Standard and explicitly correlated coupled-cluster theory computations in conjunction with large basis sets are performed to characterize [Al,P,O] isomers. Three isomers, namely, linear-AlOP, bent-AlOP, and linear-OAlP, are found to be stable species. Their optimized equilibrium geometries, harmonic vibrational frequencies, rotational constants, and relative energies are deduced. In addition, a set of spectroscopic parameters is generated from the three-dimensional potential energy surfaces of each isomer at the (R)CCSD(T)/aug-cc-pVSZ level. The linear isomers have an X-3 Sigma(-) electronic ground state and are characterized as weakly bound systems or floppy molecules due to their low-frequency bending modes (<150 cm(-1)). The dipole moment of linear-AlOP is calculated to be 1.48 D. By comparison, a much larger dipole moment is computed for linear-OAlP (5.01 D), indicating lower ionic character in AlOP. Both the linear-OAlP and linear-AlOP isomers are suggested to be good candidates for detection in interstellar media by radio astronomy.