(coexisting on another dimensional plane)
The ISS Charon was a Terran starship that was in service to the Terran Empire Starfleet in the mid-23rd century. Its captain was Maddox. Along with serving as the flagship of the Terran fleet, this vessel housed the palace of the Terran emperor, Philippa Georgiou.
Following this strike, the Emperor commanded Michael Burnham to deliver Gabriel Lorca to her aboard the Charon. Unbeknownst to Burnham, who believed Lorca to be the one from her own universe, Lorca was using her to board the Charon in an attempt to seize the throne for himself. After escaping his agony booth, he released his followers and launched his coup. They managed to eliminate Georgiou's forces and took control of the throne room, but were undermined when Georgiou and Burnham were brought in as prisoners by Lorca's troops. While this was occurring, the Federation starship USS Discovery dropped out of warp on Burnham's command and opened fire, damaging the throne room. This gave Burnham a chance to drop the containment field around the Charon's mycelial power core so the Discovery could destroy it. During this attack, Georgiou killed Lorca, and she and Burnham were transported to safety aboard the Discovery. As Lorca's troops moved to re-take control, Discovery opened fire on the Charon's power core, obliterating the vessel. (DIS: "What's Past Is Prologue")
Described as "city-sized" and divided into at least seventeen decks, the Charon contained vast hangars, an entire prison complex full of agony booths, and barracks and facilities for ten battalions of Imperial soldiers. Corridors throughout the Charon were equipped with force field emitters and hidden phaser cannons that could fire on targets automatically. Other on-board facilities included luxurious staterooms for Imperial dignitaries and multiple laboratories.
The ship was powered by a massive super-mycelial reactor, which glowed a bright orange in the center of the ship. It was armed with powerful missiles that were able to breach a planet's crust, and cause massive damage to wide areas. (DIS: "The Wolf Inside", "Vaulting Ambition", "What's Past Is Prologue")
The Charon was designed by John Eaves. The ship was originally written as a planet-destroying doomsday weapon with a palace on top; thus, Eaves took inspiration from the planet killer from "The Doomsday Machine", envisioning it "inside-out" and "made of whale bones." Eaves collaborated with Scott Schneider and William Budge in refining and finishing the model. (Star Trek: The Art of John Eaves, pp. 198–199)
Production Designer Tamara Deverell also assisted with the design. She was motivated to differentiate the architecture aboard the ship from the Klingon architectural style established earlier in the first season of Star Trek: Discovery. "I went to a kind of Brutalist aesthetic, looking at a lot of Soviet and Czechoslovakian Brutalist buildings and sculptures," she remembered. "Big shapes that we could extend with visual effects but that wouldn't break the bank, but still be really effective. And I was trying to make something that was terrifying. The Charon ship blew my mind, because we built this entire huge, enormous ship that's the size of a city. I felt like, because it's so large, it needed its own power source, so then I started playing around with this idea that it had a mini sun or moon and all its energy came from that. And then the writers took that and made it part of the story, which is the kind of thing that is just your dream as a production designer, and it became this mycelium sun." ("Designing Discovery", DIS Season 1 DVD & Blu-ray special features)
According to technical data prepared for the San Diego Comic Con in 2018, the ISS Charon had 450 decks, an unknown crew complement but capacity for 200,000+, a maximum warp of 9.6, and twelve impulse engines (approximate warp factor 0.75). A schematic revealed that it had space dedicated to mycelium farming. The central orb was described in this schematic as a "mycelium sun". 
In Star Trek Online, the Styx-class Terran dreadnought obtainable by players is based on the Charon. The wreckage of the Charon is scattered through space and time, some of it eventually coming to rest on the planet Pahvo in the 25th century. The Task Force Operation "Pahvo Dissension" involves clearing Pahvan crystals of the agonizer energy from the Charon's wreckage and defeating Terran forces who had survived the ship's destruction.