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Results (16 matches)
Download displayed columns for resultsElements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SL(2,27)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||
|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 7P | 13P | ||||||
| $\PSL(2,27)$ | 1A | $1$ | $1$ | $\PSL(2,27)$ | 1A | 1A | 1A | 1A | $ \left[ \left(\begin{array}{rr} 0 & -1 \\ -1 & 0 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 2A | $2$ | $351$ | $D_{14}$ | 1A | 2A | 2A | 2A | $ \left[ \left(\begin{array}{rr} 0 & 18 \\ 8 & 13 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 3A1 | $3$ | $364$ | $C_3^3$ | 3A-1 | 1A | 3A1 | 3A1 | $ \left[ \left(\begin{array}{rr} 7 & 9 \\ 14 & 17 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 3A-1 | $3$ | $364$ | $C_3^3$ | 3A1 | 1A | 3A-1 | 3A-1 | $ \left[ \left(\begin{array}{rr} 4 & 9 \\ 14 & 20 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 7A1 | $7$ | $702$ | $C_{14}$ | 7A2 | 7A3 | 1A | 7A1 | $ \left[ \left(\begin{array}{rr} 16 & 9 \\ 25 & 25 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 7A2 | $7$ | $702$ | $C_{14}$ | 7A3 | 7A1 | 1A | 7A2 | $ \left[ \left(\begin{array}{rr} 14 & 15 \\ 5 & 17 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 7A3 | $7$ | $702$ | $C_{14}$ | 7A1 | 7A2 | 1A | 7A3 | $ \left[ \left(\begin{array}{rr} 10 & 17 \\ 7 & 9 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 13A1 | $13$ | $756$ | $C_{13}$ | 13A2 | 13A3 | 13A6 | 1A | $ \left[ \left(\begin{array}{rr} 11 & 19 \\ 21 & 5 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 13A2 | $13$ | $756$ | $C_{13}$ | 13A4 | 13A6 | 13A1 | 1A | $ \left[ \left(\begin{array}{rr} 3 & 9 \\ 11 & 2 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 13A3 | $13$ | $756$ | $C_{13}$ | 13A6 | 13A4 | 13A5 | 1A | $ \left[ \left(\begin{array}{rr} 23 & 16 \\ 18 & 18 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 13A4 | $13$ | $756$ | $C_{13}$ | 13A5 | 13A1 | 13A2 | 1A | $ \left[ \left(\begin{array}{rr} 22 & 20 \\ 22 & 0 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 13A5 | $13$ | $756$ | $C_{13}$ | 13A3 | 13A2 | 13A4 | 1A | $ \left[ \left(\begin{array}{rr} 22 & 21 \\ 23 & 11 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 13A6 | $13$ | $756$ | $C_{13}$ | 13A1 | 13A5 | 13A3 | 1A | $ \left[ \left(\begin{array}{rr} 10 & 25 \\ 1 & 3 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 14A1 | $14$ | $702$ | $C_{14}$ | 7A1 | 14A3 | 2A | 14A1 | $ \left[ \left(\begin{array}{rr} 10 & 23 \\ 13 & 22 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 14A3 | $14$ | $702$ | $C_{14}$ | 7A3 | 14A5 | 2A | 14A3 | $ \left[ \left(\begin{array}{rr} 1 & 7 \\ 23 & 17 \end{array}\right) \right] $ |
| $\PSL(2,27)$ | 14A5 | $14$ | $702$ | $C_{14}$ | 7A2 | 14A1 | 2A | 14A5 | $ \left[ \left(\begin{array}{rr} 3 & 11 \\ 1 & 25 \end{array}\right) \right] $ |