In this work we compute the Dixmier invariants and bitan-gents of the plane quartics with 3,6 or 9-cyclic automorphisms. We find that a quartic curve with 6-cyclic automorphism will have 3 horizontal bitangents which form an asyzygetic triple. We also discuss the linear matrix representation problem of such curves, and find a degree 6 equa-tion of 1 variable which solves the symbolic solution of the linear matrix representation problem for the curve with 6-cyclic autom...
