrunning the Theleans and keeping the Centensian relics on board the Nomada safe.

The Avikan and Theleans are certainly still at war, although actual battles are rare these days as the Avikan live on a nomadic fleet, with no permanent home base (since Kadavan was taken by the Theleans). The Nomada is constantly on the move, and the Avikan take great care in keeping their location and trajectory a secret. If the Theleans managed to locate the Nomada and attack it before the Avikan can get away, the Avikan species would be in peril.

There's a lot of different ships on the Nomada, some of which are highly specialized, whilst others perform a lot of different duties. There's military vessels, small civilian ships, huge colony ships which can deploy colonies on new planets quickly, and massive lifeships which house thousands of Avikan, complete with 'greenhouses', residential sectors, sanitation areas, manufacturing sectors and more

The Nomada grows most of its supplies on board their ships, with colonies sometimes supplying additional supplies. Such supply routes aren't reliable for the Avikan, however: the ever-present Thelean threat means that the Avikan may have to suddenly move their entire fleet, which would cut supply lines. The Avikan won't risk sending ships between the Nomada and far away colonies for fear of the Theleans locating the Nomada, so any colonies that provide supplies are always in the same planetary system as the Nomada.

Avikan society is somewhat militaristic, but they do still have a very large civilian population. If need be, the Vanguard can conscript more soldiers from the civilian population, but they've rarely done so thus far. In general, volunteers are plentiful, and there's been no need for additional conscription. The Nomada and the Vanguard are mostly concerned with avoiding confrontation (with the Theleans or any other alien species) and so their military isn't actually all that large. They don't have any plans for taking the fight to the Theleans - they have given up hope on such pursuits - although minor skirmishes happen from time to time. These always happen away from the main fleet, though, and combatants take great care to avoid being tracked. The Nomada's location is a closely kept secret, and no other species has ever managed to pinpoint its ever-changing location.

As for Nomada politics, the Vanguard has slightly greater influence than the Rhaiod, mostly because the Vanguard influences day-to-day operations more than the Rhaiod does. Every civilian is trained in combat to some small degree, and all of them are taught how to hide their activities from the Theleans if they leave on journeys outside of the Nomada. Politics are dominated by the Council of Elders, who take into account the concerns of both the Rhaiod and the Vanguard. The Vanguard has more Elder members, however, so they are better represented on the Council.

If someone other than the Theleans were to locate and visit the Nomada, they'd likely be attacked by the Vanguard on first sight, while the rest of the Nomada quickly flees into hyperspace. The Nomada must always remain hidden, because the Avikan trust no-one with the fate of their species. Any non-Thelean could still be a spy for the Theleans, or just have bad intentions of their own, and the Avikan don't want to take any risks when the safety of the Nomada is at stake.

The Theleans were the Avikan's first encounter with an alien species. (unless you count Rhadeis and the Centens, whom they've only ever indirectly met) That's why they are so distrustful of alien species: their very first interaction with an alien species was a series of invasions that resulted in the loss of their home planet.

Trivia

 * In the canon lore, there are no teleporters, so all supplies would have to be carried across the stars. There are jumpgates - an originally Centensian technology that essentially opens up wormholes, allowing for instantaneous travel between systems - but the Avikan don't use this technology very often. You need two jumpgates for reliable travel (one at each end), and since the Avikan are always on the move these stationary gates aren't of much use to them.
 * The Avikan Nomada has, under extremely rare circumstances, admitted a number of alien individuals into the Nomada and the Vanguard. It's extremely rare, and such individuals are often subject to distrust from Avikan civilians so they are generally kept away from most of Avikan society. This is also an example of the differences between the canon storyverse, and the Starbound storyverse: in canon, such occurneces are extremely rare. In Starbound however, players of all species have access to the Starfarer's Refuge and the quests offered there, so lines like those aren't fully indicative of the canon lore.
 * If Stalkers ever made it onto the Nomada, the Avikan would be in big trouble. They don't have the tools to fight off in infestation if it gains any ground on board. Their species would likely survive, however: there's thousands of ships in the Nomada, and for the Stalkers to infest each of them would be incredibly unlikely. They'd lose their largest ships, and they'd lose a very significant part of their population in the process, but the species would likely survive.