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Elements of the group are displayed as matrices in $\GL_{2}(\F_{107})$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 53P | ||||||
| $D_{106}:C_{106}$ | 1A | $1$ | $1$ | $D_{106}:C_{106}$ | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 2A | $2$ | $1$ | $D_{106}:C_{106}$ | 1A | 2A | $ \left(\begin{array}{rr} 106 & 0 \\ 0 & 106 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 2B | $2$ | $2$ | $C_{106}^2$ | 1A | 2B | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 106 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 2C | $2$ | $106$ | $C_2\times C_{106}$ | 1A | 2C | $ \left(\begin{array}{rr} 0 & 101 \\ 89 & 0 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 4A | $4$ | $106$ | $C_{212}$ | 2A | 4A | $ \left(\begin{array}{rr} 0 & 69 \\ 31 & 0 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A1 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A2 | 53A13 | $ \left(\begin{array}{rr} 4 & 0 \\ 0 & 4 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-1 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-2 | 53A-13 | $ \left(\begin{array}{rr} 27 & 0 \\ 0 & 27 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A2 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A4 | 53A26 | $ \left(\begin{array}{rr} 16 & 0 \\ 0 & 16 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-2 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-4 | 53A-26 | $ \left(\begin{array}{rr} 87 & 0 \\ 0 & 87 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A3 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A6 | 53A-14 | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 64 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-3 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-6 | 53A14 | $ \left(\begin{array}{rr} 102 & 0 \\ 0 & 102 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A4 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A8 | 53A-1 | $ \left(\begin{array}{rr} 42 & 0 \\ 0 & 42 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-4 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-8 | 53A1 | $ \left(\begin{array}{rr} 79 & 0 \\ 0 & 79 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A5 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A10 | 53A12 | $ \left(\begin{array}{rr} 61 & 0 \\ 0 & 61 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-5 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-10 | 53A-12 | $ \left(\begin{array}{rr} 100 & 0 \\ 0 & 100 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A6 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A12 | 53A25 | $ \left(\begin{array}{rr} 30 & 0 \\ 0 & 30 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-6 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-12 | 53A-25 | $ \left(\begin{array}{rr} 25 & 0 \\ 0 & 25 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A7 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A14 | 53A-15 | $ \left(\begin{array}{rr} 13 & 0 \\ 0 & 13 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-7 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-14 | 53A15 | $ \left(\begin{array}{rr} 33 & 0 \\ 0 & 33 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A8 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A16 | 53A-2 | $ \left(\begin{array}{rr} 52 & 0 \\ 0 & 52 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-8 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-16 | 53A2 | $ \left(\begin{array}{rr} 35 & 0 \\ 0 & 35 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A9 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A18 | 53A11 | $ \left(\begin{array}{rr} 101 & 0 \\ 0 & 101 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-9 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-18 | 53A-11 | $ \left(\begin{array}{rr} 89 & 0 \\ 0 & 89 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A10 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A20 | 53A24 | $ \left(\begin{array}{rr} 83 & 0 \\ 0 & 83 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-10 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-20 | 53A-24 | $ \left(\begin{array}{rr} 49 & 0 \\ 0 & 49 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A11 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A22 | 53A-16 | $ \left(\begin{array}{rr} 11 & 0 \\ 0 & 11 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-11 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-22 | 53A16 | $ \left(\begin{array}{rr} 39 & 0 \\ 0 & 39 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A12 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A24 | 53A-3 | $ \left(\begin{array}{rr} 44 & 0 \\ 0 & 44 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-12 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-24 | 53A3 | $ \left(\begin{array}{rr} 90 & 0 \\ 0 & 90 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A13 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A26 | 53A10 | $ \left(\begin{array}{rr} 69 & 0 \\ 0 & 69 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-13 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-26 | 53A-10 | $ \left(\begin{array}{rr} 76 & 0 \\ 0 & 76 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A14 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-25 | 53A23 | $ \left(\begin{array}{rr} 62 & 0 \\ 0 & 62 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-14 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A25 | 53A-23 | $ \left(\begin{array}{rr} 19 & 0 \\ 0 & 19 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A15 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-23 | 53A-17 | $ \left(\begin{array}{rr} 34 & 0 \\ 0 & 34 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-15 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A23 | 53A17 | $ \left(\begin{array}{rr} 85 & 0 \\ 0 & 85 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A16 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-21 | 53A-4 | $ \left(\begin{array}{rr} 29 & 0 \\ 0 & 29 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-16 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A21 | 53A4 | $ \left(\begin{array}{rr} 48 & 0 \\ 0 & 48 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A17 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-19 | 53A9 | $ \left(\begin{array}{rr} 9 & 0 \\ 0 & 9 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-17 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A19 | 53A-9 | $ \left(\begin{array}{rr} 12 & 0 \\ 0 & 12 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A18 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-17 | 53A22 | $ \left(\begin{array}{rr} 36 & 0 \\ 0 & 36 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-18 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A17 | 53A-22 | $ \left(\begin{array}{rr} 3 & 0 \\ 0 & 3 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A19 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-15 | 53A-18 | $ \left(\begin{array}{rr} 37 & 0 \\ 0 & 37 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-19 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A15 | 53A18 | $ \left(\begin{array}{rr} 81 & 0 \\ 0 & 81 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A20 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-13 | 53A-5 | $ \left(\begin{array}{rr} 41 & 0 \\ 0 & 41 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-20 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A13 | 53A5 | $ \left(\begin{array}{rr} 47 & 0 \\ 0 & 47 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A21 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-11 | 53A8 | $ \left(\begin{array}{rr} 57 & 0 \\ 0 & 57 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-21 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A11 | 53A-8 | $ \left(\begin{array}{rr} 92 & 0 \\ 0 & 92 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A22 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-9 | 53A21 | $ \left(\begin{array}{rr} 14 & 0 \\ 0 & 14 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A-22 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A9 | 53A-21 | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 23 \end{array}\right) $ |
| $D_{106}:C_{106}$ | 53A23 | $53$ | $1$ | $D_{106}:C_{106}$ | 53A-7 | 53A-19 | $ \left(\begin{array}{rr} 56 & 0 \\ 0 & 56 \end{array}\right) $ |