M_{12}.2

{4^{2} : (6 × 2) ≤ \atop 4^{2} : D_{12}.2} 990 1a^{+} + 16ab + 45a^{−} + 54a^{±} + 55a^{±}bc +

66a^{+} + 99a^{±} + 144a^{+} + 176a^{+}

13

\begin{matrix}M_{12}.2 & S_{1} & S_{2} & S_{3} & S_{4} & S_{5} & S_{6} & S_{7} \\ χ_{1} & 1 & 192 & 96 & 48 & 64 & 64 & 192 \\ χ_{2} & 1 & −12 & −12 & 0 & 4 & 4 & 24 \\ χ_{3} & 1 & −12 & 0 & 0 & −12 & 12 & 0 \\ χ_{4} & 1 & −12 & 0 & 0 & 8 & −8 & 0 \\ χ_{5} & 1 & −12 & 8 & 0 & 4 & 4 & 4 \\ χ_{6} & 1 & −4b5 & 8 & 2 + 6r5 & −8 + 4b5 & −8 + 4b5 & −12 − 4r5 \\ χ_{7} & 1 & 12 & −12 & 12 & −12 & −12 & 24 \\ χ_{8} & 1 & 12 & −12 & 12 & 10 & 10 & −42 \\ χ_{9} & 1 & 12 & −24 & 0 & −4 & 4 & 0 \\ χ_{10} & 1 & 12 & −4 & −12 & 4 & 4 & −8 \\ χ_{11} & 1 & 12 & 12 & 0 & −4 & 4 & 0 \\ χ_{12} & 1 & 2 + 2r5 & 8 & 2 − 6r5 & −10 − 2r5 & −10 − 2r5 & −8 + 8b5 \\ χ_{13} & 1 & 24 & 0 & 0 & 8 & −8 & 0 \end{matrix}

\begin{matrix}M_{12}.2 & S_{8} & S_{9} & S_{10} & S_{11} & S_{12} & S_{13} \\ χ_{1} & 96 & 192 & 12 & 16 & 16 & 1 \\ χ_{2} & −12 & −12 & 6 & 4 & 4 & 1 \\ χ_{3} & 0 & 12 & 0 & 4 & −4 & −1 \\ χ_{4} & 0 & 12 & 0 & −1 & 1 & −1 \\ χ_{5} & 8 & −12 & −4 & −1 & −1 & 1 \\ χ_{6} & 8 & −4b5 & 4 + 2r5 & −4b5 & −4b5 & 1 \\ χ_{7} & −12 & 12 & −6 & −4 & −4 & 1 \\ χ_{8} & −12 & 12 & −6 & 7 & 7 & 1 \\ χ_{9} & 24 & −12 & 0 & −4 & 4 & −1 \\ χ_{10} & −4 & 12 & 2 & −4 & −4 & 1 \\ χ_{11} & −12 & −12 & 0 & −4 & 4 & −1 \\ χ_{12} & 8 & 2 + 2r5 & 4 − 2r5 & 2 + 2r5 & 2 + 2r5 & 1 \\ χ_{13} & 0 & −24 & 0 & 8 & −8 & −1 \end{matrix}

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