© 2018 American Physical Society. The key parameter to discuss the possibility of the pion condensation in nuclear matter, i.e., the so-called Landau-Migdal parameter g′, was extracted by measuring the double-differential cross sections for the (p,n) reaction at 216 MeV/u on a neutron-rich doubly magic unstable nucleus, Sn132 with the quality comparable to data taken with stable nuclei. The extracted strengths for Gamow-Teller (GT) transitions from Sn132 leading to Sb132 exhibit the GT giant resonance (GTR) at the excitation energy of 16.3±0.4(stat)±0.4(syst) MeV with the width of Γ=4.7±0.8 MeV. The integrated GT strength up to Ex=25 MeV is SGT-=53±5(stat)-10+11(syst), corresponding to 56% of Ikeda's sum rule of 3(N-Z)=96. The present result accurately constrains the Landau-Migdal parameter as g′=0.68±0.07, thanks to the high sensitivity of the GTR energy to g′. In combination with previous studies on the GTR for Zr90 and Pb208, the result of this work shows the constancy of this parameter in the nuclear chart region with (N-Z)/A=0.11 to 0.24 and A=90 to 208.