In 2364, the T'Acog was sent to apprehend the Klingon criminals Korris, Konmel, and Kunivas, who had commandeered the Talarian freighter Batris. By feigning a power failure, the fugitives were able to lure the T'Acog into close range, and then destroyed it with a barrage of merculite rockets when the cruiser lowered its shields to board the freighter. There were no survivors. (TNG: "Heart of Glory")
Despite the ship's name being spelled as "T'Acog" in both the Encyclopedia and the episode's shooting script, K'Nera mispronounces the ship's name as "K'Atog" in the only occasion when the ship's name is mentioned in dialogue.
According to Star Trek: Star Charts (p. 65) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), there was a system named T'Acog, which might be the possible origin for the name of this starship, in the Beta Quadrant. The system's primary was a B-class star. This system was the site of a historic battle.
The Starships RPG sourcebook gives its registry as IKC-7750.