A metric is given which has no scalar invariants formed from its Riemann tensor or derivatives of its Riemann tensor and which admits, in its general form, no local homotheties or isometries. It is conformally flat and describes pure radiation. Subcases of this metric are the plane wave metric and a metric of Wils.

It is shown that the conformally flat radiation metric found by Wils (1989) requires the fourth covariant derivative of the Riemann tensor for the Karlhede classification to terminate. This contradicts a widely held opinion that the true upper bound is three. The metric can admit at most one Killing vector and/or a homothety.

It is shown that in many cases nontrivial Killing tensors and conformal Killing tensors can be obtained explicitly without having to solve the usually cumbersome Killing tensor equations just by knowing the Killing vectors and conformal Killing vectors of a spacetime. Two examples are given, the first is one of the Kimura metrics and the second an unphysical spacetime constructed to illustrate the method.

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