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Results (33 matches)
Download displayed columns for resultsElements of the group are displayed as matrices in $\SL(2,32)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||
|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 11P | 31P | ||||||
| $\SL(2,32)$ | 1A | $1$ | $1$ | $\SL(2,32)$ | 1A | 1A | 1A | 1A | $\left(\begin{array}{ll}1 & 0 \\ 0 & 1 \\ \end{array}\right)$ |
| $\SL(2,32)$ | 2A | $2$ | $1023$ | $C_2^5$ | 1A | 2A | 2A | 2A | $\left(\begin{array}{ll}\alpha^{9} & \alpha^{2} \\ \alpha^{30} & \alpha^{9} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 3A | $3$ | $992$ | $C_{33}$ | 3A | 1A | 3A | 3A | $\left(\begin{array}{ll}\alpha^{6} & \alpha^{25} \\ \alpha^{11} & \alpha^{27} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 11A1 | $11$ | $992$ | $C_{33}$ | 11A2 | 11A3 | 11A5 | 1A | $\left(\begin{array}{ll}\alpha^{18} & \alpha^{3} \\ \alpha^{20} & \alpha^{25} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 11A2 | $11$ | $992$ | $C_{33}$ | 11A4 | 11A5 | 11A1 | 1A | $\left(\begin{array}{ll}\alpha^{6} & \alpha^{12} \\ \alpha^{29} & \alpha^{29} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 11A3 | $11$ | $992$ | $C_{33}$ | 11A5 | 11A2 | 11A4 | 1A | $\left(\begin{array}{ll}\alpha^{13} & \alpha^{4} \\ \alpha^{21} & \alpha^{8} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 11A4 | $11$ | $992$ | $C_{33}$ | 11A3 | 11A1 | 11A2 | 1A | $\left(\begin{array}{ll}\alpha^{15} & \alpha^{30} \\ \alpha^{16} & \alpha^{9} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 11A5 | $11$ | $992$ | $C_{33}$ | 11A1 | 11A4 | 11A3 | 1A | $\left(\begin{array}{ll}\alpha & \alpha^{14} \\ 1 & \alpha^{12} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A1 | $31$ | $1056$ | $C_{31}$ | 31A2 | 31A3 | 31A5 | 31A11 | $\left(\begin{array}{ll}\alpha^{22} & \alpha^{28} \\ \alpha^{21} & \alpha^{10} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A2 | $31$ | $1056$ | $C_{31}$ | 31A4 | 31A6 | 31A10 | 31A9 | $\left(\begin{array}{ll}\alpha^{15} & \alpha^{30} \\ \alpha^{23} & \alpha^{23} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A3 | $31$ | $1056$ | $C_{31}$ | 31A6 | 31A9 | 31A15 | 31A2 | $\left(\begin{array}{ll}\alpha^{19} & \alpha^{7} \\ 1 & \alpha^{3} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A4 | $31$ | $1056$ | $C_{31}$ | 31A8 | 31A12 | 31A11 | 31A13 | $\left(\begin{array}{ll}\alpha^{11} & \alpha^{3} \\ \alpha^{27} & \alpha^{6} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A5 | $31$ | $1056$ | $C_{31}$ | 31A10 | 31A15 | 31A6 | 31A7 | $\left(\begin{array}{ll}\alpha^{9} & \alpha^{10} \\ \alpha^{3} & \alpha^{5} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A6 | $31$ | $1056$ | $C_{31}$ | 31A12 | 31A13 | 31A1 | 31A4 | $\left(\begin{array}{ll}0 & \alpha^{19} \\ \alpha^{12} & \alpha^{24} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A7 | $31$ | $1056$ | $C_{31}$ | 31A14 | 31A10 | 31A4 | 31A15 | $\left(\begin{array}{ll}\alpha^{9} & \alpha^{29} \\ \alpha^{22} & \alpha^{30} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A8 | $31$ | $1056$ | $C_{31}$ | 31A15 | 31A7 | 31A9 | 31A5 | $\left(\begin{array}{ll}\alpha^{11} & \alpha^{11} \\ \alpha^{4} & \alpha^{13} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A9 | $31$ | $1056$ | $C_{31}$ | 31A13 | 31A4 | 31A14 | 31A6 | $\left(\begin{array}{ll}\alpha^{19} & \alpha^{22} \\ \alpha^{15} & \alpha^{8} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A10 | $31$ | $1056$ | $C_{31}$ | 31A11 | 31A1 | 31A12 | 31A14 | $\left(\begin{array}{ll}\alpha^{15} & \alpha^{25} \\ \alpha^{18} & \alpha^{8} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A11 | $31$ | $1056$ | $C_{31}$ | 31A9 | 31A2 | 31A7 | 31A3 | $\left(\begin{array}{ll}\alpha^{22} & \alpha^{24} \\ \alpha^{17} & \alpha^{13} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A12 | $31$ | $1056$ | $C_{31}$ | 31A7 | 31A5 | 31A2 | 31A8 | $\left(\begin{array}{ll}1 & \alpha^{12} \\ \alpha^{5} & \alpha^{30} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A13 | $31$ | $1056$ | $C_{31}$ | 31A5 | 31A8 | 31A3 | 31A12 | $\left(\begin{array}{ll}\alpha^{10} & \alpha^{18} \\ \alpha^{11} & \alpha^{24} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A14 | $31$ | $1056$ | $C_{31}$ | 31A3 | 31A11 | 31A8 | 31A1 | $\left(\begin{array}{ll}\alpha^{23} & \alpha \\ \alpha^{25} & \alpha^{5} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 31A15 | $31$ | $1056$ | $C_{31}$ | 31A1 | 31A14 | 31A13 | 31A10 | $\left(\begin{array}{ll}\alpha^{3} & \alpha^{27} \\ \alpha^{20} & \alpha^{6} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 33A1 | $33$ | $992$ | $C_{33}$ | 33A2 | 11A1 | 33A5 | 3A | $\left(\begin{array}{ll}\alpha^{28} & \alpha^{15} \\ \alpha & \alpha^{12} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 33A2 | $33$ | $992$ | $C_{33}$ | 33A4 | 11A2 | 33A10 | 3A | $\left(\begin{array}{ll}\alpha & \alpha^{5} \\ \alpha^{22} & \alpha^{5} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 33A4 | $33$ | $992$ | $C_{33}$ | 33A8 | 11A4 | 33A13 | 3A | $\left(\begin{array}{ll}\alpha^{23} & \alpha^{16} \\ \alpha^{2} & \alpha^{9} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 33A5 | $33$ | $992$ | $C_{33}$ | 33A10 | 11A5 | 33A8 | 3A | $\left(\begin{array}{ll}\alpha^{15} & \alpha \\ \alpha^{18} & \alpha^{27} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 33A7 | $33$ | $992$ | $C_{33}$ | 33A14 | 11A4 | 33A2 | 3A | $\left(\begin{array}{ll}\alpha^{7} & \alpha^{19} \\ \alpha^{5} & \alpha^{8} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 33A8 | $33$ | $992$ | $C_{33}$ | 33A16 | 11A3 | 33A7 | 3A | $\left(\begin{array}{ll}\alpha^{13} & \alpha^{7} \\ \alpha^{24} & 0 \\ \end{array}\right)$ |
| $\SL(2,32)$ | 33A10 | $33$ | $992$ | $C_{33}$ | 33A13 | 11A1 | 33A16 | 3A | $\left(\begin{array}{ll}\alpha^{7} & \alpha^{8} \\ \alpha^{25} & \alpha^{29} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 33A13 | $33$ | $992$ | $C_{33}$ | 33A7 | 11A2 | 33A1 | 3A | $\left(\begin{array}{ll}\alpha^{23} & \alpha^{22} \\ \alpha^{8} & \alpha^{25} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 33A14 | $33$ | $992$ | $C_{33}$ | 33A5 | 11A3 | 33A4 | 3A | $\left(\begin{array}{ll}\alpha^{18} & \alpha^{13} \\ \alpha^{30} & \alpha^{5} \\ \end{array}\right)$ |
| $\SL(2,32)$ | 33A16 | $33$ | $992$ | $C_{33}$ | 33A1 | 11A5 | 33A14 | 3A | $\left(\begin{array}{ll}\alpha^{28} & \alpha^{20} \\ \alpha^{6} & 1 \\ \end{array}\right)$ |