Spectroscopy of doubly magic $^{132}_{50}$Sn$_{82}$ has been performed with the GRIFFIN spectrometer at TRIUMF-ISAC following the $beta$ decay of $^{132}_{49}$In$_{83}$. The analysis has allowed for the placement of a total of 70 transitions and 29 excited states in $^{132}$Sn. Detailed spectroscopy has also been performed on $^{131}$Sb, resulting from the $beta$ decay of $^{131}$Sn, produced from the $beta$-delayed neutron decay of $^{132}$In. Measurement of $gamma$-rays in both $^{131}$Sn and $^{131}$Sb has led to the determination of the $beta$-delayed neutron emission probability, $P_{n}$, from $^{132}$In. This is the first time the $P_{n}$ has been measured for this nucleus using $gamma$ spectroscopy, and the new value of 12.3(4)% is consistent with the most recent $beta-n$ counting experiment. Additionally, $gamma$-$gamma$ angular correlations have been performed in $^{132}$Sn, supporting the spin assignments of several excited states. Novel ab initio calculations are presented which describe several of the excited states, and these are compared to the experimental spectrum.
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