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Elements of the group are displayed as matrices in $\SOPlus(6,4)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 7P | 17P | ||||||
| $\SOPlus(6,4)$ | 1A | $1$ | $1$ | not computed | 1A | 1A | 1A | 1A | 1A | $\left(\begin{array}{llllll}1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 2A | $2$ | $1008$ | not computed | 1A | 2A | 2A | 2A | 2A | $\left(\begin{array}{llllll}1 & 1 & \alpha^{2} & 0 & \alpha^{2} & \alpha^{2} \\ 0 & 0 & \alpha^{2} & 0 & \alpha^{2} & \alpha^{2} \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & \alpha^{2} & 1 & \alpha^{2} & \alpha^{2} \\ 0 & \alpha & 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 2B | $2$ | $5355$ | not computed | 1A | 2B | 2B | 2B | 2B | $\left(\begin{array}{llllll}0 & \alpha^{2} & 1 & \alpha^{2} & 1 & 0 \\ \alpha & 0 & \alpha & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 & 1 & \alpha^{2} \\ 0 & 0 & 0 & 1 & \alpha & 1 \\ 0 & 0 & 0 & 0 & 0 & \alpha^{2} \\ 0 & 0 & 0 & 0 & \alpha & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 2C | $2$ | $64260$ | not computed | 1A | 2C | 2C | 2C | 2C | $\left(\begin{array}{llllll}1 & \alpha & 1 & \alpha^{2} & \alpha^{2} & \alpha \\ 1 & \alpha & 1 & \alpha & \alpha^{2} & \alpha^{2} \\ \alpha & \alpha^{2} & \alpha & 0 & \alpha & \alpha^{2} \\ \alpha & 1 & \alpha & \alpha & 1 & 1 \\ 0 & \alpha & 1 & \alpha^{2} & \alpha & \alpha \\ \alpha^{2} & 0 & \alpha & \alpha & 1 & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 2D | $2$ | $257040$ | not computed | 1A | 2D | 2D | 2D | 2D | $\left(\begin{array}{llllll}\alpha^{2} & \alpha^{2} & \alpha^{2} & \alpha^{2} & 0 & \alpha^{2} \\ 1 & 0 & 0 & \alpha^{2} & \alpha & 0 \\ 0 & \alpha^{2} & \alpha^{2} & \alpha^{2} & \alpha^{2} & \alpha^{2} \\ \alpha & 1 & \alpha & \alpha^{2} & 0 & \alpha^{2} \\ 1 & \alpha^{2} & 1 & \alpha^{2} & 0 & \alpha^{2} \\ \alpha & 1 & \alpha & 0 & 1 & \alpha^{2} \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 3A | $3$ | $10880$ | not computed | 3A | 1A | 3A | 3A | 3A | $\left(\begin{array}{llllll}0 & \alpha^{2} & \alpha^{2} & 1 & 1 & 0 \\ 0 & \alpha^{2} & \alpha^{2} & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 & 0 & 1 \\ \alpha & \alpha & 0 & 0 & \alpha^{2} & \alpha^{2} \\ \alpha^{2} & 0 & \alpha & 1 & \alpha & \alpha^{2} \\ 0 & \alpha^{2} & \alpha & 0 & 0 & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 3B | $3$ | $91392$ | not computed | 3B | 1A | 3B | 3B | 3B | $\left(\begin{array}{llllll}1 & 0 & \alpha & 0 & \alpha & 0 \\ 0 & 1 & 0 & \alpha^{2} & 0 & \alpha^{2} \\ 0 & 0 & \alpha^{2} & 0 & \alpha & 0 \\ 0 & 0 & 0 & \alpha & 0 & \alpha^{2} \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 3C | $3$ | $1827840$ | not computed | 3C | 1A | 3C | 3C | 3C | $\left(\begin{array}{llllll}\alpha & 1 & \alpha & \alpha^{2} & \alpha & \alpha \\ 0 & \alpha & 0 & \alpha^{2} & 0 & 1 \\ 0 & \alpha & \alpha^{2} & \alpha^{2} & 1 & \alpha^{2} \\ 0 & 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & \alpha & 0 & 0 & \alpha \\ 0 & 0 & 0 & 0 & 0 & \alpha^{2} \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 4A | $4$ | $1285200$ | not computed | 2B | 4A | 4A | 4A | 4A | $\left(\begin{array}{llllll}1 & 1 & \alpha^{2} & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ \alpha & \alpha & \alpha^{2} & 0 & 1 & 1 \\ \alpha & 0 & 1 & 1 & 0 & \alpha^{2} \\ 0 & \alpha & \alpha & 0 & 0 & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 4B | $4$ | $1542240$ | not computed | 2C | 4B | 4B | 4B | 4B | $\left(\begin{array}{llllll}0 & \alpha^{2} & 0 & 0 & 0 & \alpha \\ \alpha & \alpha & \alpha & \alpha^{2} & 1 & \alpha \\ 1 & 0 & 1 & \alpha^{2} & \alpha^{2} & \alpha^{2} \\ \alpha^{2} & \alpha^{2} & \alpha & 1 & \alpha & 1 \\ \alpha & \alpha^{2} & 1 & 1 & 1 & 1 \\ \alpha & \alpha & 0 & \alpha^{2} & \alpha^{2} & \alpha^{2} \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 4C | $4$ | $2570400$ | not computed | 2C | 4C | 4C | 4C | 4C | $\left(\begin{array}{llllll}\alpha & 0 & \alpha & 0 & \alpha^{2} & 0 \\ \alpha^{2} & 0 & 1 & 0 & 1 & 0 \\ \alpha^{2} & 0 & \alpha^{2} & 0 & \alpha^{2} & 0 \\ 1 & \alpha^{2} & \alpha & 0 & \alpha & 1 \\ 1 & 0 & 1 & \alpha^{2} & 1 & \alpha^{2} \\ 0 & 1 & 0 & 1 & 0 & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 4D | $4$ | $15422400$ | not computed | 2C | 4D | 4D | 4D | 4D | $\left(\begin{array}{llllll}\alpha^{2} & 0 & \alpha^{2} & 0 & \alpha & 0 \\ \alpha & 0 & 1 & 0 & 1 & 0 \\ \alpha^{2} & 1 & \alpha^{2} & 0 & \alpha & \alpha^{2} \\ 0 & 0 & \alpha & 0 & 1 & 0 \\ \alpha^{2} & \alpha^{2} & \alpha^{2} & \alpha & \alpha & 0 \\ \alpha & \alpha & \alpha^{2} & 1 & 0 & \alpha \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 5A1 | $5$ | $48384$ | not computed | 5A2 | 5A2 | 1A | 5A2 | 5A2 | $\left(\begin{array}{llllll}\alpha & 1 & 1 & 0 & 1 & \alpha^{2} \\ 1 & \alpha^{2} & \alpha & 0 & \alpha & 1 \\ \alpha^{2} & 0 & \alpha^{2} & \alpha & \alpha^{2} & \alpha \\ \alpha^{2} & \alpha & \alpha^{2} & 0 & 0 & 0 \\ 0 & \alpha & 1 & \alpha^{2} & \alpha & \alpha \\ 1 & 1 & 0 & 1 & \alpha^{2} & \alpha^{2} \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 5A2 | $5$ | $48384$ | not computed | 5A1 | 5A1 | 1A | 5A1 | 5A1 | $\left(\begin{array}{llllll}\alpha & 0 & \alpha & \alpha & \alpha^{2} & \alpha \\ 1 & 1 & \alpha^{2} & \alpha^{2} & 1 & \alpha^{2} \\ 0 & \alpha^{2} & \alpha^{2} & 1 & 1 & \alpha^{2} \\ 1 & \alpha & \alpha & 1 & \alpha & 1 \\ 1 & 1 & 0 & 1 & \alpha & \alpha \\ \alpha^{2} & \alpha & \alpha^{2} & 1 & 0 & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 5B1 | $5$ | $1096704$ | not computed | 5B2 | 5B2 | 1A | 5B2 | 5B2 | $\left(\begin{array}{llllll}0 & 0 & \alpha & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 & \alpha \\ \alpha^{2} & \alpha^{2} & \alpha & \alpha & 1 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ \alpha^{2} & \alpha^{2} & \alpha^{2} & \alpha & 0 & \alpha \\ 0 & \alpha^{2} & 0 & \alpha^{2} & 0 & \alpha^{2} \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 5B2 | $5$ | $1096704$ | not computed | 5B1 | 5B1 | 1A | 5B1 | 5B1 | $\left(\begin{array}{llllll}1 & \alpha & \alpha^{2} & 0 & \alpha & \alpha^{2} \\ 0 & 0 & 0 & 1 & 0 & \alpha^{2} \\ \alpha & \alpha^{2} & 1 & 1 & \alpha & 0 \\ 0 & 1 & 0 & 0 & 0 & \alpha \\ \alpha & \alpha & 0 & 0 & \alpha^{2} & \alpha^{2} \\ 0 & \alpha & 0 & \alpha & 0 & \alpha^{2} \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 5C | $5$ | $13160448$ | not computed | 5C | 5C | 1A | 5C | 5C | $\left(\begin{array}{llllll}\alpha & \alpha & 0 & 0 & 1 & 1 \\ \alpha & 0 & 0 & \alpha^{2} & 1 & 0 \\ 1 & \alpha^{2} & \alpha^{2} & \alpha^{2} & \alpha & \alpha^{2} \\ 1 & 0 & 0 & 0 & \alpha^{2} & 0 \\ 0 & 1 & \alpha & 0 & 0 & \alpha^{2} \\ \alpha^{2} & 0 & 0 & \alpha & 1 & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 6A | $6$ | $2741760$ | not computed | 3B | 2B | 6A | 6A | 6A | $\left(\begin{array}{llllll}0 & \alpha^{2} & \alpha & \alpha^{2} & \alpha & 0 \\ \alpha & 0 & \alpha & \alpha^{2} & 0 & \alpha^{2} \\ 0 & 0 & \alpha & 0 & \alpha & \alpha^{2} \\ 0 & 0 & 0 & \alpha^{2} & \alpha & \alpha^{2} \\ 0 & 0 & 0 & 0 & 0 & \alpha^{2} \\ 0 & 0 & 0 & 0 & \alpha & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 6B | $6$ | $3427200$ | not computed | 3A | 2B | 6B | 6B | 6B | $\left(\begin{array}{llllll}\alpha^{2} & 0 & 0 & \alpha^{2} & \alpha^{2} & 0 \\ 0 & \alpha & 1 & 0 & 0 & \alpha^{2} \\ 0 & 0 & \alpha^{2} & 0 & 0 & \alpha^{2} \\ 0 & 1 & \alpha^{2} & \alpha & 1 & \alpha \\ 0 & 0 & \alpha & 0 & \alpha^{2} & \alpha \\ 0 & 0 & 0 & 0 & 0 & \alpha \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 6C | $6$ | $5483520$ | not computed | 3C | 2A | 6C | 6C | 6C | $\left(\begin{array}{llllll}\alpha^{2} & 1 & 0 & \alpha & 0 & 0 \\ 0 & \alpha & \alpha^{2} & \alpha & \alpha^{2} & \alpha^{2} \\ 0 & \alpha & \alpha^{2} & 0 & 0 & \alpha \\ 0 & 0 & \alpha^{2} & 0 & \alpha^{2} & \alpha^{2} \\ 0 & 0 & \alpha^{2} & 0 & 0 & \alpha \\ 0 & 0 & 0 & 0 & 0 & \alpha \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 6D | $6$ | $5483520$ | not computed | 3B | 2A | 6D | 6D | 6D | $\left(\begin{array}{llllll}1 & \alpha^{2} & 0 & 1 & \alpha^{2} & \alpha \\ 0 & 0 & \alpha & 0 & \alpha^{2} & 0 \\ \alpha^{2} & \alpha & 0 & \alpha^{2} & \alpha^{2} & \alpha \\ \alpha & 0 & \alpha & 0 & \alpha & 0 \\ \alpha & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & \alpha & 0 & \alpha & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 6E | $6$ | $20563200$ | not computed | 3B | 2C | 6E | 6E | 6E | $\left(\begin{array}{llllll}\alpha & 1 & 0 & \alpha & 1 & \alpha^{2} \\ 1 & \alpha & 1 & \alpha & 0 & \alpha \\ \alpha & 0 & 0 & 1 & 1 & 0 \\ 1 & 0 & \alpha^{2} & \alpha & 0 & 1 \\ 1 & 0 & 0 & \alpha & \alpha^{2} & 0 \\ \alpha & 0 & 0 & \alpha^{2} & 0 & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 6F | $6$ | $27417600$ | not computed | 3C | 2B | 6F | 6F | 6F | $\left(\begin{array}{llllll}1 & 0 & \alpha^{2} & 0 & 1 & 0 \\ \alpha & \alpha & \alpha^{2} & 1 & \alpha^{2} & 1 \\ 0 & 0 & \alpha & 0 & 1 & 0 \\ 1 & \alpha^{2} & 0 & 1 & 0 & 0 \\ \alpha & 0 & \alpha & 0 & \alpha^{2} & 0 \\ \alpha^{2} & \alpha^{2} & \alpha & \alpha & \alpha & \alpha^{2} \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 6G | $6$ | $82252800$ | not computed | 3C | 2D | 6G | 6G | 6G | $\left(\begin{array}{llllll}0 & \alpha^{2} & \alpha & \alpha^{2} & \alpha & \alpha^{2} \\ 1 & 0 & 1 & \alpha & 1 & \alpha \\ \alpha^{2} & \alpha^{2} & 1 & \alpha^{2} & \alpha & \alpha^{2} \\ 0 & \alpha & 0 & \alpha & 0 & 0 \\ 0 & \alpha^{2} & 1 & \alpha^{2} & 1 & \alpha^{2} \\ \alpha^{2} & \alpha & \alpha^{2} & 0 & \alpha^{2} & \alpha \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 7A | $7$ | $31334400$ | not computed | 7A | 7A | 7A | 1A | 7A | $\left(\begin{array}{llllll}\alpha & \alpha^{2} & 1 & 0 & 1 & \alpha \\ \alpha^{2} & \alpha^{2} & 0 & 1 & \alpha^{2} & \alpha^{2} \\ 1 & 1 & \alpha & \alpha & 0 & \alpha^{2} \\ \alpha & 1 & \alpha^{2} & \alpha & \alpha^{2} & 1 \\ 0 & \alpha^{2} & 1 & \alpha^{2} & 1 & \alpha \\ 1 & 1 & 1 & \alpha & \alpha^{2} & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 8A | $8$ | $61689600$ | not computed | 4A | 8A | 8A | 8A | 8A | $\left(\begin{array}{llllll}1 & \alpha & 0 & 1 & \alpha & \alpha^{2} \\ \alpha & 1 & 0 & 0 & \alpha^{2} & \alpha \\ \alpha & 0 & 0 & \alpha & \alpha^{2} & 0 \\ \alpha & \alpha^{2} & \alpha & \alpha & 1 & 0 \\ 0 & 0 & \alpha^{2} & 0 & 0 & \alpha^{2} \\ \alpha^{2} & 0 & \alpha & \alpha^{2} & \alpha & \alpha \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 9A | $9$ | $31334400$ | not computed | 9A | 3A | 9A | 9A | 9A | $\left(\begin{array}{llllll}\alpha^{2} & \alpha & \alpha & 0 & \alpha^{2} & \alpha \\ \alpha^{2} & \alpha^{2} & \alpha & \alpha^{2} & \alpha^{2} & 1 \\ 0 & \alpha^{2} & \alpha^{2} & \alpha & \alpha & \alpha^{2} \\ 1 & \alpha^{2} & \alpha^{2} & \alpha & 1 & \alpha \\ 1 & \alpha^{2} & \alpha^{2} & 1 & 0 & \alpha^{2} \\ 1 & 0 & \alpha & \alpha^{2} & \alpha^{2} & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 10A1 | $10$ | $3290112$ | not computed | 5B1 | 10A3 | 2A | 10A3 | 10A3 | $\left(\begin{array}{llllll}\alpha^{2} & 0 & \alpha^{2} & 1 & \alpha & 1 \\ 0 & 1 & \alpha^{2} & 1 & \alpha^{2} & \alpha^{2} \\ \alpha & \alpha & \alpha^{2} & \alpha & \alpha & 1 \\ 0 & \alpha & \alpha^{2} & \alpha & \alpha^{2} & \alpha \\ \alpha & \alpha^{2} & \alpha^{2} & 1 & \alpha & 1 \\ 0 & \alpha & 0 & \alpha & 0 & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 10A3 | $10$ | $3290112$ | not computed | 5B2 | 10A1 | 2A | 10A1 | 10A1 | $\left(\begin{array}{llllll}\alpha^{2} & 1 & 1 & 1 & \alpha^{2} & \alpha^{2} \\ 0 & \alpha & \alpha^{2} & \alpha & \alpha^{2} & 1 \\ \alpha^{2} & 0 & \alpha^{2} & 1 & \alpha^{2} & 1 \\ 0 & 1 & \alpha^{2} & 1 & \alpha^{2} & \alpha^{2} \\ \alpha^{2} & \alpha & \alpha^{2} & 1 & \alpha^{2} & \alpha^{2} \\ 0 & \alpha^{2} & 0 & \alpha^{2} & 0 & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 10B1 | $10$ | $3290112$ | not computed | 5A2 | 10B3 | 2A | 10B3 | 10B3 | $\left(\begin{array}{llllll}1 & \alpha^{2} & \alpha^{2} & 0 & \alpha & 1 \\ \alpha & 0 & \alpha & 0 & \alpha^{2} & 0 \\ 1 & 0 & 1 & \alpha & \alpha^{2} & \alpha \\ \alpha & \alpha & 0 & 0 & \alpha^{2} & \alpha^{2} \\ 0 & \alpha & \alpha^{2} & 1 & \alpha & 1 \\ \alpha & 0 & \alpha & 1 & \alpha & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 10B3 | $10$ | $3290112$ | not computed | 5A1 | 10B1 | 2A | 10B1 | 10B1 | $\left(\begin{array}{llllll}1 & 1 & \alpha & \alpha^{2} & \alpha & \alpha^{2} \\ \alpha & 1 & 0 & \alpha^{2} & 1 & \alpha^{2} \\ 1 & \alpha & 1 & 0 & 1 & \alpha \\ \alpha & \alpha^{2} & \alpha^{2} & \alpha & \alpha^{2} & \alpha \\ 0 & 1 & 0 & 1 & 0 & 0 \\ \alpha & 0 & \alpha & 1 & \alpha & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 10C1 | $10$ | $12337920$ | not computed | 5A2 | 10C3 | 2C | 10C3 | 10C3 | $\left(\begin{array}{llllll}\alpha^{2} & 1 & \alpha & 1 & 0 & \alpha^{2} \\ 1 & \alpha & \alpha^{2} & \alpha & \alpha^{2} & 0 \\ 1 & \alpha & \alpha^{2} & \alpha^{2} & 0 & \alpha \\ 1 & \alpha & \alpha & \alpha & 1 & 1 \\ \alpha^{2} & \alpha^{2} & \alpha & \alpha^{2} & 0 & \alpha \\ \alpha^{2} & \alpha & 0 & 0 & 1 & \alpha^{2} \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 10C3 | $10$ | $12337920$ | not computed | 5A1 | 10C1 | 2C | 10C1 | 10C1 | $\left(\begin{array}{llllll}1 & 1 & \alpha & \alpha^{2} & \alpha^{2} & \alpha \\ 0 & \alpha & \alpha^{2} & \alpha^{2} & 1 & \alpha^{2} \\ 0 & 0 & 1 & 0 & \alpha & 1 \\ \alpha^{2} & 0 & 0 & \alpha & \alpha & 0 \\ 1 & 1 & 0 & \alpha^{2} & \alpha^{2} & \alpha^{2} \\ 0 & \alpha & 0 & \alpha^{2} & 0 & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 10D1 | $10$ | $16450560$ | not computed | 5B1 | 10D3 | 2B | 10D3 | 10D3 | $\left(\begin{array}{llllll}0 & \alpha & 1 & \alpha & 1 & \alpha^{2} \\ \alpha & 0 & \alpha & 1 & \alpha & 1 \\ 0 & 1 & 1 & 1 & 1 & \alpha^{2} \\ \alpha^{2} & 0 & \alpha^{2} & 1 & 1 & 1 \\ 0 & 1 & 0 & 1 & 0 & \alpha^{2} \\ \alpha^{2} & 0 & \alpha^{2} & 0 & 1 & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 10D3 | $10$ | $16450560$ | not computed | 5B2 | 10D1 | 2B | 10D1 | 10D1 | $\left(\begin{array}{llllll}0 & \alpha & 1 & \alpha & 1 & 1 \\ 0 & 0 & 0 & 1 & \alpha^{2} & 1 \\ 0 & \alpha & 1 & \alpha & 1 & 0 \\ 1 & 0 & 1 & 1 & 1 & 1 \\ 0 & \alpha & 0 & \alpha & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 10E | $10$ | $39481344$ | not computed | 5C | 10E | 2A | 10E | 10E | $\left(\begin{array}{llllll}1 & \alpha^{2} & \alpha^{2} & 1 & 1 & 0 \\ \alpha & 1 & 1 & \alpha & 0 & 1 \\ \alpha^{2} & \alpha & 0 & \alpha^{2} & 0 & 0 \\ \alpha & 1 & 1 & 1 & \alpha & \alpha \\ \alpha & \alpha & 1 & \alpha^{2} & \alpha & 0 \\ \alpha & 0 & \alpha & \alpha & 0 & \alpha \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 10F1 | $10$ | $49351680$ | not computed | 5B2 | 10F3 | 2D | 10F3 | 10F3 | $\left(\begin{array}{llllll}\alpha^{2} & \alpha^{2} & \alpha^{2} & \alpha & 0 & \alpha \\ \alpha & \alpha & 1 & 1 & \alpha & 1 \\ \alpha^{2} & \alpha^{2} & 1 & \alpha & 0 & \alpha^{2} \\ \alpha^{2} & \alpha & 0 & 1 & \alpha & 1 \\ 0 & \alpha^{2} & \alpha & 0 & 0 & 1 \\ \alpha^{2} & 0 & \alpha^{2} & 1 & \alpha & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 10F3 | $10$ | $49351680$ | not computed | 5B1 | 10F1 | 2D | 10F1 | 10F1 | $\left(\begin{array}{llllll}0 & 0 & 0 & \alpha & \alpha & 0 \\ \alpha^{2} & \alpha & \alpha & 0 & \alpha & 1 \\ 1 & \alpha & \alpha & 0 & \alpha^{2} & 1 \\ 1 & \alpha^{2} & \alpha^{2} & \alpha & 0 & 1 \\ \alpha & \alpha^{2} & \alpha^{2} & 0 & \alpha^{2} & 1 \\ 1 & \alpha & 1 & 0 & \alpha^{2} & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 12A | $12$ | $41126400$ | not computed | 6B | 4A | 12A | 12A | 12A | $\left(\begin{array}{llllll}\alpha & 1 & \alpha & \alpha^{2} & \alpha^{2} & 1 \\ 0 & 0 & \alpha & 0 & 0 & \alpha^{2} \\ 0 & \alpha^{2} & 1 & 0 & 0 & \alpha^{2} \\ \alpha^{2} & \alpha & 1 & 1 & \alpha^{2} & 0 \\ \alpha^{2} & 1 & \alpha & \alpha & 0 & 1 \\ 0 & 1 & 1 & 0 & 0 & \alpha^{2} \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 12B | $12$ | $82252800$ | not computed | 6E | 4C | 12B | 12B | 12B | $\left(\begin{array}{llllll}1 & \alpha^{2} & 1 & \alpha & 1 & 1 \\ \alpha^{2} & \alpha & 1 & 1 & 1 & 1 \\ \alpha & 1 & \alpha & \alpha^{2} & 1 & 0 \\ \alpha^{2} & 0 & \alpha^{2} & \alpha^{2} & \alpha^{2} & \alpha^{2} \\ \alpha & 1 & \alpha & 0 & \alpha & 1 \\ 0 & \alpha^{2} & \alpha^{2} & 1 & 1 & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 15A1 | $15$ | $2193408$ | not computed | 15A2 | 5B1 | 3B | 15A2 | 15A2 | $\left(\begin{array}{llllll}1 & 0 & \alpha^{2} & 0 & \alpha & 0 \\ 0 & \alpha^{2} & 0 & 0 & 0 & 1 \\ \alpha & 0 & 0 & 0 & \alpha^{2} & 0 \\ 0 & \alpha & 0 & 1 & 0 & 0 \\ \alpha & 0 & \alpha & 0 & 1 & 0 \\ 0 & \alpha & 0 & \alpha & 0 & \alpha^{2} \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 15A2 | $15$ | $2193408$ | not computed | 15A1 | 5B2 | 3B | 15A1 | 15A1 | $\left(\begin{array}{llllll}\alpha^{2} & 0 & 0 & 0 & \alpha & 0 \\ 0 & 0 & 0 & \alpha & 0 & 0 \\ \alpha^{2} & 0 & 0 & 0 & 0 & 0 \\ 0 & \alpha^{2} & 0 & 1 & 0 & \alpha \\ \alpha^{2} & 0 & \alpha^{2} & 0 & \alpha^{2} & 0 \\ 0 & \alpha^{2} & 0 & \alpha^{2} & 0 & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 15B1 | $15$ | $13160448$ | not computed | 15B2 | 5A2 | 3B | 15B2 | 15B2 | $\left(\begin{array}{llllll}1 & \alpha & \alpha^{2} & \alpha^{2} & \alpha^{2} & \alpha^{2} \\ \alpha & \alpha^{2} & 1 & \alpha^{2} & 0 & \alpha \\ \alpha & \alpha^{2} & 1 & 1 & \alpha^{2} & \alpha \\ 0 & \alpha^{2} & \alpha & 0 & 0 & \alpha^{2} \\ \alpha & \alpha^{2} & \alpha & 1 & 1 & \alpha^{2} \\ \alpha^{2} & 0 & 0 & 1 & 0 & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 15B2 | $15$ | $13160448$ | not computed | 15B1 | 5A1 | 3B | 15B1 | 15B1 | $\left(\begin{array}{llllll}0 & 1 & \alpha & 1 & \alpha & 1 \\ 0 & 0 & \alpha & 0 & \alpha & 0 \\ 1 & \alpha^{2} & 0 & \alpha^{2} & 1 & \alpha^{2} \\ 0 & \alpha^{2} & 1 & \alpha^{2} & 1 & \alpha \\ 0 & 0 & 0 & \alpha^{2} & 1 & \alpha^{2} \\ \alpha^{2} & \alpha & 0 & \alpha & \alpha & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 15C1 | $15$ | $21934080$ | not computed | 15C2 | 5B1 | 3C | 15C2 | 15C2 | $\left(\begin{array}{llllll}\alpha^{2} & 0 & \alpha^{2} & 0 & 0 & 0 \\ 0 & \alpha & 0 & \alpha^{2} & 0 & \alpha^{2} \\ 1 & \alpha^{2} & 0 & 1 & \alpha & 1 \\ 0 & 0 & 0 & 1 & 0 & 1 \\ 1 & 0 & 1 & \alpha & \alpha^{2} & \alpha \\ 0 & \alpha^{2} & 0 & \alpha^{2} & 0 & 1 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 15C2 | $15$ | $21934080$ | not computed | 15C1 | 5B2 | 3C | 15C1 | 15C1 | $\left(\begin{array}{llllll}1 & \alpha & \alpha & \alpha^{2} & 1 & \alpha^{2} \\ 0 & 1 & 0 & 0 & 0 & 1 \\ 1 & \alpha & 1 & \alpha^{2} & 1 & 1 \\ 0 & \alpha^{2} & 0 & \alpha & 0 & 0 \\ 1 & \alpha & 0 & \alpha^{2} & 0 & 0 \\ 0 & \alpha & 0 & \alpha & 0 & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 15D | $15$ | $26320896$ | not computed | 15D | 5C | 3B | 15D | 15D | $\left(\begin{array}{llllll}\alpha^{2} & \alpha & \alpha^{2} & 0 & 0 & 0 \\ 0 & \alpha^{2} & 0 & \alpha & 0 & \alpha \\ 1 & \alpha & \alpha & \alpha^{2} & \alpha & \alpha \\ \alpha & 1 & \alpha & \alpha & 0 & \alpha \\ \alpha^{2} & \alpha & \alpha^{2} & \alpha^{2} & \alpha & \alpha \\ \alpha^{2} & \alpha & 1 & \alpha^{2} & 1 & \alpha \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 15E1 | $15$ | $43868160$ | not computed | 15E2 | 5B2 | 3A | 15E2 | 15E2 | $\left(\begin{array}{llllll}1 & 1 & \alpha^{2} & \alpha^{2} & \alpha & 0 \\ 0 & \alpha & \alpha^{2} & 1 & \alpha & 0 \\ \alpha^{2} & 1 & 0 & \alpha^{2} & 0 & 0 \\ \alpha & 0 & \alpha & 1 & \alpha^{2} & 1 \\ 1 & \alpha^{2} & 1 & \alpha^{2} & \alpha & \alpha \\ 1 & 1 & 1 & 0 & \alpha & \alpha \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 15E2 | $15$ | $43868160$ | not computed | 15E1 | 5B1 | 3A | 15E1 | 15E1 | $\left(\begin{array}{llllll}0 & 1 & \alpha^{2} & \alpha & 1 & 0 \\ \alpha & 1 & 1 & 0 & \alpha^{2} & \alpha \\ \alpha & 1 & 0 & 0 & 1 & \alpha^{2} \\ \alpha^{2} & \alpha^{2} & 1 & \alpha^{2} & \alpha^{2} & \alpha \\ \alpha^{2} & \alpha & 0 & 1 & 1 & \alpha^{2} \\ \alpha & 1 & 0 & 0 & 0 & 0 \\ \end{array}\right)$ |
| $\SOPlus(6,4)$ | 17A1 | $17$ | $11612160$ | not computed | 17A2 | 17A3 | 17A3 | 17A6 | 1A | $\left(\begin{array}{llllll}\alpha & \alpha & 0 & \alpha & \alpha & \alpha \\ \alpha^{2} & 0 & \alpha & \alpha^{2} & \alpha^{2} & \alpha \\ \alpha & \alpha^{2} & \alpha & \alpha & \alpha & 1 \\ 1 & \alpha^{2} & 1 & 0 & \alpha & 1 \\ \alpha^{2} & 0 & 1 & 1 & 0 & \alpha \\ 0 & 1 & 1 & \alpha & \alpha & 1 \\ \end{array}\right)$ |