Refine search
Results (39 matches)
Download displayed columns for resultsElements of the group are displayed as matrices in $\GL_{4}(\F_{11})$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||
|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 11P | ||||||
| $\SL(2,11):C_2^2$ | 1A | $1$ | $1$ | $\SL(2,11):C_2^2$ | 1A | 1A | 1A | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 2A | $2$ | $1$ | $\SL(2,11):C_2^2$ | 1A | 2A | 2A | 2A | $ \left(\begin{array}{rrrr} 10 & 0 & 0 & 0 \\ 0 & 10 & 0 & 0 \\ 0 & 0 & 10 & 0 \\ 0 & 0 & 0 & 10 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 2B | $2$ | $110$ | $C_2\times D_{12}$ | 1A | 2B | 2B | 2B | $ \left(\begin{array}{rrrr} 2 & 4 & 3 & 0 \\ 8 & 9 & 0 & 8 \\ 3 & 0 & 9 & 4 \\ 0 & 8 & 8 & 2 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 2C | $2$ | $110$ | $C_2\times D_{12}$ | 1A | 2C | 2C | 2C | $ \left(\begin{array}{rrrr} 0 & 0 & 7 & 3 \\ 6 & 10 & 6 & 7 \\ 0 & 0 & 1 & 0 \\ 4 & 0 & 5 & 0 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 2D | $2$ | $110$ | $C_2\times D_{12}$ | 1A | 2D | 2D | 2D | $ \left(\begin{array}{rrrr} 8 & 3 & 10 & 7 \\ 6 & 8 & 3 & 10 \\ 8 & 5 & 3 & 8 \\ 10 & 8 & 5 & 3 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 3A | $3$ | $110$ | $D_4:C_6$ | 3A | 1A | 3A | 3A | $ \left(\begin{array}{rrrr} 7 & 0 & 9 & 3 \\ 1 & 3 & 10 & 9 \\ 10 & 4 & 7 & 0 \\ 6 & 10 & 10 & 3 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 4A | $4$ | $2$ | $\SL(2,11):C_2$ | 2A | 4A | 4A | 4A | $ \left(\begin{array}{rrrr} 10 & 10 & 4 & 5 \\ 7 & 4 & 0 & 4 \\ 3 & 8 & 7 & 1 \\ 3 & 3 & 4 & 1 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 4B | $4$ | $2$ | $\SL(2,11):C_2$ | 2A | 4B | 4B | 4B | $ \left(\begin{array}{rrrr} 1 & 3 & 5 & 0 \\ 5 & 10 & 0 & 6 \\ 1 & 0 & 10 & 3 \\ 0 & 10 & 5 & 1 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 4C | $4$ | $2$ | $\SL(2,11):C_2$ | 2A | 4C | 4C | 4C | $ \left(\begin{array}{rrrr} 2 & 7 & 6 & 0 \\ 6 & 9 & 0 & 5 \\ 5 & 0 & 9 & 7 \\ 0 & 6 & 6 & 2 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 4D | $4$ | $110$ | $D_4:C_6$ | 2A | 4D | 4D | 4D | $ \left(\begin{array}{rrrr} 1 & 3 & 5 & 0 \\ 3 & 8 & 8 & 5 \\ 0 & 10 & 3 & 8 \\ 10 & 0 & 8 & 10 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 5A1 | $5$ | $132$ | $C_5\times Q_8$ | 5A2 | 5A2 | 1A | 5A1 | $ \left(\begin{array}{rrrr} 1 & 9 & 10 & 6 \\ 6 & 3 & 5 & 10 \\ 3 & 5 & 0 & 2 \\ 10 & 3 & 5 & 2 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 5A2 | $5$ | $132$ | $C_5\times Q_8$ | 5A1 | 5A1 | 1A | 5A2 | $ \left(\begin{array}{rrrr} 2 & 5 & 8 & 7 \\ 7 & 8 & 4 & 8 \\ 9 & 4 & 10 & 6 \\ 8 & 9 & 4 & 5 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 6A | $6$ | $110$ | $D_4:C_6$ | 3A | 2A | 6A | 6A | $ \left(\begin{array}{rrrr} 8 & 0 & 9 & 3 \\ 1 & 4 & 10 & 9 \\ 10 & 4 & 8 & 0 \\ 6 & 10 & 10 & 4 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 6B | $6$ | $220$ | $C_2\times C_{12}$ | 3A | 2B | 6B | 6B | $ \left(\begin{array}{rrrr} 7 & 6 & 5 & 4 \\ 6 & 2 & 0 & 8 \\ 2 & 2 & 0 & 1 \\ 9 & 5 & 8 & 2 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 6C | $6$ | $220$ | $C_2\times C_{12}$ | 3A | 2C | 6C | 6C | $ \left(\begin{array}{rrrr} 3 & 9 & 6 & 4 \\ 1 & 3 & 8 & 9 \\ 3 & 0 & 2 & 9 \\ 9 & 8 & 7 & 3 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 6D | $6$ | $220$ | $C_2\times C_{12}$ | 3A | 2D | 6D | 6D | $ \left(\begin{array}{rrrr} 2 & 3 & 2 & 2 \\ 4 & 1 & 4 & 10 \\ 0 & 3 & 9 & 6 \\ 6 & 3 & 10 & 10 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 10A1 | $10$ | $132$ | $C_5\times Q_8$ | 5A1 | 10A3 | 2A | 10A1 | $ \left(\begin{array}{rrrr} 6 & 5 & 8 & 7 \\ 7 & 1 & 4 & 8 \\ 9 & 4 & 3 & 6 \\ 8 & 9 & 4 & 9 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 10A3 | $10$ | $132$ | $C_5\times Q_8$ | 5A2 | 10A1 | 2A | 10A3 | $ \left(\begin{array}{rrrr} 9 & 9 & 10 & 6 \\ 6 & 0 & 5 & 10 \\ 3 & 5 & 8 & 2 \\ 10 & 3 & 5 & 10 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 11A1 | $11$ | $60$ | $Q_8\times C_{11}$ | 11A-1 | 11A1 | 11A1 | 1A | $ \left(\begin{array}{rrrr} 1 & 5 & 7 & 6 \\ 2 & 1 & 9 & 7 \\ 3 & 10 & 1 & 6 \\ 4 & 3 & 9 & 1 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 11A-1 | $11$ | $60$ | $Q_8\times C_{11}$ | 11A1 | 11A-1 | 11A-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 6 & 4 & 5 \\ 9 & 1 & 2 & 4 \\ 8 & 1 & 1 & 5 \\ 7 & 8 & 2 & 1 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 12A1 | $12$ | $110$ | $D_4:C_6$ | 6A | 4D | 12A5 | 12A1 | $ \left(\begin{array}{rrrr} 9 & 7 & 8 & 0 \\ 7 & 7 & 4 & 8 \\ 0 & 5 & 10 & 4 \\ 5 & 0 & 4 & 8 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 12A5 | $12$ | $110$ | $D_4:C_6$ | 6A | 4D | 12A1 | 12A5 | $ \left(\begin{array}{rrrr} 3 & 7 & 8 & 0 \\ 7 & 1 & 4 & 8 \\ 0 & 5 & 4 & 4 \\ 5 & 0 & 4 & 2 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 12B | $12$ | $220$ | $C_2\times C_{12}$ | 6A | 4C | 12B | 12B | $ \left(\begin{array}{rrrr} 7 & 10 & 2 & 8 \\ 7 & 0 & 4 & 7 \\ 9 & 4 & 9 & 8 \\ 10 & 4 & 10 & 6 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 12C | $12$ | $220$ | $C_2\times C_{12}$ | 6A | 4B | 12C | 12C | $ \left(\begin{array}{rrrr} 3 & 9 & 0 & 9 \\ 10 & 5 & 1 & 5 \\ 3 & 0 & 7 & 10 \\ 7 & 4 & 7 & 7 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 12D | $12$ | $220$ | $C_2\times C_{12}$ | 6A | 4A | 12D | 12D | $ \left(\begin{array}{rrrr} 5 & 9 & 7 & 3 \\ 6 & 10 & 0 & 0 \\ 6 & 7 & 3 & 8 \\ 4 & 2 & 2 & 4 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 20A1 | $20$ | $264$ | $C_{20}$ | 10A1 | 20A3 | 4A | 20A1 | $ \left(\begin{array}{rrrr} 8 & 7 & 2 & 2 \\ 5 & 2 & 0 & 10 \\ 4 & 1 & 1 & 10 \\ 10 & 5 & 6 & 0 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 20A3 | $20$ | $264$ | $C_{20}$ | 10A3 | 20A1 | 4A | 20A3 | $ \left(\begin{array}{rrrr} 10 & 7 & 7 & 10 \\ 3 & 7 & 0 & 9 \\ 10 & 5 & 2 & 0 \\ 6 & 2 & 8 & 3 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 20B1 | $20$ | $264$ | $C_{20}$ | 10A3 | 20B3 | 4C | 20B1 | $ \left(\begin{array}{rrrr} 8 & 3 & 4 & 4 \\ 8 & 7 & 4 & 6 \\ 8 & 5 & 1 & 2 \\ 7 & 6 & 1 & 6 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 20B3 | $20$ | $264$ | $C_{20}$ | 10A1 | 20B1 | 4C | 20B3 | $ \left(\begin{array}{rrrr} 4 & 4 & 4 & 6 \\ 10 & 2 & 6 & 0 \\ 3 & 2 & 4 & 8 \\ 5 & 7 & 5 & 1 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 20C1 | $20$ | $264$ | $C_{20}$ | 10A1 | 20C3 | 4B | 20C1 | $ \left(\begin{array}{rrrr} 4 & 2 & 2 & 9 \\ 4 & 6 & 6 & 9 \\ 0 & 5 & 2 & 7 \\ 4 & 8 & 0 & 10 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 20C3 | $20$ | $264$ | $C_{20}$ | 10A3 | 20C1 | 4B | 20C3 | $ \left(\begin{array}{rrrr} 4 & 4 & 10 & 5 \\ 5 & 4 & 7 & 1 \\ 3 & 4 & 3 & 8 \\ 1 & 10 & 4 & 0 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 22A1 | $22$ | $60$ | $Q_8\times C_{11}$ | 11A1 | 22A1 | 22A1 | 2A | $ \left(\begin{array}{rrrr} 10 & 3 & 2 & 8 \\ 10 & 10 & 1 & 2 \\ 4 & 6 & 10 & 8 \\ 9 & 4 & 1 & 10 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 22A-1 | $22$ | $60$ | $Q_8\times C_{11}$ | 11A-1 | 22A-1 | 22A-1 | 2A | $ \left(\begin{array}{rrrr} 10 & 8 & 9 & 3 \\ 1 & 10 & 10 & 9 \\ 7 & 5 & 10 & 3 \\ 2 & 7 & 10 & 10 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 44A1 | $44$ | $120$ | $C_{44}$ | 22A1 | 44A1 | 44A1 | 4B | $ \left(\begin{array}{rrrr} 2 & 8 & 3 & 5 \\ 6 & 4 & 2 & 2 \\ 5 & 10 & 9 & 8 \\ 4 & 7 & 6 & 7 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 44A-1 | $44$ | $120$ | $C_{44}$ | 22A-1 | 44A-1 | 44A-1 | 4B | $ \left(\begin{array}{rrrr} 4 & 3 & 2 & 5 \\ 5 & 2 & 2 & 3 \\ 7 & 10 & 7 & 3 \\ 4 & 5 & 5 & 9 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 44B1 | $44$ | $120$ | $C_{44}$ | 22A-1 | 44B1 | 44B1 | 4C | $ \left(\begin{array}{rrrr} 1 & 6 & 7 & 4 \\ 1 & 3 & 1 & 8 \\ 7 & 5 & 1 & 2 \\ 2 & 6 & 9 & 6 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 44B-1 | $44$ | $120$ | $C_{44}$ | 22A1 | 44B-1 | 44B-1 | 4C | $ \left(\begin{array}{rrrr} 5 & 9 & 8 & 4 \\ 2 & 10 & 1 & 7 \\ 6 & 5 & 8 & 5 \\ 2 & 7 & 10 & 10 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 44C1 | $44$ | $120$ | $C_{44}$ | 22A-1 | 44C1 | 44C1 | 4A | $ \left(\begin{array}{rrrr} 7 & 3 & 8 & 6 \\ 2 & 1 & 0 & 6 \\ 9 & 3 & 9 & 1 \\ 8 & 7 & 5 & 5 \end{array}\right) $ |
| $\SL(2,11):C_2^2$ | 44C-1 | $44$ | $120$ | $C_{44}$ | 22A1 | 44C-1 | 44C-1 | 4A | $ \left(\begin{array}{rrrr} 5 & 1 & 5 & 5 \\ 5 & 9 & 0 & 3 \\ 4 & 8 & 1 & 3 \\ 3 & 2 & 2 & 7 \end{array}\right) $ |