KIC 3868420: A high-amplitude $\delta$ Scuti-$\gamma$ Dor hybrid star crossing the Hertzsprung gap

We report a photometric and asteroseismic analysis of KIC 3868420, a newly identified high-amplitude $\delta$ Scuti-$\gamma$ Doradus hybrid star located in the Hertzsprung gap - a short-lived and rarely observed post-main-sequence phase. Using four years of Kepler long-cadence photometry, we detect 36 significant frequencies, including 11 independent modes spanning both low- and high-frequency regimes. Grid-based modeling with MESA and GYRE, including rotation, shows that five independent frequencies match a combination of radial p-modes and non-radial g-modes, supporting its hybrid nature. The best-fit models yield an evolved post-main-sequence star ($M\sim 2.26-2.30M_{\odot }$, $R\sim 4.41-4.43R_{\odot }$, $\tau \sim 5.4\times {10}^8$ yr), although degeneracies from rotation and unknown inclination preclude a unique solution. KIC 3868420 thus represents a rare example of a high-amplitude hybrid pulsator in the Hertzsprung gap, demonstrating that high-amplitude pulsation can coexist with mixed p/g-mode behavior in a rapidly evolving star. This finding highlights the value of space-based photometry for identifying such rare objects.