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Using the generalised invariant formalism we derive a class of conformallyflat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalarcomponent. The method used is a development of the methods used earlier forpure radiation spacetimes of Petrov types O and N respectively. In this paperwe demonstrate how to handle, in the generalised invariant formalism,spacetimes with isotropy freedom and rich Killing vector structure. Once thespacetimes have been constructed, it is straightforward to deduce theirKarlhede classification: the Karlhede algorithm terminates at the fourthderivative order, and the spacetimes all have one degree of null isotropy andthree, four or five Killing vectors.Comment: 29 page

Obtaining a class of type O pure radiation metrics with a negative cosmological constant, using invariant operators