$$BR^3_{1}\quad U=\pmatrix{1 & 2 & 3 \cr 1 & 3 & 2 \cr 1 & 3 & 2}\quad D=\pmatrix{1 & 3 & 2 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad \hbox{order 4} \quad c_1 = 2, c_2 = 0$$
$$BR^3_{2}\quad U=\pmatrix{1 & 3 & 2 \cr 1 & 2 & 3 \cr 1 & 2 & 3}\quad D=\pmatrix{1 & 3 & 2 \cr 1 & 3 & 2 \cr 1 & 3 & 2}\quad \hbox{order 4} \quad c_1 = 4, c_2 = 2$$
$$BR^3_{3}\quad U=\pmatrix{2 & 3 & 1 \cr 2 & 3 & 1 \cr 2 & 3 & 1}\quad D=\pmatrix{2 & 3 & 1 \cr 2 & 3 & 1 \cr 2 & 3 & 1}\quad \hbox{order 6} \quad S, c_1 = 6, c_2 = 0$$