  We present an analytic computation of the gluon-initiated contribution to
diphoton plus jet production at hadron colliders up to two loops in QCD. We
reconstruct the analytic form of the finite remainders from numerical
evaluations over finite fields including all colour contributions. Compact
expressions are found using the pentagon function basis. We provide a fast and
stable implementation for the colour- and helicity-summed interference between
the one-loop and two-loop finite remainders in C++ as part of the NJet library.
