$beta$ decay of $^{26}$P was used to populate the astrophysically important $E_x=$5929.4(8) keV $J^{pi}=3{^+}$ state of $^{26}$Si. Both $beta$-delayed proton at 418(8) keV and gamma ray at 1742(2) keV emitted from this state were measured simultaneously for the first time with corresponding absolute intensities of 11.1(12)% and 0.59(44)%, respectively. Besides, shell model calculations with weakly bound effects were performed to investigate the decay properties of other resonant states and a spin-parity of $4^+$ rather than $0^+$ was favored for the $E_x=$5945.9(40) keV state. Combining the experimental results and theoretical calculations, $^{25}$Al($p,gamma$)$^{26}$Si reaction rate in explosive hydrogen burning environments was calculated and compared with previous studies.
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