TESS Hunt for Young and Maturing Exoplanets (THYME). VII. Membership, Rotation, and Lithium in the Young Cluster Group-X and a New Young Exoplanet

The public, all-sky surveys Gaia and TESS provide the ability to identify new young associations determine their ages. These enable study of planetary evolution by providing opportunities discover exoplanets. A association was recently identified Tang et al. F{\"u}rnkranz using astrometry from (called "Group-X" former). In this work, we investigate age membership association; validate exoplanet TOI 2048 b, which transit a young, late G dwarf in Group-X photometry TESS. We first candidate members EDR3 data. To infer association, measured rotation periods for clear color--period sequence indicates that is same as $300\pm50$ Myr-old NGC 3532. obtained optical spectra show lithium absorption consistent with age. Further, serendipitously new, small nearby Group-X, call MELANGE-2. Lastly, statistically $2.6\pm0.2$ \rearth\ radius planet on 13.8-day orbit around its 300 host star.