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Results (40 matches)
Download displayed columns for resultsElements of the group are displayed as matrices in $\GL_{2}(\Z/{51}\Z)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $\GL(2,3):D_4$ | 1A | $1$ | $1$ | $\GL(2,3):D_4$ | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 2A | $2$ | $1$ | $\GL(2,3):D_4$ | 1A | 2A | $ \left(\begin{array}{rr} 35 & 0 \\ 0 & 35 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 2B | $2$ | $1$ | $\GL(2,3):D_4$ | 1A | 2B | $ \left(\begin{array}{rr} 16 & 0 \\ 0 & 16 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 2C | $2$ | $1$ | $\GL(2,3):D_4$ | 1A | 2C | $ \left(\begin{array}{rr} 50 & 0 \\ 0 & 50 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 2D | $2$ | $2$ | $C_2^2\times \GL(2,3)$ | 1A | 2D | $ \left(\begin{array}{rr} 35 & 0 \\ 17 & 1 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 2E | $2$ | $2$ | $C_2^2\times \GL(2,3)$ | 1A | 2E | $ \left(\begin{array}{rr} 50 & 0 \\ 17 & 16 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 2F | $2$ | $12$ | $C_2^3:C_4$ | 1A | 2F | $ \left(\begin{array}{rr} 16 & 0 \\ 0 & 1 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 2G | $2$ | $12$ | $C_2^2\times C_8$ | 1A | 2G | $ \left(\begin{array}{rr} 34 & 49 \\ 42 & 17 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 2H | $2$ | $12$ | $C_2^3:C_4$ | 1A | 2H | $ \left(\begin{array}{rr} 8 & 15 \\ 6 & 26 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 2I | $2$ | $24$ | $C_2^4$ | 1A | 2I | $ \left(\begin{array}{rr} 25 & 15 \\ 40 & 26 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 3A | $3$ | $8$ | $C_2^2:C_{12}$ | 3A | 1A | $ \left(\begin{array}{rr} 25 & 36 \\ 6 & 25 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 4A1 | $4$ | $2$ | $C_4\times \GL(2,3)$ | 2C | 4A-1 | $ \left(\begin{array}{rr} 38 & 17 \\ 17 & 4 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 4A-1 | $4$ | $2$ | $C_4\times \GL(2,3)$ | 2C | 4A1 | $ \left(\begin{array}{rr} 13 & 34 \\ 34 & 47 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 4B1 | $4$ | $2$ | $\GL(2,3):C_2^2$ | 2B | 4B-1 | $ \left(\begin{array}{rr} 13 & 34 \\ 0 & 47 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 4B-1 | $4$ | $2$ | $\GL(2,3):C_2^2$ | 2B | 4B1 | $ \left(\begin{array}{rr} 4 & 34 \\ 0 & 38 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 4C | $4$ | $6$ | $C_8\times D_4$ | 2B | 4C | $ \left(\begin{array}{rr} 34 & 9 \\ 15 & 34 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 4D | $4$ | $6$ | $C_8\times D_4$ | 2B | 4D | $ \left(\begin{array}{rr} 5 & 45 \\ 27 & 29 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 4E | $4$ | $12$ | $C_4\times C_8$ | 2A | 4E | $ \left(\begin{array}{rr} 17 & 32 \\ 8 & 34 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 4F | $4$ | $12$ | $C_2^2\times C_8$ | 2B | 4F | $ \left(\begin{array}{rr} 34 & 9 \\ 49 & 17 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 4G | $4$ | $24$ | $C_2^2\times C_4$ | 2C | 4G | $ \left(\begin{array}{rr} 47 & 17 \\ 17 & 4 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 4H | $4$ | $24$ | $C_2^2\times C_4$ | 2B | 4H | $ \left(\begin{array}{rr} 19 & 25 \\ 27 & 32 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 6A | $6$ | $8$ | $C_2^2:C_{12}$ | 3A | 2A | $ \left(\begin{array}{rr} 8 & 15 \\ 45 & 8 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 6B | $6$ | $8$ | $C_2^2:C_{12}$ | 3A | 2C | $ \left(\begin{array}{rr} 26 & 36 \\ 6 & 26 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 6C | $6$ | $8$ | $C_2^2:C_{12}$ | 3A | 2B | $ \left(\begin{array}{rr} 43 & 36 \\ 6 & 43 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 6D | $6$ | $16$ | $C_2^2\times C_6$ | 3A | 2D | $ \left(\begin{array}{rr} 8 & 36 \\ 23 & 25 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 6E | $6$ | $16$ | $C_2^2\times C_6$ | 3A | 2E | $ \left(\begin{array}{rr} 26 & 15 \\ 11 & 43 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 8A1 | $8$ | $6$ | $C_8\times D_4$ | 4C | 8A1 | $ \left(\begin{array}{rr} 46 & 45 \\ 24 & 46 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 8A-1 | $8$ | $6$ | $C_8\times D_4$ | 4C | 8A-1 | $ \left(\begin{array}{rr} 22 & 6 \\ 27 & 22 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 8B1 | $8$ | $6$ | $C_8\times D_4$ | 4C | 8B1 | $ \left(\begin{array}{rr} 47 & 30 \\ 18 & 14 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 8B-1 | $8$ | $6$ | $C_8\times D_4$ | 4C | 8B-1 | $ \left(\begin{array}{rr} 38 & 21 \\ 33 & 20 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 8C1 | $8$ | $12$ | $C_4\times C_8$ | 4D | 8C3 | $ \left(\begin{array}{rr} 16 & 1 \\ 4 & 29 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 8C3 | $8$ | $12$ | $C_4\times C_8$ | 4D | 8C1 | $ \left(\begin{array}{rr} 1 & 16 \\ 13 & 5 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 8D1 | $8$ | $12$ | $C_2^2\times C_8$ | 4C | 8D3 | $ \left(\begin{array}{rr} 31 & 10 \\ 45 & 14 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 8D3 | $8$ | $12$ | $C_2^2\times C_8$ | 4C | 8D1 | $ \left(\begin{array}{rr} 37 & 7 \\ 6 & 20 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 8E1 | $8$ | $12$ | $C_2^2\times C_8$ | 4C | 8E1 | $ \left(\begin{array}{rr} 47 & 21 \\ 50 & 31 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 8E-1 | $8$ | $12$ | $C_2^2\times C_8$ | 4C | 8E-1 | $ \left(\begin{array}{rr} 38 & 30 \\ 35 & 37 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 12A1 | $12$ | $16$ | $C_2\times C_{12}$ | 6B | 4A1 | $ \left(\begin{array}{rr} 19 & 43 \\ 10 & 2 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 12A-1 | $12$ | $16$ | $C_2\times C_{12}$ | 6B | 4A-1 | $ \left(\begin{array}{rr} 49 & 25 \\ 7 & 32 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 12B1 | $12$ | $16$ | $C_2\times C_{12}$ | 6C | 4B1 | $ \left(\begin{array}{rr} 49 & 25 \\ 24 & 32 \end{array}\right) $ |
| $\GL(2,3):D_4$ | 12B-1 | $12$ | $16$ | $C_2\times C_{12}$ | 6C | 4B-1 | $ \left(\begin{array}{rr} 2 & 8 \\ 24 & 19 \end{array}\right) $ |