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Results (20 matches)
Download displayed columns for resultsElements of the group are displayed as matrices in $\SU(4,2)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | ||||||
| $\SU(4,2)$ | 1A | $1$ | $1$ | $\SU(4,2)$ | 1A | 1A | 1A | $\left(\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array}\right)$ |
| $\SU(4,2)$ | 2A | $2$ | $45$ | $\OmegaPlus(4,3):C_2$ | 1A | 2A | 2A | $\left(\begin{array}{llll}\alpha & 1 & \alpha^{2} & 1 \\ 1 & \alpha^{2} & 1 & \alpha \\ \alpha^{2} & 1 & \alpha & 1 \\ 1 & \alpha & 1 & \alpha^{2} \\ \end{array}\right)$ |
| $\SU(4,2)$ | 2B | $2$ | $270$ | $\GL(2,\mathbb{Z}/4)$ | 1A | 2B | 2B | $\left(\begin{array}{llll}0 & \alpha & \alpha & 1 \\ \alpha^{2} & 1 & 0 & \alpha^{2} \\ \alpha^{2} & 0 & 1 & \alpha^{2} \\ 1 & \alpha & \alpha & 0 \\ \end{array}\right)$ |
| $\SU(4,2)$ | 3A1 | $3$ | $40$ | $\Unitary(3,2)$ | 3A-1 | 1A | 3A-1 | $\left(\begin{array}{llll}0 & 0 & \alpha & \alpha^{2} \\ \alpha^{2} & \alpha & \alpha^{2} & 1 \\ 0 & 0 & \alpha & 0 \\ \alpha^{2} & 0 & \alpha^{2} & \alpha^{2} \\ \end{array}\right)$ |
| $\SU(4,2)$ | 3A-1 | $3$ | $40$ | $\Unitary(3,2)$ | 3A1 | 1A | 3A1 | $\left(\begin{array}{llll}\alpha & 0 & 1 & \alpha \\ \alpha & \alpha^{2} & \alpha & \alpha^{2} \\ 0 & 0 & \alpha^{2} & 0 \\ \alpha & 0 & \alpha & 0 \\ \end{array}\right)$ |
| $\SU(4,2)$ | 3B | $3$ | $240$ | $C_3\times S_3^2$ | 3B | 1A | 3B | $\left(\begin{array}{llll}\alpha^{2} & 0 & 0 & 0 \\ 1 & \alpha & 0 & 0 \\ 0 & 0 & \alpha & 0 \\ 0 & 0 & 1 & \alpha^{2} \\ \end{array}\right)$ |
| $\SU(4,2)$ | 3C | $3$ | $480$ | $S_3\times C_3^2$ | 3C | 1A | 3C | $\left(\begin{array}{llll}0 & 0 & \alpha^{2} & 1 \\ \alpha & 1 & \alpha^{2} & \alpha^{2} \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 1 & 1 \\ \end{array}\right)$ |
| $\SU(4,2)$ | 4A | $4$ | $540$ | $\SL(2,3):C_2$ | 2A | 4A | 4A | $\left(\begin{array}{llll}\alpha^{2} & 1 & 0 & 0 \\ \alpha^{2} & \alpha^{2} & 0 & 0 \\ 1 & \alpha & \alpha & 1 \\ \alpha & \alpha & \alpha & \alpha \\ \end{array}\right)$ |
| $\SU(4,2)$ | 4B | $4$ | $3240$ | $C_2\times C_4$ | 2B | 4B | 4B | $\left(\begin{array}{llll}\alpha^{2} & \alpha & 1 & 1 \\ 0 & 0 & \alpha & \alpha^{2} \\ \alpha & \alpha^{2} & 1 & 1 \\ 0 & 0 & \alpha^{2} & \alpha \\ \end{array}\right)$ |
| $\SU(4,2)$ | 5A | $5$ | $5184$ | $C_5$ | 5A | 5A | 1A | $\left(\begin{array}{llll}1 & 1 & 0 & 0 \\ \alpha^{2} & \alpha & 0 & 0 \\ 1 & 0 & 1 & 1 \\ \alpha & 1 & \alpha & \alpha^{2} \\ \end{array}\right)$ |
| $\SU(4,2)$ | 6A1 | $6$ | $360$ | $C_3\times \SL(2,3)$ | 3A1 | 2A | 6A-1 | $\left(\begin{array}{llll}\alpha & 0 & 1 & \alpha \\ \alpha & \alpha^{2} & \alpha & \alpha^{2} \\ 1 & \alpha^{2} & \alpha^{2} & 0 \\ 1 & \alpha & \alpha & 0 \\ \end{array}\right)$ |
| $\SU(4,2)$ | 6A-1 | $6$ | $360$ | $C_3\times \SL(2,3)$ | 3A-1 | 2A | 6A1 | $\left(\begin{array}{llll}0 & 0 & \alpha & \alpha^{2} \\ \alpha^{2} & \alpha & \alpha^{2} & 1 \\ \alpha^{2} & \alpha & \alpha & 0 \\ 1 & 1 & \alpha^{2} & \alpha^{2} \\ \end{array}\right)$ |
| $\SU(4,2)$ | 6B1 | $6$ | $720$ | $C_6\times S_3$ | 3B | 2A | 6B-1 | $\left(\begin{array}{llll}0 & \alpha & \alpha & 0 \\ \alpha^{2} & \alpha^{2} & \alpha^{2} & \alpha^{2} \\ 0 & \alpha & \alpha & \alpha^{2} \\ \alpha^{2} & 1 & \alpha^{2} & 1 \\ \end{array}\right)$ |
| $\SU(4,2)$ | 6B-1 | $6$ | $720$ | $C_6\times S_3$ | 3B | 2A | 6B1 | $\left(\begin{array}{llll}1 & \alpha & \alpha & 0 \\ \alpha & \alpha^{2} & \alpha & \alpha^{2} \\ 1 & \alpha^{2} & \alpha & \alpha^{2} \\ \alpha & 0 & \alpha & 0 \\ \end{array}\right)$ |
| $\SU(4,2)$ | 6C | $6$ | $1440$ | $C_3\times C_6$ | 3C | 2A | 6C | $\left(\begin{array}{llll}\alpha & 1 & 1 & 0 \\ 0 & \alpha^{2} & \alpha^{2} & 0 \\ \alpha^{2} & 1 & \alpha & 1 \\ 0 & \alpha & \alpha & \alpha \\ \end{array}\right)$ |
| $\SU(4,2)$ | 6D | $6$ | $2160$ | $C_2\times C_6$ | 3B | 2B | 6D | $\left(\begin{array}{llll}0 & 0 & \alpha & \alpha \\ \alpha^{2} & \alpha^{2} & \alpha & \alpha \\ \alpha^{2} & \alpha^{2} & \alpha^{2} & 0 \\ 1 & \alpha^{2} & \alpha^{2} & 0 \\ \end{array}\right)$ |
| $\SU(4,2)$ | 9A1 | $9$ | $2880$ | $C_9$ | 9A-1 | 3A1 | 9A-1 | $\left(\begin{array}{llll}0 & \alpha & 0 & 0 \\ 0 & 0 & 0 & \alpha^{2} \\ \alpha^{2} & \alpha & 0 & 0 \\ 0 & 0 & \alpha & \alpha^{2} \\ \end{array}\right)$ |
| $\SU(4,2)$ | 9A-1 | $9$ | $2880$ | $C_9$ | 9A1 | 3A-1 | 9A1 | $\left(\begin{array}{llll}\alpha & 0 & \alpha & 0 \\ \alpha^{2} & 0 & 0 & 0 \\ 0 & \alpha^{2} & 0 & \alpha^{2} \\ 0 & \alpha & 0 & 0 \\ \end{array}\right)$ |
| $\SU(4,2)$ | 12A1 | $12$ | $2160$ | $C_{12}$ | 6A1 | 4A | 12A-1 | $\left(\begin{array}{llll}\alpha^{2} & \alpha & \alpha & \alpha^{2} \\ \alpha & 1 & \alpha^{2} & 1 \\ 1 & 1 & \alpha^{2} & \alpha \\ \alpha & \alpha & 0 & \alpha \\ \end{array}\right)$ |
| $\SU(4,2)$ | 12A-1 | $12$ | $2160$ | $C_{12}$ | 6A-1 | 4A | 12A1 | $\left(\begin{array}{llll}\alpha^{2} & \alpha^{2} & 1 & \alpha \\ 0 & \alpha & \alpha & \alpha^{2} \\ \alpha^{2} & 1 & 1 & \alpha^{2} \\ \alpha^{2} & 1 & \alpha^{2} & \alpha \\ \end{array}\right)$ |