Ship on the pic is the Ulysses, the flagship of Admiral Yang Wenli.
Ship of this class were first launched in last years of 740's (space calendar). Those first ships were designated as GW-H1. Over the course of few decades around two hundred thousand of them were built(i personally do not believe that there were 200,000 ships built of this class. The whole Alliance fleet was not that big. But it is possible since Alliance was in war with Empire for 150 years, and it its possible that between 740's to 801 that many were built, i believe personally that around 20-50 thousand were built and that would be more realistically then 200k. )
Standard Alliance battleship (or simply call it Ulysses type) is 624 meters long(my scale is slightly off). It has crew of 660 officers and enlisted. Armament: 8x 20cm neutron beam cannons (nose or bow cannons), 22x 15cm electron beam cannons, 6x 12cm railguns, 12x multiple missile launchers, 22x lasers in single mounts, 10x dual mount lasers, 12x spartanian fighters (2x main fighter launcher bays).
Its smaller, more modular and faster then its Imperial counterpart. Due fact that both Alliance and Empire had highly advanced shipyards which were almost fully automated, they could built massive number of this ships in relative short time. Civilian experts believed that for every new ships of this class need between 4-8 months although they could be built in shorter time of 2-3 months if needed.
These class of ships served as backbone of Alliance heavy fleet and later Yang fleet. It is unknown if they remain in service after 801, but it is possibly that they did (even as irregulars, once again)
There is few subclasses that were created over the years, like carrier variant, heavy attack variant (Muffanese - possibly only one retrofited).
Free Planets Alliance - Standard cruiser (unofficially called Thanatos type) (not 100% accurate)
Backbone of all Alliance fleets from 740's this small and agile warship was one of most numerous ships in Alliance fleet. It is 372 meters long, it has 393 officers and enlisted. Armament: 6x 12cm neutron beam cannons, 2x 4cm railguns, 8x multiple missile launchers, 3x spartanian fighters.
Built in massive numbers this warship served Alliance from at least 740's(space calendar) to the 801, it is unkown how many survived the war against Empire.
Free Planets Alliance Standard destroyer
Smallest combat warp capable unit of the FPA, i do not know what is real name of this ship although there was few, i keep calling it standard alliance destroyer. Its not 100% accurate but it looks nice as it is.
Backbone of the Alliance attack fleets. Smallest and most versatile ship in the fleet, also most numerous of all classes and types. They usually serve as battleship and flagship escorts, but were often used as scouts. Most common tactic is attacking in wolf squadrons. Alliance destroyer is 208m long (my variant is slightly longer, my mistake). It has crew of 164 officers and enlisted. Armament: 6x neutron beam cannon (foward-bow cannons), missile launchers and short range lasers. It cannot carry fighters and shuttles dock outside.
Free Planets Alliance - Standard Carrier
Standard carrier that serve Alliance fleet during the last decades Imperial-Alliance war.
Unlike their Imperial counterpart which were larger but carried less fighters, Alliance carrier could carry up to hundred Spartanian fighter crafts. They were built on enlarged GW battleship frame which is heavily changed and in the end shaped into full fledged carrier.
Alliance carrier is 952 meters long and have around 1500 crew. Armament: It has eight battleship sized neutron cannons on its bow and multiple of smaller weapons for protection.
Due fact that is half open and do not have armor on its belly where the spartanians were launched from its usually on the rear of the fleet. Most of Alliance carriers were lost during the war with Empire, and from those that survived, most were scrapped due treaty of Baalat. Few survived and join Yang Wenli fleet. It is unknown if any still exist.
Free Planets Alliance - Battleship Muffuese
Muffuese is modification of standard Alliance battleship (GW), intended as squadron leader. It is created to for specialized missions like breaking through enemy lines. Most noticeable modification is on its bow. Standard box shaped bow was replaced with hammerhead bow which house more cannons then standard battleship. However four of the eight long range neutron cannons that standard Alliance battleship have was remove to add additional weapons. This make smaller problems as different calibers have different range.
As designed for breakthrough missions, its defenses were boosted, it has stronger shields then standard battleships but armor was the same. Originally Alliance engineers want to add more front armor, however that would make serious problems, more armor means more mass and ship would lose his speed thus it was decided that only shields were to be upgraded, however some armor adjustments were added to the engine block.
Ship is 627 meters long and have 720 crew. Armament: Instead of eight long range neutron cannons that standard battleships have, Muffuese have only four of them located on lower part of the bow. Remaining fifteen guns were medium range beam cannons. Twelve located on hammers (six on each side) and three in the middle). There seventeen port and seventeen starboard cannons, multiple missile launchers and space for three to six Spartanian fighters (although Muffuese usually have only shuttles instead fighters).
Muffuese was experiment, to create better and stronger variant of already proven GW battleship but instead of mass production it was intend to be only as squadron leader ship. While Muffuese firepower was almost double of standard battleship and its forward shields equal in strength to that of Ajax class battleship, it was expensive and rather unfit for longer engagements. Due larger energy demand ship had more energy reactors to power the main weapons however in the end it was shown that although with great firepower and excellent protection, Muffuese suffer from many problems and it has shorter endurance then standard battleships.
Muffuese was the only ship that was constructed although few more was considered. Commodore Marino was commanding officer of this ship. Muffuese survived the battle of Vermilion and later battle of the Coridor and Shiva. It is unknown what happen to this ship but it is quit possible that it is still active with "Irregulars"
Free Planets Alliance Battleship Hyperion.
Probably one of most known battleships in LOGH universe and royal pain in side for Reinhard von Lohengramm, Hyperion was the flagship of brilliant tactician Yang Wenli.
It was given to Yang Wenli after battle of Astarte. Hyperion was flagship of 13th fleet, later called Irregulars or Yang fleet. Ship saw lots of combat during its active service. After battle of Vermilion it was given to high admiral Merkatz who use it as his own flagship and slowly gathering Alliance forces again. Yang Wenli transfer his flag to battleship Ulysses and Merkatz remain in command of Hyperion. At the battle of Shiva, Hyperion is heavily damaged(possibly destroyed) and admiral Merkatz was killed. It is unknown if ship really survived or not.
Ship is 911 meters long and have 915 officers and enlisted. Armament: 32x forward neutron beams, 80x (40 on each side) cannons, multiple missile launchers, 24 spartanian fighters.
Together with Brunhild, Hyperion is one of two ships never been boarded or damaged in battle, both ships however were damaged (and Brunhild was boarded) during the final battle of the series, battle of Shiva.
(its not fully accurate, but it looks good enough).