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Elements of the group are displayed as matrices in $\GL_{2}(\F_{241})$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 5P | ||||||
| $C_{80}.D_{80}$ | 1A | $1$ | $1$ | not computed | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 2A | $2$ | $1$ | not computed | 1A | 2A | $ \left(\begin{array}{rr} 240 & 0 \\ 0 & 240 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 2B | $2$ | $2$ | not computed | 1A | 2B | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 240 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 2C | $2$ | $80$ | not computed | 1A | 2C | $ \left(\begin{array}{rr} 0 & 98 \\ 91 & 0 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 4A1 | $4$ | $1$ | not computed | 2A | 4A1 | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 64 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 4A-1 | $4$ | $1$ | not computed | 2A | 4A-1 | $ \left(\begin{array}{rr} 177 & 0 \\ 0 & 177 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 4B | $4$ | $2$ | not computed | 2A | 4B | $ \left(\begin{array}{rr} 177 & 0 \\ 0 & 64 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 4C1 | $4$ | $2$ | not computed | 2B | 4C1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 177 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 4C-1 | $4$ | $2$ | not computed | 2B | 4C-1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 64 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 4D1 | $4$ | $2$ | not computed | 2B | 4D1 | $ \left(\begin{array}{rr} 240 & 0 \\ 0 & 177 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 4D-1 | $4$ | $2$ | not computed | 2B | 4D-1 | $ \left(\begin{array}{rr} 240 & 0 \\ 0 & 64 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 4E | $4$ | $80$ | not computed | 2A | 4E | $ \left(\begin{array}{rr} 0 & 91 \\ 143 & 0 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5A1 | $5$ | $1$ | not computed | 5A2 | 1A | $ \left(\begin{array}{rr} 87 & 0 \\ 0 & 87 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5A-1 | $5$ | $1$ | not computed | 5A-2 | 1A | $ \left(\begin{array}{rr} 205 & 0 \\ 0 & 205 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5A2 | $5$ | $1$ | not computed | 5A-1 | 1A | $ \left(\begin{array}{rr} 98 & 0 \\ 0 & 98 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5A-2 | $5$ | $1$ | not computed | 5A1 | 1A | $ \left(\begin{array}{rr} 91 & 0 \\ 0 & 91 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5B1 | $5$ | $2$ | not computed | 5B2 | 1A | $ \left(\begin{array}{rr} 87 & 0 \\ 0 & 205 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5B2 | $5$ | $2$ | not computed | 5B1 | 1A | $ \left(\begin{array}{rr} 98 & 0 \\ 0 & 91 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5C1 | $5$ | $2$ | not computed | 5C2 | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 87 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5C-1 | $5$ | $2$ | not computed | 5C-2 | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 205 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5C2 | $5$ | $2$ | not computed | 5C-1 | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 98 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5C-2 | $5$ | $2$ | not computed | 5C1 | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 91 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5D1 | $5$ | $2$ | not computed | 5D2 | 1A | $ \left(\begin{array}{rr} 91 & 0 \\ 0 & 87 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5D-1 | $5$ | $2$ | not computed | 5D-2 | 1A | $ \left(\begin{array}{rr} 98 & 0 \\ 0 & 205 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5D2 | $5$ | $2$ | not computed | 5D-1 | 1A | $ \left(\begin{array}{rr} 87 & 0 \\ 0 & 98 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 5D-2 | $5$ | $2$ | not computed | 5D1 | 1A | $ \left(\begin{array}{rr} 205 & 0 \\ 0 & 91 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8A1 | $8$ | $1$ | not computed | 4A-1 | 8A-3 | $ \left(\begin{array}{rr} 211 & 0 \\ 0 & 211 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8A-1 | $8$ | $1$ | not computed | 4A1 | 8A3 | $ \left(\begin{array}{rr} 8 & 0 \\ 0 & 8 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8A3 | $8$ | $1$ | not computed | 4A1 | 8A-1 | $ \left(\begin{array}{rr} 233 & 0 \\ 0 & 233 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8A-3 | $8$ | $1$ | not computed | 4A-1 | 8A1 | $ \left(\begin{array}{rr} 30 & 0 \\ 0 & 30 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8B1 | $8$ | $2$ | not computed | 4B | 8B3 | $ \left(\begin{array}{rr} 211 & 0 \\ 0 & 8 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8B3 | $8$ | $2$ | not computed | 4B | 8B1 | $ \left(\begin{array}{rr} 233 & 0 \\ 0 & 30 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8C1 | $8$ | $2$ | not computed | 4B | 8C-1 | $ \left(\begin{array}{rr} 211 & 0 \\ 0 & 233 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8C-1 | $8$ | $2$ | not computed | 4B | 8C1 | $ \left(\begin{array}{rr} 8 & 0 \\ 0 & 30 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8D1 | $8$ | $2$ | not computed | 4A-1 | 8D1 | $ \left(\begin{array}{rr} 211 & 0 \\ 0 & 30 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8D-1 | $8$ | $2$ | not computed | 4A1 | 8D-1 | $ \left(\begin{array}{rr} 8 & 0 \\ 0 & 233 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8E1 | $8$ | $2$ | not computed | 4C1 | 8E-3 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 211 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8E-1 | $8$ | $2$ | not computed | 4C-1 | 8E3 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 8 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8E3 | $8$ | $2$ | not computed | 4C-1 | 8E-1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 233 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8E-3 | $8$ | $2$ | not computed | 4C1 | 8E1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 30 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8F1 | $8$ | $2$ | not computed | 4D1 | 8F-3 | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 211 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8F-1 | $8$ | $2$ | not computed | 4D-1 | 8F3 | $ \left(\begin{array}{rr} 177 & 0 \\ 0 & 8 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8F3 | $8$ | $2$ | not computed | 4D-1 | 8F-1 | $ \left(\begin{array}{rr} 177 & 0 \\ 0 & 233 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8F-3 | $8$ | $2$ | not computed | 4D1 | 8F1 | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 30 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8G1 | $8$ | $2$ | not computed | 4D-1 | 8G-3 | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 8 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8G-1 | $8$ | $2$ | not computed | 4D1 | 8G3 | $ \left(\begin{array}{rr} 177 & 0 \\ 0 & 211 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8G3 | $8$ | $2$ | not computed | 4D1 | 8G-1 | $ \left(\begin{array}{rr} 177 & 0 \\ 0 & 30 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8G-3 | $8$ | $2$ | not computed | 4D-1 | 8G1 | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 233 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8H1 | $8$ | $2$ | not computed | 4C1 | 8H-3 | $ \left(\begin{array}{rr} 240 & 0 \\ 0 & 211 \end{array}\right) $ |
| $C_{80}.D_{80}$ | 8H-1 | $8$ | $2$ | not computed | 4C-1 | 8H3 | $ \left(\begin{array}{rr} 240 & 0 \\ 0 & 8 \end{array}\right) $ |