MSG 162.74
\[\begin{align*}
&E_{2}^{1,-1}=\mathbb{Z}^4\\
&E_{1}^{0,-1}=\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{A}_5}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{C}_3}]\oplus\mathbb{Z}_2[\boldsymbol{b}^{(0)}_{\text{D}_5}]\oplus\mathbb{Z}[\boldsymbol{b}^{(0)}_{\text{F}_3}]\\
&E_{1}^{1,-1}=\mathbb{Z}[\boldsymbol{b}^{(1)}_{a_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{b_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{c_3}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{e_1}]\oplus\mathbb{Z}[\boldsymbol{b}^{(1)}_{f_1}]\\
&E_{1}^{2,-1}=0
\end{align*}\]
\[\begin{align*}
&[X^{(1)}]^{-1}=\left(
\begin{array}{ccccc}
a_3 & b_3 & c_3 & e_1 & f_1 \\
0 & -1 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 \\
0 & -1 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 1 \\
\end{array}
\right)\\
&[V^{(0)}]^{-1}=\left(
\begin{array}{cccc}
\text{A}_5 & \text{C}_3 & \text{D}_5 & \text{F}_3 \\
0 & 1 & 0 & -1 \\
1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{array}
\right)\\
&\Lambda^{(0)}=\left(
\begin{array}{cccc}
1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
\end{array}
\right)
\end{align*}
\]