Complete caps in PG(3,q)PG(3,q) with q odd

In PG(3,q)PG(3,q) with q≡3mod4 and q⩾7q⩾7, a complete (q2+q+4)/2(q2+q+4)/2-cap is constructed. A characterization in terms of the collineation group preserving such a cap is also provided.