MSG 57.385

\[\begin{align*} &E_{2}^{1,-1}=\mathbb{Z} \times \mathbb{Z}_2\\ &E_{1}^{0,-1}=\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{A}_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{B}_1}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{G}_1}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{H}_1}]\\ &E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_1}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(1)}_{h_1}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(1)}_{h_2}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{k_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{l_1}]\\ &E_{1}^{2,-1}=2\mathbb{Z}[\boldsymbol{b}^{(2)}_{\beta _1}]\oplus2\mathbb{Z}[\boldsymbol{b}^{(2)}_{\zeta _1}] \end{align*}\]

\[\begin{align*} &[X^{(1)}]^{-1}=\left( \begin{array}{ccccc} e_1 & h_1 & h_2 & k_1 & l_1 \\ 1 & 0 & -2 & 1 & -1 \\ 0 & 1 & 1 & -1 & 1 \\ 0 & 0 & -1 & 1 & 0 \\ 0 & 0 & -2 & 1 & 0 \\ 0 & 0 & 2 & -1 & 1 \\ \end{array} \right)\\ &[V^{(0)}]^{-1}=\left( \begin{array}{cccc} \text{A}_1 & \text{B}_1 & \text{G}_1 & \text{H}_1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ \end{array} \right)\\ &\Lambda^{(0)}=\left( \begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \end{array} \right)\\ &[V^{(1)}]^{-1}=\left( \begin{array}{ccccc} e_1 & h_1 & h_2 & k_1 & l_1 \\ 1 & 0 & -2 & 1 & -1 \\ 0 & 1 & 1 & -1 & 1 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ \end{array} \right)\\ &\Sigma^{(1)}=\left( \begin{array}{ccccc} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ \end{array} \right) \end{align*} \]