From Halopedia, the Halo wiki
UNSC Belfast participated in the Battle for Arcadia in February 2531 along with the cruiser UNSC Pillar of Autumn, the UNSC Texas, the UNSC Armstrong, and later the support ship UNSC Spirit of Fire. Her and the other UNSC vessels deployed were able to destroy a CCS-class battlecruiser designated CCS-U321 which had her shields down at the time of the action. However, Belfast, along with Texas, was destroyed by the other battlecruiser present, CCS-U624.
The UNSC Belfast is most likely named after the modern-day capital of Northern Ireland, which was once a large port and shipbuilder famous for building the Titanic, or possibly HMS Belfast, a cruiser of the Royal Navy famous for helping sink the Scharnhorst during World War II.
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