We study the isometry groups and Killing vector fields of a family of
pseudo-Riemannian metrics on Euclidean space which have neutral signature
(3+2p,3+2p). All are p+2 curvature homogeneous, all have vanishing Weyl scalar
invariants, all are geodesically complete, and all are 0-curvature modeled on
an indecomposible symmetric space. Some of these manifolds are not p+3
curvature homogeneous. Some are homogeneous but not symmetric
