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Elements of the group are displayed as matrices in $\GL_{4}(\F_{11})$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 5P | 11P | ||||||
| $\He_{11}.(C_{10}\times F_{11})$ | 1A | $1$ | $1$ | not computed | 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) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 2A | $2$ | $1$ | not computed | 1A | 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) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 2B | $2$ | $1331$ | not computed | 1A | 2B | 2B | $ \left(\begin{array}{rrrr} 7 & 0 & 6 & 0 \\ 5 & 7 & 1 & 6 \\ 3 & 0 & 4 & 0 \\ 8 & 3 & 6 & 4 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 2C | $2$ | $1331$ | not computed | 1A | 2C | 2C | $ \left(\begin{array}{rrrr} 5 & 0 & 3 & 0 \\ 10 & 5 & 2 & 3 \\ 3 & 0 & 6 & 0 \\ 5 & 3 & 1 & 6 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5A1 | $5$ | $1331$ | not computed | 5A2 | 1A | 5A1 | $ \left(\begin{array}{rrrr} 10 & 2 & 6 & 10 \\ 1 & 2 & 2 & 4 \\ 7 & 5 & 10 & 8 \\ 4 & 5 & 5 & 5 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5A-1 | $5$ | $1331$ | not computed | 5A-2 | 1A | 5A-1 | $ \left(\begin{array}{rrrr} 5 & 8 & 7 & 1 \\ 5 & 10 & 9 & 5 \\ 6 & 6 & 2 & 2 \\ 7 & 4 & 1 & 10 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5A2 | $5$ | $1331$ | not computed | 5A-1 | 1A | 5A2 | $ \left(\begin{array}{rrrr} 8 & 5 & 9 & 8 \\ 9 & 3 & 6 & 10 \\ 1 & 4 & 5 & 1 \\ 1 & 2 & 10 & 4 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5A-2 | $5$ | $1331$ | not computed | 5A1 | 1A | 5A-2 | $ \left(\begin{array}{rrrr} 4 & 1 & 1 & 3 \\ 10 & 5 & 5 & 2 \\ 9 & 7 & 3 & 5 \\ 10 & 10 & 9 & 8 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5B1 | $5$ | $1331$ | not computed | 5B2 | 1A | 5B1 | $ \left(\begin{array}{rrrr} 10 & 1 & 9 & 9 \\ 10 & 10 & 2 & 9 \\ 9 & 6 & 2 & 10 \\ 5 & 9 & 1 & 2 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5B-1 | $5$ | $1331$ | not computed | 5B-2 | 1A | 5B-1 | $ \left(\begin{array}{rrrr} 7 & 2 & 7 & 7 \\ 9 & 7 & 4 & 7 \\ 7 & 1 & 2 & 9 \\ 10 & 7 & 2 & 2 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5B2 | $5$ | $1331$ | not computed | 5B-1 | 1A | 5B2 | $ \left(\begin{array}{rrrr} 5 & 1 & 9 & 9 \\ 10 & 5 & 2 & 9 \\ 9 & 6 & 8 & 10 \\ 5 & 9 & 1 & 8 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5B-2 | $5$ | $1331$ | not computed | 5B1 | 1A | 5B-2 | $ \left(\begin{array}{rrrr} 10 & 7 & 8 & 8 \\ 4 & 10 & 3 & 8 \\ 8 & 9 & 9 & 4 \\ 2 & 8 & 7 & 9 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5C1 | $5$ | $1331$ | not computed | 5C2 | 1A | 5C1 | $ \left(\begin{array}{rrrr} 8 & 8 & 8 & 0 \\ 7 & 3 & 6 & 8 \\ 9 & 8 & 5 & 3 \\ 3 & 9 & 4 & 0 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5C-1 | $5$ | $1331$ | not computed | 5C-2 | 1A | 5C-1 | $ \left(\begin{array}{rrrr} 0 & 9 & 9 & 0 \\ 1 & 4 & 4 & 9 \\ 6 & 9 & 9 & 2 \\ 2 & 6 & 10 & 2 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5C2 | $5$ | $1331$ | not computed | 5C-1 | 1A | 5C2 | $ \left(\begin{array}{rrrr} 5 & 9 & 9 & 0 \\ 1 & 9 & 4 & 9 \\ 6 & 9 & 3 & 2 \\ 2 & 6 & 10 & 7 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5C-2 | $5$ | $1331$ | not computed | 5C1 | 1A | 5C-2 | $ \left(\begin{array}{rrrr} 8 & 7 & 7 & 0 \\ 2 & 5 & 8 & 7 \\ 1 & 7 & 4 & 4 \\ 4 & 1 & 9 & 1 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5D1 | $5$ | $1331$ | not computed | 5D2 | 1A | 5D1 | $ \left(\begin{array}{rrrr} 8 & 1 & 3 & 5 \\ 9 & 6 & 4 & 6 \\ 8 & 8 & 10 & 4 \\ 10 & 1 & 2 & 7 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5D-1 | $5$ | $1331$ | not computed | 5D-2 | 1A | 5D-1 | $ \left(\begin{array}{rrrr} 8 & 3 & 1 & 10 \\ 7 & 2 & 8 & 6 \\ 2 & 5 & 10 & 9 \\ 9 & 5 & 4 & 6 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5D2 | $5$ | $1331$ | not computed | 5D-1 | 1A | 5D2 | $ \left(\begin{array}{rrrr} 4 & 10 & 2 & 5 \\ 9 & 6 & 4 & 7 \\ 3 & 8 & 10 & 2 \\ 10 & 6 & 2 & 3 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5D-2 | $5$ | $1331$ | not computed | 5D1 | 1A | 5D-2 | $ \left(\begin{array}{rrrr} 1 & 8 & 5 & 2 \\ 8 & 7 & 6 & 3 \\ 9 & 1 & 2 & 7 \\ 4 & 10 & 3 & 5 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5E1 | $5$ | $14641$ | not computed | 5E2 | 1A | 5E1 | $ \left(\begin{array}{rrrr} 0 & 3 & 6 & 2 \\ 8 & 4 & 6 & 0 \\ 1 & 2 & 1 & 0 \\ 4 & 7 & 3 & 1 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5E-1 | $5$ | $14641$ | not computed | 5E-2 | 1A | 5E-1 | $ \left(\begin{array}{rrrr} 4 & 0 & 0 & 3 \\ 1 & 4 & 9 & 9 \\ 5 & 3 & 5 & 1 \\ 6 & 7 & 10 & 0 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5E2 | $5$ | $14641$ | not computed | 5E-1 | 1A | 5E2 | $ \left(\begin{array}{rrrr} 5 & 5 & 8 & 2 \\ 5 & 8 & 1 & 5 \\ 6 & 2 & 8 & 2 \\ 8 & 9 & 6 & 9 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5E-2 | $5$ | $14641$ | not computed | 5E1 | 1A | 5E-2 | $ \left(\begin{array}{rrrr} 1 & 10 & 8 & 1 \\ 8 & 7 & 6 & 4 \\ 10 & 1 & 7 & 3 \\ 4 & 3 & 3 & 3 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5F1 | $5$ | $14641$ | not computed | 5F2 | 1A | 5F1 | $ \left(\begin{array}{rrrr} 9 & 5 & 1 & 4 \\ 2 & 5 & 3 & 1 \\ 0 & 9 & 4 & 0 \\ 7 & 8 & 6 & 6 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5F-1 | $5$ | $14641$ | not computed | 5F-2 | 1A | 5F-1 | $ \left(\begin{array}{rrrr} 7 & 0 & 8 & 10 \\ 7 & 1 & 2 & 8 \\ 9 & 6 & 4 & 4 \\ 1 & 0 & 6 & 5 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5F2 | $5$ | $14641$ | not computed | 5F-1 | 1A | 5F2 | $ \left(\begin{array}{rrrr} 9 & 1 & 8 & 10 \\ 2 & 4 & 2 & 8 \\ 7 & 4 & 10 & 9 \\ 0 & 1 & 3 & 6 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 5F-2 | $5$ | $14641$ | not computed | 5F1 | 1A | 5F-2 | $ \left(\begin{array}{rrrr} 10 & 4 & 5 & 9 \\ 5 & 2 & 4 & 5 \\ 2 & 8 & 3 & 9 \\ 0 & 3 & 7 & 4 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10A1 | $10$ | $1331$ | not computed | 5B1 | 2C | 10A1 | $ \left(\begin{array}{rrrr} 8 & 5 & 1 & 1 \\ 6 & 8 & 10 & 1 \\ 1 & 8 & 1 & 6 \\ 3 & 1 & 5 & 1 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10A-1 | $10$ | $1331$ | not computed | 5B-1 | 2C | 10A-1 | $ \left(\begin{array}{rrrr} 8 & 4 & 3 & 3 \\ 7 & 8 & 8 & 3 \\ 3 & 2 & 9 & 7 \\ 9 & 3 & 4 & 9 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10A3 | $10$ | $1331$ | not computed | 5B-2 | 2C | 10A3 | $ \left(\begin{array}{rrrr} 1 & 7 & 8 & 8 \\ 4 & 1 & 3 & 8 \\ 8 & 9 & 0 & 4 \\ 2 & 8 & 7 & 0 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10A-3 | $10$ | $1331$ | not computed | 5B2 | 2C | 10A-3 | $ \left(\begin{array}{rrrr} 0 & 2 & 7 & 7 \\ 9 & 0 & 4 & 7 \\ 7 & 1 & 6 & 9 \\ 10 & 7 & 2 & 6 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10B1 | $10$ | $1331$ | not computed | 5B-2 | 2A | 10B1 | $ \left(\begin{array}{rrrr} 2 & 1 & 8 & 9 \\ 4 & 2 & 3 & 8 \\ 3 & 6 & 0 & 10 \\ 2 & 3 & 7 & 0 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10B-1 | $10$ | $1331$ | not computed | 5B2 | 2A | 10B-1 | $ \left(\begin{array}{rrrr} 0 & 6 & 4 & 10 \\ 2 & 0 & 7 & 4 \\ 7 & 3 & 10 & 5 \\ 1 & 7 & 9 & 10 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10B3 | $10$ | $1331$ | not computed | 5B-1 | 2A | 10B3 | $ \left(\begin{array}{rrrr} 5 & 6 & 4 & 10 \\ 2 & 5 & 7 & 4 \\ 7 & 3 & 4 & 5 \\ 1 & 7 & 9 & 4 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10B-3 | $10$ | $1331$ | not computed | 5B1 | 2A | 10B-3 | $ \left(\begin{array}{rrrr} 5 & 9 & 6 & 4 \\ 3 & 5 & 5 & 6 \\ 5 & 10 & 9 & 2 \\ 7 & 5 & 8 & 9 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10C1 | $10$ | $1331$ | not computed | 5C2 | 2A | 10C1 | $ \left(\begin{array}{rrrr} 2 & 10 & 5 & 8 \\ 1 & 7 & 0 & 5 \\ 7 & 1 & 7 & 1 \\ 1 & 7 & 10 & 1 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10C-1 | $10$ | $1331$ | not computed | 5C-2 | 2A | 10C-1 | $ \left(\begin{array}{rrrr} 3 & 3 & 7 & 9 \\ 8 & 10 & 0 & 7 \\ 1 & 8 & 10 & 8 \\ 8 & 1 & 3 & 6 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10C3 | $10$ | $1331$ | not computed | 5C1 | 2A | 10C3 | $ \left(\begin{array}{rrrr} 9 & 6 & 3 & 7 \\ 5 & 1 & 0 & 3 \\ 2 & 5 & 1 & 5 \\ 5 & 2 & 6 & 4 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10C-3 | $10$ | $1331$ | not computed | 5C-1 | 2A | 10C-3 | $ \left(\begin{array}{rrrr} 9 & 3 & 7 & 9 \\ 8 & 5 & 0 & 7 \\ 1 & 8 & 5 & 8 \\ 8 & 1 & 3 & 1 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10D1 | $10$ | $1331$ | not computed | 5A-2 | 2A | 10D1 | $ \left(\begin{array}{rrrr} 9 & 2 & 5 & 6 \\ 5 & 7 & 3 & 9 \\ 6 & 8 & 5 & 0 \\ 5 & 5 & 2 & 7 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10D-1 | $10$ | $1331$ | not computed | 5A2 | 2A | 10D-1 | $ \left(\begin{array}{rrrr} 7 & 0 & 2 & 5 \\ 2 & 5 & 8 & 6 \\ 6 & 3 & 7 & 2 \\ 6 & 5 & 5 & 9 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10D3 | $10$ | $1331$ | not computed | 5A-1 | 2A | 10D3 | $ \left(\begin{array}{rrrr} 8 & 2 & 2 & 4 \\ 2 & 9 & 2 & 0 \\ 8 & 9 & 4 & 8 \\ 7 & 3 & 0 & 3 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10D-3 | $10$ | $1331$ | not computed | 5A1 | 2A | 10D-3 | $ \left(\begin{array}{rrrr} 3 & 8 & 0 & 7 \\ 0 & 4 & 9 & 9 \\ 8 & 2 & 9 & 2 \\ 4 & 3 & 2 & 8 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10E1 | $10$ | $1331$ | not computed | 5D1 | 2A | 10E1 | $ \left(\begin{array}{rrrr} 0 & 7 & 4 & 1 \\ 6 & 5 & 10 & 6 \\ 8 & 1 & 8 & 0 \\ 3 & 7 & 5 & 5 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10E-1 | $10$ | $1331$ | not computed | 5D-1 | 2A | 10E-1 | $ \left(\begin{array}{rrrr} 4 & 0 & 4 & 8 \\ 4 & 2 & 3 & 10 \\ 1 & 8 & 4 & 10 \\ 2 & 9 & 7 & 0 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10E3 | $10$ | $1331$ | not computed | 5D-2 | 2A | 10E3 | $ \left(\begin{array}{rrrr} 8 & 6 & 0 & 5 \\ 8 & 3 & 6 & 6 \\ 6 & 5 & 7 & 4 \\ 4 & 3 & 3 & 0 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10E-3 | $10$ | $1331$ | not computed | 5D2 | 2A | 10E-3 | $ \left(\begin{array}{rrrr} 0 & 9 & 3 & 8 \\ 4 & 2 & 3 & 0 \\ 7 & 8 & 4 & 8 \\ 2 & 3 & 7 & 7 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10F1 | $10$ | $1331$ | not computed | 5B-1 | 2B | 10F1 | $ \left(\begin{array}{rrrr} 8 & 2 & 9 & 7 \\ 0 & 8 & 0 & 9 \\ 5 & 1 & 8 & 9 \\ 0 & 5 & 0 & 8 \end{array}\right) $ |
| $\He_{11}.(C_{10}\times F_{11})$ | 10F-1 | $10$ | $1331$ | not computed | 5B1 | 2B | 10F-1 | $ \left(\begin{array}{rrrr} 1 & 8 & 3 & 6 \\ 0 & 1 & 0 & 3 \\ 9 & 4 & 1 & 3 \\ 0 & 9 & 0 & 1 \end{array}\right) $ |