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Elements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SL(2,139)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 7P | 23P | 139P | ||||||
| $\PSL(2,139)$ | 1A | $1$ | $1$ | $\PSL(2,139)$ | 1A | 1A | 1A | 1A | 1A | 1A | $ \left[ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 2A | $2$ | $9591$ | $D_{70}$ | 1A | 2A | 2A | 2A | 2A | 2A | $ \left[ \left(\begin{array}{rr} 52 & 35 \\ 22 & 87 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 3A | $3$ | $19460$ | $C_{69}$ | 3A | 1A | 3A | 3A | 3A | 3A | $ \left[ \left(\begin{array}{rr} 125 & 36 \\ 137 & 15 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 5A1 | $5$ | $19182$ | $C_{70}$ | 5A2 | 5A2 | 1A | 5A2 | 5A1 | 5A2 | $ \left[ \left(\begin{array}{rr} 123 & 108 \\ 52 & 92 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 5A2 | $5$ | $19182$ | $C_{70}$ | 5A1 | 5A1 | 1A | 5A1 | 5A2 | 5A1 | $ \left[ \left(\begin{array}{rr} 34 & 7 \\ 60 & 41 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 7A1 | $7$ | $19182$ | $C_{70}$ | 7A2 | 7A3 | 7A2 | 1A | 7A3 | 7A2 | $ \left[ \left(\begin{array}{rr} 83 & 117 \\ 10 & 61 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 7A2 | $7$ | $19182$ | $C_{70}$ | 7A3 | 7A1 | 7A3 | 1A | 7A1 | 7A3 | $ \left[ \left(\begin{array}{rr} 3 & 110 \\ 89 & 113 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 7A3 | $7$ | $19182$ | $C_{70}$ | 7A1 | 7A2 | 7A1 | 1A | 7A2 | 7A1 | $ \left[ \left(\begin{array}{rr} 98 & 111 \\ 38 & 70 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 10A1 | $10$ | $19182$ | $C_{70}$ | 5A1 | 10A3 | 2A | 10A3 | 10A1 | 10A3 | $ \left[ \left(\begin{array}{rr} 107 & 8 \\ 9 & 115 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 10A3 | $10$ | $19182$ | $C_{70}$ | 5A2 | 10A1 | 2A | 10A1 | 10A3 | 10A1 | $ \left[ \left(\begin{array}{rr} 45 & 79 \\ 2 & 124 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 14A1 | $14$ | $19182$ | $C_{70}$ | 7A1 | 14A3 | 14A5 | 2A | 14A3 | 14A5 | $ \left[ \left(\begin{array}{rr} 86 & 21 \\ 41 & 107 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 14A3 | $14$ | $19182$ | $C_{70}$ | 7A3 | 14A5 | 14A1 | 2A | 14A5 | 14A1 | $ \left[ \left(\begin{array}{rr} 19 & 55 \\ 114 & 74 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 14A5 | $14$ | $19182$ | $C_{70}$ | 7A2 | 14A1 | 14A3 | 2A | 14A1 | 14A3 | $ \left[ \left(\begin{array}{rr} 42 & 18 \\ 55 & 60 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 23A1 | $23$ | $19460$ | $C_{69}$ | 23A2 | 23A3 | 23A5 | 23A7 | 23A11 | 1A | $ \left[ \left(\begin{array}{rr} 45 & 64 \\ 120 & 112 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 23A2 | $23$ | $19460$ | $C_{69}$ | 23A4 | 23A6 | 23A10 | 23A9 | 23A1 | 1A | $ \left[ \left(\begin{array}{rr} 25 & 99 \\ 64 & 70 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 23A3 | $23$ | $19460$ | $C_{69}$ | 23A6 | 23A9 | 23A8 | 23A2 | 23A10 | 1A | $ \left[ \left(\begin{array}{rr} 61 & 100 \\ 118 & 18 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 23A4 | $23$ | $19460$ | $C_{69}$ | 23A8 | 23A11 | 23A3 | 23A5 | 23A2 | 1A | $ \left[ \left(\begin{array}{rr} 128 & 47 \\ 36 & 23 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 23A5 | $23$ | $19460$ | $C_{69}$ | 23A10 | 23A8 | 23A2 | 23A11 | 23A9 | 1A | $ \left[ \left(\begin{array}{rr} 137 & 27 \\ 68 & 124 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 23A6 | $23$ | $19460$ | $C_{69}$ | 23A11 | 23A5 | 23A7 | 23A4 | 23A3 | 1A | $ \left[ \left(\begin{array}{rr} 47 & 23 \\ 130 & 108 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 23A7 | $23$ | $19460$ | $C_{69}$ | 23A9 | 23A2 | 23A11 | 23A3 | 23A8 | 1A | $ \left[ \left(\begin{array}{rr} 10 & 24 \\ 45 & 122 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 23A8 | $23$ | $19460$ | $C_{69}$ | 23A7 | 23A1 | 23A6 | 23A10 | 23A4 | 1A | $ \left[ \left(\begin{array}{rr} 6 & 8 \\ 15 & 136 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 23A9 | $23$ | $19460$ | $C_{69}$ | 23A5 | 23A4 | 23A1 | 23A6 | 23A7 | 1A | $ \left[ \left(\begin{array}{rr} 21 & 110 \\ 102 & 71 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 23A10 | $23$ | $19460$ | $C_{69}$ | 23A3 | 23A7 | 23A4 | 23A1 | 23A5 | 1A | $ \left[ \left(\begin{array}{rr} 106 & 42 \\ 44 & 24 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 23A11 | $23$ | $19460$ | $C_{69}$ | 23A1 | 23A10 | 23A9 | 23A8 | 23A6 | 1A | $ \left[ \left(\begin{array}{rr} 80 & 90 \\ 134 & 83 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A1 | $35$ | $19182$ | $C_{70}$ | 35A2 | 35A3 | 7A1 | 5A1 | 35A11 | 35A12 | $ \left[ \left(\begin{array}{rr} 138 & 30 \\ 138 & 29 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A2 | $35$ | $19182$ | $C_{70}$ | 35A4 | 35A6 | 7A2 | 5A2 | 35A13 | 35A11 | $ \left[ \left(\begin{array}{rr} 29 & 133 \\ 28 & 23 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A3 | $35$ | $19182$ | $C_{70}$ | 35A6 | 35A9 | 7A3 | 5A2 | 35A2 | 35A1 | $ \left[ \left(\begin{array}{rr} 116 & 1 \\ 88 & 117 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A4 | $35$ | $19182$ | $C_{70}$ | 35A8 | 35A12 | 7A3 | 5A1 | 35A9 | 35A13 | $ \left[ \left(\begin{array}{rr} 22 & 34 \\ 73 & 56 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A6 | $35$ | $19182$ | $C_{70}$ | 35A12 | 35A17 | 7A1 | 5A1 | 35A4 | 35A2 | $ \left[ \left(\begin{array}{rr} 61 & 94 \\ 71 & 16 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A8 | $35$ | $19182$ | $C_{70}$ | 35A16 | 35A11 | 7A1 | 5A2 | 35A17 | 35A9 | $ \left[ \left(\begin{array}{rr} 92 & 128 \\ 5 & 81 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A9 | $35$ | $19182$ | $C_{70}$ | 35A17 | 35A8 | 7A2 | 5A1 | 35A6 | 35A3 | $ \left[ \left(\begin{array}{rr} 81 & 61 \\ 86 & 3 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A11 | $35$ | $19182$ | $C_{70}$ | 35A13 | 35A2 | 7A3 | 5A1 | 35A16 | 35A8 | $ \left[ \left(\begin{array}{rr} 113 & 56 \\ 63 & 30 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A12 | $35$ | $19182$ | $C_{70}$ | 35A11 | 35A1 | 7A2 | 5A2 | 35A8 | 35A4 | $ \left[ \left(\begin{array}{rr} 30 & 129 \\ 93 & 20 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A13 | $35$ | $19182$ | $C_{70}$ | 35A9 | 35A4 | 7A1 | 5A2 | 35A3 | 35A16 | $ \left[ \left(\begin{array}{rr} 20 & 85 \\ 113 & 105 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A16 | $35$ | $19182$ | $C_{70}$ | 35A3 | 35A13 | 7A2 | 5A1 | 35A1 | 35A17 | $ \left[ \left(\begin{array}{rr} 70 & 96 \\ 108 & 27 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 35A17 | $35$ | $19182$ | $C_{70}$ | 35A1 | 35A16 | 7A3 | 5A2 | 35A12 | 35A6 | $ \left[ \left(\begin{array}{rr} 112 & 19 \\ 4 & 131 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A1 | $69$ | $19460$ | $C_{69}$ | 69A2 | 23A1 | 69A5 | 69A7 | 69A11 | 3A | $ \left[ \left(\begin{array}{rr} 106 & 89 \\ 80 & 58 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A2 | $69$ | $19460$ | $C_{69}$ | 69A4 | 23A2 | 69A10 | 69A14 | 69A22 | 3A | $ \left[ \left(\begin{array}{rr} 8 & 1 \\ 54 & 59 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A4 | $69$ | $19460$ | $C_{69}$ | 69A8 | 23A4 | 69A20 | 69A28 | 69A25 | 3A | $ \left[ \left(\begin{array}{rr} 118 & 67 \\ 4 & 60 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A5 | $69$ | $19460$ | $C_{69}$ | 69A10 | 23A5 | 69A25 | 69A34 | 69A14 | 3A | $ \left[ \left(\begin{array}{rr} 76 & 71 \\ 81 & 83 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A7 | $69$ | $19460$ | $C_{69}$ | 69A14 | 23A7 | 69A34 | 69A20 | 69A8 | 3A | $ \left[ \left(\begin{array}{rr} 133 & 95 \\ 126 & 113 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A8 | $69$ | $19460$ | $C_{69}$ | 69A16 | 23A8 | 69A29 | 69A13 | 69A19 | 3A | $ \left[ \left(\begin{array}{rr} 14 & 111 \\ 17 & 115 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A10 | $69$ | $19460$ | $C_{69}$ | 69A20 | 23A10 | 69A19 | 69A1 | 69A28 | 3A | $ \left[ \left(\begin{array}{rr} 10 & 109 \\ 48 & 9 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A11 | $69$ | $19460$ | $C_{69}$ | 69A22 | 23A11 | 69A14 | 69A8 | 69A17 | 3A | $ \left[ \left(\begin{array}{rr} 89 & 16 \\ 30 & 71 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A13 | $69$ | $19460$ | $C_{69}$ | 69A26 | 23A10 | 69A4 | 69A22 | 69A5 | 3A | $ \left[ \left(\begin{array}{rr} 47 & 60 \\ 43 & 49 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A14 | $69$ | $19460$ | $C_{69}$ | 69A28 | 23A9 | 69A1 | 69A29 | 69A16 | 3A | $ \left[ \left(\begin{array}{rr} 52 & 18 \\ 138 & 136 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A16 | $69$ | $19460$ | $C_{69}$ | 69A32 | 23A7 | 69A11 | 69A26 | 69A31 | 3A | $ \left[ \left(\begin{array}{rr} 137 & 2 \\ 108 & 100 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A17 | $69$ | $19460$ | $C_{69}$ | 69A34 | 23A6 | 69A16 | 69A19 | 69A20 | 3A | $ \left[ \left(\begin{array}{rr} 87 & 77 \\ 127 & 122 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A19 | $69$ | $19460$ | $C_{69}$ | 69A31 | 23A4 | 69A26 | 69A5 | 69A2 | 3A | $ \left[ \left(\begin{array}{rr} 11 & 96 \\ 41 & 42 \end{array}\right) \right] $ |
| $\PSL(2,139)$ | 69A20 | $69$ | $19460$ | $C_{69}$ | 69A29 | 23A3 | 69A31 | 69A2 | 69A13 | 3A | $ \left[ \left(\begin{array}{rr} 50 & 125 \\ 78 & 31 \end{array}\right) \right] $ |