Background: Measurements of $beta$ decay provide important nuclear structure information that can be used to probe isospin asymmetries and inform nuclear astrophysics studies. Purpose: To measure the $beta$-delayed $gamma$ decay of $^{26}$P and compare the results with previous experimental results and shell-model calculations. Method: A $^{26}$P fast beam produced using nuclear fragmentation was implanted into a planar germanium detector. Its $beta$-delayed $gamma$-ray emission was measured with an array of 16 high-purity germanium detectors. Positrons emitted in the decay were detected in coincidence to reduce the background. Results: The absolute intensities of $^{26}$P $beta$-delayed $gamma$-rays were determined. A total of six new $beta$-decay branches and 15 new $gamma$-ray lines have been observed for the first time in $^{26}$P $beta$-decay. A complete $beta$-decay scheme was built for the allowed transitions to bound excited states of $^{26}$Si. $ft$ values and Gamow-Teller strengths were also determined for these transitions and compared with shell model calculations and the mirror $beta$-decay of $^{26}$Na, revealing significant mirror asymmetries. Conclusions: A very good agreement with theoretical predictions based on the USDB shell model is observed. The significant mirror asymmetry observed for the transition to the first excited state ($delta=51(10)%$) may be evidence for a proton halo in $^{26}$P.
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