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Elements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SL(2,103)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 13P | 17P | 103P | ||||||
| $\PSL(2,103)$ | 1A | $1$ | $1$ | $\PSL(2,103)$ | 1A | 1A | 1A | 1A | 1A | $ \left[ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 2A | $2$ | $5253$ | $D_{52}$ | 1A | 2A | 2A | 2A | 2A | $ \left[ \left(\begin{array}{rr} 67 & 78 \\ 56 & 36 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 3A | $3$ | $10712$ | $C_{51}$ | 3A | 1A | 3A | 3A | 3A | $ \left[ \left(\begin{array}{rr} 26 & 94 \\ 38 & 78 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 4A | $4$ | $10506$ | $C_{52}$ | 2A | 4A | 4A | 4A | 4A | $ \left[ \left(\begin{array}{rr} 18 & 40 \\ 34 & 47 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 13A1 | $13$ | $10506$ | $C_{52}$ | 13A2 | 13A3 | 1A | 13A4 | 13A1 | $ \left[ \left(\begin{array}{rr} 97 & 31 \\ 83 & 86 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 13A2 | $13$ | $10506$ | $C_{52}$ | 13A4 | 13A6 | 1A | 13A5 | 13A2 | $ \left[ \left(\begin{array}{rr} 34 & 8 \\ 48 & 81 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 13A3 | $13$ | $10506$ | $C_{52}$ | 13A6 | 13A4 | 1A | 13A1 | 13A3 | $ \left[ \left(\begin{array}{rr} 48 & 94 \\ 49 & 8 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 13A4 | $13$ | $10506$ | $C_{52}$ | 13A5 | 13A1 | 1A | 13A3 | 13A4 | $ \left[ \left(\begin{array}{rr} 98 & 96 \\ 61 & 44 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 13A5 | $13$ | $10506$ | $C_{52}$ | 13A3 | 13A2 | 1A | 13A6 | 13A5 | $ \left[ \left(\begin{array}{rr} 67 & 67 \\ 93 & 10 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 13A6 | $13$ | $10506$ | $C_{52}$ | 13A1 | 13A5 | 1A | 13A2 | 13A6 | $ \left[ \left(\begin{array}{rr} 94 & 92 \\ 37 & 68 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 17A1 | $17$ | $10712$ | $C_{51}$ | 17A2 | 17A3 | 17A4 | 1A | 17A1 | $ \left[ \left(\begin{array}{rr} 100 & 12 \\ 18 & 65 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 17A2 | $17$ | $10712$ | $C_{51}$ | 17A4 | 17A6 | 17A8 | 1A | 17A2 | $ \left[ \left(\begin{array}{rr} 84 & 80 \\ 17 & 91 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 17A3 | $17$ | $10712$ | $C_{51}$ | 17A6 | 17A8 | 17A5 | 1A | 17A3 | $ \left[ \left(\begin{array}{rr} 55 & 28 \\ 42 & 42 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 17A4 | $17$ | $10712$ | $C_{51}$ | 17A8 | 17A5 | 17A1 | 1A | 17A4 | $ \left[ \left(\begin{array}{rr} 30 & 8 \\ 12 & 41 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 17A5 | $17$ | $10712$ | $C_{51}$ | 17A7 | 17A2 | 17A3 | 1A | 17A5 | $ \left[ \left(\begin{array}{rr} 49 & 47 \\ 19 & 75 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 17A6 | $17$ | $10712$ | $C_{51}$ | 17A5 | 17A1 | 17A7 | 1A | 17A6 | $ \left[ \left(\begin{array}{rr} 81 & 38 \\ 57 & 56 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 17A7 | $17$ | $10712$ | $C_{51}$ | 17A3 | 17A4 | 17A6 | 1A | 17A7 | $ \left[ \left(\begin{array}{rr} 29 & 43 \\ 13 & 101 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 17A8 | $17$ | $10712$ | $C_{51}$ | 17A1 | 17A7 | 17A2 | 1A | 17A8 | $ \left[ \left(\begin{array}{rr} 34 & 50 \\ 75 & 77 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 26A1 | $26$ | $10506$ | $C_{52}$ | 13A1 | 26A3 | 2A | 26A9 | 26A1 | $ \left[ \left(\begin{array}{rr} 81 & 68 \\ 99 & 17 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 26A3 | $26$ | $10506$ | $C_{52}$ | 13A3 | 26A9 | 2A | 26A1 | 26A3 | $ \left[ \left(\begin{array}{rr} 95 & 87 \\ 7 & 1 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 26A5 | $26$ | $10506$ | $C_{52}$ | 13A5 | 26A11 | 2A | 26A7 | 26A5 | $ \left[ \left(\begin{array}{rr} 44 & 79 \\ 62 & 6 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 26A7 | $26$ | $10506$ | $C_{52}$ | 13A6 | 26A5 | 2A | 26A11 | 26A7 | $ \left[ \left(\begin{array}{rr} 10 & 21 \\ 23 & 69 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 26A9 | $26$ | $10506$ | $C_{52}$ | 13A4 | 26A1 | 2A | 26A3 | 26A9 | $ \left[ \left(\begin{array}{rr} 68 & 47 \\ 76 & 48 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 26A11 | $26$ | $10506$ | $C_{52}$ | 13A2 | 26A7 | 2A | 26A5 | 26A11 | $ \left[ \left(\begin{array}{rr} 94 & 73 \\ 26 & 98 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A1 | $51$ | $10712$ | $C_{51}$ | 51A2 | 17A1 | 51A13 | 3A | 51A1 | $ \left[ \left(\begin{array}{rr} 70 & 34 \\ 51 & 91 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A2 | $51$ | $10712$ | $C_{51}$ | 51A4 | 17A2 | 51A25 | 3A | 51A2 | $ \left[ \left(\begin{array}{rr} 61 & 88 \\ 29 & 79 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A4 | $51$ | $10712$ | $C_{51}$ | 51A8 | 17A4 | 51A1 | 3A | 51A4 | $ \left[ \left(\begin{array}{rr} 93 & 63 \\ 43 & 38 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A5 | $51$ | $10712$ | $C_{51}$ | 51A10 | 17A5 | 51A14 | 3A | 51A5 | $ \left[ \left(\begin{array}{rr} 62 & 66 \\ 99 & 24 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A7 | $51$ | $10712$ | $C_{51}$ | 51A14 | 17A7 | 51A11 | 3A | 51A7 | $ \left[ \left(\begin{array}{rr} 72 & 42 \\ 63 & 1 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A8 | $51$ | $10712$ | $C_{51}$ | 51A16 | 17A8 | 51A2 | 3A | 51A8 | $ \left[ \left(\begin{array}{rr} 28 & 13 \\ 71 & 33 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A10 | $51$ | $10712$ | $C_{51}$ | 51A20 | 17A7 | 51A23 | 3A | 51A10 | $ \left[ \left(\begin{array}{rr} 25 & 92 \\ 35 & 100 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A11 | $51$ | $10712$ | $C_{51}$ | 51A22 | 17A6 | 51A10 | 3A | 51A11 | $ \left[ \left(\begin{array}{rr} 56 & 55 \\ 31 & 93 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A13 | $51$ | $10712$ | $C_{51}$ | 51A25 | 17A4 | 51A16 | 3A | 51A13 | $ \left[ \left(\begin{array}{rr} 67 & 3 \\ 56 & 84 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A14 | $51$ | $10712$ | $C_{51}$ | 51A23 | 17A3 | 51A22 | 3A | 51A14 | $ \left[ \left(\begin{array}{rr} 2 & 79 \\ 67 & 72 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A16 | $51$ | $10712$ | $C_{51}$ | 51A19 | 17A1 | 51A4 | 3A | 51A16 | $ \left[ \left(\begin{array}{rr} 44 & 31 \\ 98 & 48 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A19 | $51$ | $10712$ | $C_{51}$ | 51A13 | 17A2 | 51A8 | 3A | 51A19 | $ \left[ \left(\begin{array}{rr} 89 & 32 \\ 48 & 30 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A20 | $51$ | $10712$ | $C_{51}$ | 51A11 | 17A3 | 51A5 | 3A | 51A20 | $ \left[ \left(\begin{array}{rr} 34 & 67 \\ 49 & 36 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A22 | $51$ | $10712$ | $C_{51}$ | 51A7 | 17A5 | 51A20 | 3A | 51A22 | $ \left[ \left(\begin{array}{rr} 0 & 45 \\ 16 & 49 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A23 | $51$ | $10712$ | $C_{51}$ | 51A5 | 17A6 | 51A7 | 3A | 51A23 | $ \left[ \left(\begin{array}{rr} 29 & 78 \\ 14 & 59 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 51A25 | $51$ | $10712$ | $C_{51}$ | 51A1 | 17A8 | 51A19 | 3A | 51A25 | $ \left[ \left(\begin{array}{rr} 89 & 41 \\ 10 & 81 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 52A1 | $52$ | $10506$ | $C_{52}$ | 26A1 | 52A3 | 4A | 52A17 | 52A1 | $ \left[ \left(\begin{array}{rr} 38 & 22 \\ 29 & 90 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 52A3 | $52$ | $10506$ | $C_{52}$ | 26A3 | 52A9 | 4A | 52A1 | 52A3 | $ \left[ \left(\begin{array}{rr} 3 & 74 \\ 32 & 0 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 52A5 | $52$ | $10506$ | $C_{52}$ | 26A5 | 52A15 | 4A | 52A19 | 52A5 | $ \left[ \left(\begin{array}{rr} 53 & 83 \\ 86 & 90 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 52A7 | $52$ | $10506$ | $C_{52}$ | 26A7 | 52A21 | 4A | 52A15 | 52A7 | $ \left[ \left(\begin{array}{rr} 56 & 32 \\ 89 & 38 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 52A9 | $52$ | $10506$ | $C_{52}$ | 26A9 | 52A25 | 4A | 52A3 | 52A9 | $ \left[ \left(\begin{array}{rr} 82 & 26 \\ 53 & 3 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 52A11 | $52$ | $10506$ | $C_{52}$ | 26A11 | 52A19 | 4A | 52A21 | 52A11 | $ \left[ \left(\begin{array}{rr} 49 & 44 \\ 58 & 50 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 52A15 | $52$ | $10506$ | $C_{52}$ | 26A11 | 52A7 | 4A | 52A5 | 52A15 | $ \left[ \left(\begin{array}{rr} 41 & 53 \\ 9 & 82 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 52A17 | $52$ | $10506$ | $C_{52}$ | 26A9 | 52A1 | 4A | 52A23 | 52A17 | $ \left[ \left(\begin{array}{rr} 19 & 84 \\ 92 & 49 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 52A19 | $52$ | $10506$ | $C_{52}$ | 26A7 | 52A5 | 4A | 52A11 | 52A19 | $ \left[ \left(\begin{array}{rr} 33 & 61 \\ 57 & 18 \end{array}\right) \right] $ |
| $\PSL(2,103)$ | 52A21 | $52$ | $10506$ | $C_{52}$ | 26A5 | 52A11 | 4A | 52A7 | 52A21 | $ \left[ \left(\begin{array}{rr} 60 & 88 \\ 13 & 62 \end{array}\right) \right] $ |