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Elements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SL(2,107)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||
|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 53P | 107P | ||||||
| $\PSL(2,107)$ | 1A | $1$ | $1$ | $\PSL(2,107)$ | 1A | 1A | 1A | 1A | $ \left[ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 2A | $2$ | $5671$ | $D_{54}$ | 1A | 2A | 2A | 2A | $ \left[ \left(\begin{array}{rr} 83 & 67 \\ 92 & 24 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 3A | $3$ | $11342$ | $C_{54}$ | 3A | 1A | 3A | 3A | $ \left[ \left(\begin{array}{rr} 56 & 39 \\ 28 & 52 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 6A | $6$ | $11342$ | $C_{54}$ | 3A | 2A | 6A | 6A | $ \left[ \left(\begin{array}{rr} 86 & 87 \\ 46 & 3 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 9A1 | $9$ | $11342$ | $C_{54}$ | 9A2 | 3A | 9A4 | 9A1 | $ \left[ \left(\begin{array}{rr} 16 & 60 \\ 76 & 51 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 9A2 | $9$ | $11342$ | $C_{54}$ | 9A4 | 3A | 9A1 | 9A2 | $ \left[ \left(\begin{array}{rr} 106 & 46 \\ 44 & 8 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 9A4 | $9$ | $11342$ | $C_{54}$ | 9A1 | 3A | 9A2 | 9A4 | $ \left[ \left(\begin{array}{rr} 99 & 1 \\ 94 & 55 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 18A1 | $18$ | $11342$ | $C_{54}$ | 9A1 | 6A | 18A5 | 18A1 | $ \left[ \left(\begin{array}{rr} 86 & 23 \\ 22 & 37 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 18A5 | $18$ | $11342$ | $C_{54}$ | 9A4 | 6A | 18A7 | 18A5 | $ \left[ \left(\begin{array}{rr} 70 & 74 \\ 1 & 24 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 18A7 | $18$ | $11342$ | $C_{54}$ | 9A2 | 6A | 18A1 | 18A7 | $ \left[ \left(\begin{array}{rr} 3 & 56 \\ 21 & 0 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 27A1 | $27$ | $11342$ | $C_{54}$ | 27A2 | 9A1 | 27A13 | 27A1 | $ \left[ \left(\begin{array}{rr} 30 & 7 \\ 16 & 43 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 27A2 | $27$ | $11342$ | $C_{54}$ | 27A4 | 9A2 | 27A1 | 27A2 | $ \left[ \left(\begin{array}{rr} 49 & 83 \\ 98 & 35 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 27A4 | $27$ | $11342$ | $C_{54}$ | 27A8 | 9A4 | 27A2 | 27A4 | $ \left[ \left(\begin{array}{rr} 58 & 90 \\ 7 & 57 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 27A5 | $27$ | $11342$ | $C_{54}$ | 27A10 | 9A4 | 27A11 | 27A5 | $ \left[ \left(\begin{array}{rr} 30 & 4 \\ 55 & 68 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 27A7 | $27$ | $11342$ | $C_{54}$ | 27A13 | 9A2 | 27A10 | 27A7 | $ \left[ \left(\begin{array}{rr} 64 & 45 \\ 57 & 10 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 27A8 | $27$ | $11342$ | $C_{54}$ | 27A11 | 9A1 | 27A4 | 27A8 | $ \left[ \left(\begin{array}{rr} 35 & 78 \\ 56 & 27 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 27A10 | $27$ | $11342$ | $C_{54}$ | 27A7 | 9A1 | 27A5 | 27A10 | $ \left[ \left(\begin{array}{rr} 50 & 71 \\ 40 & 29 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 27A11 | $27$ | $11342$ | $C_{54}$ | 27A5 | 9A2 | 27A8 | 27A11 | $ \left[ \left(\begin{array}{rr} 39 & 21 \\ 48 & 78 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 27A13 | $27$ | $11342$ | $C_{54}$ | 27A1 | 9A4 | 27A7 | 27A13 | $ \left[ \left(\begin{array}{rr} 10 & 13 \\ 45 & 80 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A1 | $53$ | $11556$ | $C_{53}$ | 53A2 | 53A3 | 53A13 | 1A | $ \left[ \left(\begin{array}{rr} 44 & 6 \\ 2 & 100 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A2 | $53$ | $11556$ | $C_{53}$ | 53A4 | 53A6 | 53A26 | 1A | $ \left[ \left(\begin{array}{rr} 22 & 8 \\ 74 & 61 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A3 | $53$ | $11556$ | $C_{53}$ | 53A6 | 53A9 | 53A14 | 1A | $ \left[ \left(\begin{array}{rr} 86 & 31 \\ 46 & 90 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A4 | $53$ | $11556$ | $C_{53}$ | 53A8 | 53A12 | 53A1 | 1A | $ \left[ \left(\begin{array}{rr} 101 & 85 \\ 64 & 74 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A5 | $53$ | $11556$ | $C_{53}$ | 53A10 | 53A15 | 53A12 | 1A | $ \left[ \left(\begin{array}{rr} 94 & 96 \\ 32 & 27 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A6 | $53$ | $11556$ | $C_{53}$ | 53A12 | 53A18 | 53A25 | 1A | $ \left[ \left(\begin{array}{rr} 59 & 1 \\ 36 & 104 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A7 | $53$ | $11556$ | $C_{53}$ | 53A14 | 53A21 | 53A15 | 1A | $ \left[ \left(\begin{array}{rr} 77 & 81 \\ 27 & 84 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A8 | $53$ | $11556$ | $C_{53}$ | 53A16 | 53A24 | 53A2 | 1A | $ \left[ \left(\begin{array}{rr} 88 & 105 \\ 35 & 105 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A9 | $53$ | $11556$ | $C_{53}$ | 53A18 | 53A26 | 53A11 | 1A | $ \left[ \left(\begin{array}{rr} 16 & 7 \\ 38 & 10 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A10 | $53$ | $11556$ | $C_{53}$ | 53A20 | 53A23 | 53A24 | 1A | $ \left[ \left(\begin{array}{rr} 76 & 47 \\ 87 & 51 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A11 | $53$ | $11556$ | $C_{53}$ | 53A22 | 53A20 | 53A16 | 1A | $ \left[ \left(\begin{array}{rr} 93 & 87 \\ 29 & 49 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A12 | $53$ | $11556$ | $C_{53}$ | 53A24 | 53A17 | 53A3 | 1A | $ \left[ \left(\begin{array}{rr} 93 & 56 \\ 90 & 45 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A13 | $53$ | $11556$ | $C_{53}$ | 53A26 | 53A14 | 53A10 | 1A | $ \left[ \left(\begin{array}{rr} 76 & 48 \\ 16 & 96 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A14 | $53$ | $11556$ | $C_{53}$ | 53A25 | 53A11 | 53A23 | 1A | $ \left[ \left(\begin{array}{rr} 91 & 94 \\ 67 & 41 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A15 | $53$ | $11556$ | $C_{53}$ | 53A23 | 53A8 | 53A17 | 1A | $ \left[ \left(\begin{array}{rr} 88 & 5 \\ 73 & 99 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A16 | $53$ | $11556$ | $C_{53}$ | 53A21 | 53A5 | 53A4 | 1A | $ \left[ \left(\begin{array}{rr} 77 & 42 \\ 14 & 41 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A17 | $53$ | $11556$ | $C_{53}$ | 53A19 | 53A2 | 53A9 | 1A | $ \left[ \left(\begin{array}{rr} 48 & 61 \\ 56 & 11 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A18 | $53$ | $11556$ | $C_{53}$ | 53A17 | 53A1 | 53A22 | 1A | $ \left[ \left(\begin{array}{rr} 94 & 75 \\ 25 & 45 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A19 | $53$ | $11556$ | $C_{53}$ | 53A15 | 53A4 | 53A18 | 1A | $ \left[ \left(\begin{array}{rr} 6 & 39 \\ 13 & 49 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A20 | $53$ | $11556$ | $C_{53}$ | 53A13 | 53A7 | 53A5 | 1A | $ \left[ \left(\begin{array}{rr} 21 & 84 \\ 28 & 56 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A21 | $53$ | $11556$ | $C_{53}$ | 53A11 | 53A10 | 53A8 | 1A | $ \left[ \left(\begin{array}{rr} 22 & 73 \\ 60 & 97 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A22 | $53$ | $11556$ | $C_{53}$ | 53A9 | 53A13 | 53A21 | 1A | $ \left[ \left(\begin{array}{rr} 44 & 49 \\ 52 & 2 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A23 | $53$ | $11556$ | $C_{53}$ | 53A7 | 53A16 | 53A19 | 1A | $ \left[ \left(\begin{array}{rr} 106 & 79 \\ 62 & 23 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A24 | $53$ | $11556$ | $C_{53}$ | 53A5 | 53A19 | 53A6 | 1A | $ \left[ \left(\begin{array}{rr} 100 & 24 \\ 8 & 3 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A25 | $53$ | $11556$ | $C_{53}$ | 53A3 | 53A22 | 53A7 | 1A | $ \left[ \left(\begin{array}{rr} 46 & 103 \\ 70 & 80 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 53A26 | $53$ | $11556$ | $C_{53}$ | 53A1 | 53A25 | 53A20 | 1A | $ \left[ \left(\begin{array}{rr} 17 & 17 \\ 77 & 33 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 54A1 | $54$ | $11342$ | $C_{54}$ | 27A1 | 18A1 | 54A13 | 54A1 | $ \left[ \left(\begin{array}{rr} 94 & 19 \\ 74 & 7 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 54A5 | $54$ | $11342$ | $C_{54}$ | 27A5 | 18A5 | 54A11 | 54A5 | $ \left[ \left(\begin{array}{rr} 59 & 93 \\ 75 & 33 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 54A7 | $54$ | $11342$ | $C_{54}$ | 27A7 | 18A7 | 54A17 | 54A7 | $ \left[ \left(\begin{array}{rr} 48 & 25 \\ 103 & 18 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 54A11 | $54$ | $11342$ | $C_{54}$ | 27A11 | 18A7 | 54A19 | 54A11 | $ \left[ \left(\begin{array}{rr} 94 & 44 \\ 70 & 84 \end{array}\right) \right] $ |
| $\PSL(2,107)$ | 54A13 | $54$ | $11342$ | $C_{54}$ | 27A13 | 18A5 | 54A7 | 54A13 | $ \left[ \left(\begin{array}{rr} 100 & 89 \\ 20 & 36 \end{array}\right) \right] $ |