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Elements of the group are displayed as matrices in $\GL_{2}(\F_{97})$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_{96}.D_{96}$ | 1A | $1$ | $1$ | not computed | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 2A | $2$ | $1$ | not computed | 1A | 2A | $ \left(\begin{array}{rr} 96 & 0 \\ 0 & 96 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 2B | $2$ | $2$ | not computed | 1A | 2B | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 96 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 2C | $2$ | $96$ | not computed | 1A | 2C | $ \left(\begin{array}{rr} 0 & 35 \\ 61 & 0 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 3A1 | $3$ | $1$ | not computed | 3A-1 | 1A | $ \left(\begin{array}{rr} 35 & 0 \\ 0 & 35 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 3A-1 | $3$ | $1$ | not computed | 3A1 | 1A | $ \left(\begin{array}{rr} 61 & 0 \\ 0 & 61 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 3B | $3$ | $2$ | not computed | 3B | 1A | $ \left(\begin{array}{rr} 35 & 0 \\ 0 & 61 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 3C1 | $3$ | $2$ | not computed | 3C-1 | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 35 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 3C-1 | $3$ | $2$ | not computed | 3C1 | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 61 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 4A1 | $4$ | $1$ | not computed | 2A | 4A-1 | $ \left(\begin{array}{rr} 22 & 0 \\ 0 & 22 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 4A-1 | $4$ | $1$ | not computed | 2A | 4A1 | $ \left(\begin{array}{rr} 75 & 0 \\ 0 & 75 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 4B | $4$ | $2$ | not computed | 2A | 4B | $ \left(\begin{array}{rr} 22 & 0 \\ 0 & 75 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 4C1 | $4$ | $2$ | not computed | 2B | 4C-1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 22 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 4C-1 | $4$ | $2$ | not computed | 2B | 4C1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 75 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 4D1 | $4$ | $2$ | not computed | 2B | 4D-1 | $ \left(\begin{array}{rr} 96 & 0 \\ 0 & 22 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 4D-1 | $4$ | $2$ | not computed | 2B | 4D1 | $ \left(\begin{array}{rr} 96 & 0 \\ 0 & 75 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 4E | $4$ | $96$ | not computed | 2A | 4E | $ \left(\begin{array}{rr} 0 & 36 \\ 35 & 0 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6A1 | $6$ | $1$ | not computed | 3A1 | 2A | $ \left(\begin{array}{rr} 36 & 0 \\ 0 & 36 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6A-1 | $6$ | $1$ | not computed | 3A-1 | 2A | $ \left(\begin{array}{rr} 62 & 0 \\ 0 & 62 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6B | $6$ | $2$ | not computed | 3B | 2A | $ \left(\begin{array}{rr} 36 & 0 \\ 0 & 62 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6C1 | $6$ | $2$ | not computed | 3C1 | 2B | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 36 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6C-1 | $6$ | $2$ | not computed | 3C-1 | 2B | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 62 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6D1 | $6$ | $2$ | not computed | 3A1 | 2B | $ \left(\begin{array}{rr} 61 & 0 \\ 0 & 36 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6D-1 | $6$ | $2$ | not computed | 3A-1 | 2B | $ \left(\begin{array}{rr} 35 & 0 \\ 0 & 62 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6E1 | $6$ | $2$ | not computed | 3B | 2B | $ \left(\begin{array}{rr} 61 & 0 \\ 0 & 62 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6E-1 | $6$ | $2$ | not computed | 3B | 2B | $ \left(\begin{array}{rr} 35 & 0 \\ 0 & 36 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6F1 | $6$ | $2$ | not computed | 3C1 | 2B | $ \left(\begin{array}{rr} 61 & 0 \\ 0 & 96 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6F-1 | $6$ | $2$ | not computed | 3C-1 | 2B | $ \left(\begin{array}{rr} 35 & 0 \\ 0 & 96 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6G1 | $6$ | $2$ | not computed | 3C1 | 2A | $ \left(\begin{array}{rr} 36 & 0 \\ 0 & 96 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6G-1 | $6$ | $2$ | not computed | 3C-1 | 2A | $ \left(\begin{array}{rr} 62 & 0 \\ 0 & 96 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6H1 | $6$ | $96$ | not computed | 3A1 | 2C | $ \left(\begin{array}{rr} 0 & 1 \\ 35 & 0 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 6H-1 | $6$ | $96$ | not computed | 3A-1 | 2C | $ \left(\begin{array}{rr} 0 & 1 \\ 61 & 0 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8A1 | $8$ | $1$ | not computed | 4A1 | 8A3 | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 64 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8A-1 | $8$ | $1$ | not computed | 4A-1 | 8A-3 | $ \left(\begin{array}{rr} 47 & 0 \\ 0 & 47 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8A3 | $8$ | $1$ | not computed | 4A-1 | 8A1 | $ \left(\begin{array}{rr} 50 & 0 \\ 0 & 50 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8A-3 | $8$ | $1$ | not computed | 4A1 | 8A-1 | $ \left(\begin{array}{rr} 33 & 0 \\ 0 & 33 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8B1 | $8$ | $2$ | not computed | 4B | 8B3 | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 47 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8B3 | $8$ | $2$ | not computed | 4B | 8B1 | $ \left(\begin{array}{rr} 50 & 0 \\ 0 & 33 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8C1 | $8$ | $2$ | not computed | 4B | 8C1 | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 50 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8C-1 | $8$ | $2$ | not computed | 4B | 8C-1 | $ \left(\begin{array}{rr} 47 & 0 \\ 0 & 33 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8D1 | $8$ | $2$ | not computed | 4A1 | 8D-1 | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 33 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8D-1 | $8$ | $2$ | not computed | 4A-1 | 8D1 | $ \left(\begin{array}{rr} 47 & 0 \\ 0 & 50 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8E1 | $8$ | $2$ | not computed | 4C1 | 8E3 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 64 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8E-1 | $8$ | $2$ | not computed | 4C-1 | 8E-3 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 47 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8E3 | $8$ | $2$ | not computed | 4C-1 | 8E1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 50 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8E-3 | $8$ | $2$ | not computed | 4C1 | 8E-1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 33 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8F1 | $8$ | $2$ | not computed | 4D1 | 8F3 | $ \left(\begin{array}{rr} 22 & 0 \\ 0 & 64 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8F-1 | $8$ | $2$ | not computed | 4D-1 | 8F-3 | $ \left(\begin{array}{rr} 75 & 0 \\ 0 & 47 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8F3 | $8$ | $2$ | not computed | 4D-1 | 8F1 | $ \left(\begin{array}{rr} 75 & 0 \\ 0 & 50 \end{array}\right) $ |
| $C_{96}.D_{96}$ | 8F-3 | $8$ | $2$ | not computed | 4D1 | 8F-1 | $ \left(\begin{array}{rr} 22 & 0 \\ 0 & 33 \end{array}\right) $ |