$$BR^3_{1}\quad U=\pmatrix{1 & 2 & 3 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad D=\pmatrix{1 & 2 & 3 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad \hbox{order 2} \quad S, c_1 = 6, c_2 = 0$$ $$BR^3_{2}\quad U=\pmatrix{1 & 2 & 3 \cr 1 & 3 & 2 \cr 1 & 3 & 2}\quad D=\pmatrix{1 & 2 & 3 \cr 1 & 3 & 2 \cr 1 & 3 & 2}\quad \hbox{order 2} \quad S, c_1 = 2, c_2 = 0$$ $$BR^3_{3}\quad U=\pmatrix{1 & 2 & 3 \cr 1 & 3 & 2 \cr 1 & 3 & 2}\quad D=\pmatrix{1 & 3 & 2 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad \hbox{order 4} \quad c_1 = 2, c_2 = 0$$ $$BR^3_{4}\quad U=\pmatrix{1 & 2 & 3 \cr 1 & 3 & 2 \cr 1 & 3 & 2}\quad D=\pmatrix{1 & 3 & 2 \cr 1 & 3 & 2 \cr 1 & 3 & 2}\quad \hbox{order 4} \quad c_1 = 4, c_2 = 2$$ $$BR^3_{5}\quad U=\pmatrix{1 & 2 & 3 \cr 3 & 1 & 2 \cr 2 & 3 & 1}\quad D=\pmatrix{1 & 3 & 2 \cr 1 & 3 & 2 \cr 1 & 3 & 2}\quad \hbox{order 3} \quad c_1 = 3, c_2 = 3$$ $$BR^3_{6}\quad U=\pmatrix{1 & 2 & 3 \cr 1 & 2 & 3 \cr 2 & 1 & 3}\quad D=\pmatrix{1 & 2 & 3 \cr 1 & 2 & 3 \cr 2 & 1 & 3}\quad \hbox{order 2} \quad S, c_1 = 2, c_2 = 0$$ $$BR^3_{7}\quad U=\pmatrix{1 & 3 & 2 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad D=\pmatrix{1 & 2 & 3 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad \hbox{order 4} \quad c_1 = 4, c_2 = 2$$ $$BR^3_{8}\quad U=\pmatrix{1 & 3 & 2 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad D=\pmatrix{1 & 3 & 2 \cr 1 & 3 & 2 \cr 1 & 3 & 2}\quad \hbox{order 4} \quad c_1 = 4, c_2 = 2$$ $$BR^3_{9}\quad U=\pmatrix{1 & 3 & 2 \cr 1 & 3 & 2 \cr 1 & 3 & 2}\quad D=\pmatrix{1 & 3 & 2 \cr 1 & 3 & 2 \cr 1 & 3 & 2}\quad \hbox{order 2} \quad S, c_1 = 6, c_2 = 0$$ $$BR^3_{10}\quad U=\pmatrix{1 & 3 & 2 \cr 3 & 2 & 1 \cr 2 & 1 & 3}\quad D=\pmatrix{1 & 2 & 3 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad \hbox{order 3} \quad c_1 = 3, c_2 = 3$$ $$BR^3_{11}\quad U=\pmatrix{2 & 1 & 3 \cr 1 & 3 & 2 \cr 3 & 2 & 1}\quad D=\pmatrix{2 & 3 & 1 \cr 2 & 3 & 1 \cr 2 & 3 & 1}\quad \hbox{order 3} \quad c_1 = 3, c_2 = 3$$ $$BR^3_{12}\quad U=\pmatrix{2 & 3 & 1 \cr 2 & 3 & 1 \cr 2 & 3 & 1}\quad D=\pmatrix{2 & 3 & 1 \cr 2 & 3 & 1 \cr 2 & 3 & 1}\quad \hbox{order 6} \quad S, c_1 = 6, c_2 = 0$$ $$BR^3_{13}\quad U=\pmatrix{2 & 3 & 1 \cr 2 & 3 & 1 \cr 2 & 3 & 1}\quad D=\pmatrix{3 & 1 & 2 \cr 3 & 1 & 2 \cr 3 & 1 & 2}\quad \hbox{order 2} \quad c_1 = 6, c_2 = 0$$ $$BR^3_{14}\quad U=\pmatrix{3 & 1 & 2 \cr 3 & 1 & 2 \cr 3 & 1 & 2}\quad D=\pmatrix{1 & 2 & 3 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad \hbox{order 6} \quad c_1 = 6, c_2 = 0$$ $$BR^3_{15}\quad U=\pmatrix{3 & 2 & 1 \cr 1 & 2 & 3 \cr 3 & 2 & 1}\quad D=\pmatrix{1 & 2 & 3 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad \hbox{order 4} \quad c_1 = 4, c_2 = 2$$ $$BR^3_{16}\quad U=\pmatrix{3 & 2 & 1 \cr 3 & 2 & 1 \cr 3 & 2 & 1}\quad D=\pmatrix{1 & 2 & 3 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad \hbox{order 4} \quad c_1 = 6, c_2 = 0$$