Coordinate conjugations for Metaclass VII

SetDirectory["~/writing/WIP/Conjugation/"];
<<kappaLib.m

mat1=(({{a1, 0, 0, a4, 0, 0}, {0, a2, 0, 0, a5, 0}, {0, 0, a3, 0, 0, a6}, {a4, 0, 0, a1, 0, 0}, {0, a5, 0, 0, a2, 0}, {0, 0, a6, 0, 0, a3}}));

H2=(({{0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}}));
H3=(({{0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, -1}, {1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0}, {0, 0, -1, 0, 0, 0}}));
kappa1=emMatrixToKappa[mat1];
kappa2=emMatrixToKappa[H2.mat1.H2];
kappa3=emMatrixToKappa[H3.mat1.H3];

Union[Flatten[kappa1-kappa2]]
Union[Flatten[kappa1-kappa3]]