The USS Thelonii (NCC-1742) was a Federation Constitution-class (mk IXB Achernar-subclass) class I heavy cruiser starship in service to Starfleet in the mid-to-late 23rd century. The Thelonii was authorized for construction by Starfleet appropriation on stardate 5930 (late 2260s). (TOS reference: Star Fleet Technical Manual)
Galloway served aboard the Thelonii at some point prior to his assignment to the USS Enterprise in the mid-2270s. (TOS - Star Trek II Short Stories short story: "Intelligence Test")