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Elements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SL(2,137)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 17P | 23P | 137P | ||||||
| $\PSL(2,137)$ | 1A | $1$ | $1$ | not computed | 1A | 1A | 1A | 1A | 1A | $ \left[ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 2A | $2$ | $9453$ | not computed | 1A | 2A | 2A | 2A | 2A | $ \left[ \left(\begin{array}{rr} 40 & 89 \\ 99 & 97 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 3A | $3$ | $18632$ | not computed | 3A | 1A | 3A | 3A | 3A | $ \left[ \left(\begin{array}{rr} 47 & 100 \\ 114 & 91 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 4A | $4$ | $18906$ | not computed | 2A | 4A | 4A | 4A | 4A | $ \left[ \left(\begin{array}{rr} 125 & 78 \\ 96 & 118 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 17A1 | $17$ | $18906$ | not computed | 17A2 | 17A3 | 17A6 | 1A | 17A6 | $ \left[ \left(\begin{array}{rr} 112 & 77 \\ 21 & 12 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 17A2 | $17$ | $18906$ | not computed | 17A4 | 17A6 | 17A5 | 1A | 17A5 | $ \left[ \left(\begin{array}{rr} 87 & 42 \\ 136 & 20 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 17A3 | $17$ | $18906$ | not computed | 17A6 | 17A8 | 17A1 | 1A | 17A1 | $ \left[ \left(\begin{array}{rr} 60 & 58 \\ 103 & 111 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 17A4 | $17$ | $18906$ | not computed | 17A8 | 17A5 | 17A7 | 1A | 17A7 | $ \left[ \left(\begin{array}{rr} 8 & 27 \\ 107 & 53 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 17A5 | $17$ | $18906$ | not computed | 17A7 | 17A2 | 17A4 | 1A | 17A4 | $ \left[ \left(\begin{array}{rr} 44 & 19 \\ 55 & 30 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 17A6 | $17$ | $18906$ | not computed | 17A5 | 17A1 | 17A2 | 1A | 17A2 | $ \left[ \left(\begin{array}{rr} 121 & 54 \\ 77 & 74 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 17A7 | $17$ | $18906$ | not computed | 17A3 | 17A4 | 17A8 | 1A | 17A8 | $ \left[ \left(\begin{array}{rr} 27 & 101 \\ 40 & 104 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 17A8 | $17$ | $18906$ | not computed | 17A1 | 17A7 | 17A3 | 1A | 17A3 | $ \left[ \left(\begin{array}{rr} 61 & 134 \\ 49 & 56 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 23A1 | $23$ | $18632$ | not computed | 23A2 | 23A3 | 23A11 | 23A6 | 1A | $ \left[ \left(\begin{array}{rr} 106 & 33 \\ 2 & 126 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 23A2 | $23$ | $18632$ | not computed | 23A4 | 23A6 | 23A1 | 23A11 | 1A | $ \left[ \left(\begin{array}{rr} 68 & 121 \\ 53 & 50 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 23A3 | $23$ | $18632$ | not computed | 23A6 | 23A9 | 23A10 | 23A5 | 1A | $ \left[ \left(\begin{array}{rr} 52 & 91 \\ 101 & 103 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 23A4 | $23$ | $18632$ | not computed | 23A8 | 23A11 | 23A2 | 23A1 | 1A | $ \left[ \left(\begin{array}{rr} 60 & 107 \\ 48 & 129 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 23A5 | $23$ | $18632$ | not computed | 23A10 | 23A8 | 23A9 | 23A7 | 1A | $ \left[ \left(\begin{array}{rr} 2 & 19 \\ 134 & 109 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 23A6 | $23$ | $18632$ | not computed | 23A11 | 23A5 | 23A3 | 23A10 | 1A | $ \left[ \left(\begin{array}{rr} 113 & 131 \\ 37 & 72 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 23A7 | $23$ | $18632$ | not computed | 23A9 | 23A2 | 23A8 | 23A4 | 1A | $ \left[ \left(\begin{array}{rr} 47 & 96 \\ 93 & 18 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 23A8 | $23$ | $18632$ | not computed | 23A7 | 23A1 | 23A4 | 23A2 | 1A | $ \left[ \left(\begin{array}{rr} 105 & 84 \\ 30 & 131 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 23A9 | $23$ | $18632$ | not computed | 23A5 | 23A4 | 23A7 | 23A8 | 1A | $ \left[ \left(\begin{array}{rr} 64 & 75 \\ 17 & 97 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 23A10 | $23$ | $18632$ | not computed | 23A3 | 23A7 | 23A5 | 23A9 | 1A | $ \left[ \left(\begin{array}{rr} 53 & 83 \\ 59 & 95 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 23A11 | $23$ | $18632$ | not computed | 23A1 | 23A10 | 23A6 | 23A3 | 1A | $ \left[ \left(\begin{array}{rr} 107 & 123 \\ 132 & 57 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 34A1 | $34$ | $18906$ | not computed | 17A1 | 34A3 | 34A11 | 2A | 34A11 | $ \left[ \left(\begin{array}{rr} 71 & 69 \\ 106 & 49 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 34A3 | $34$ | $18906$ | not computed | 17A3 | 34A9 | 34A1 | 2A | 34A1 | $ \left[ \left(\begin{array}{rr} 52 & 7 \\ 114 & 18 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 34A5 | $34$ | $18906$ | not computed | 17A5 | 34A15 | 34A13 | 2A | 34A13 | $ \left[ \left(\begin{array}{rr} 80 & 115 \\ 131 & 89 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 34A7 | $34$ | $18906$ | not computed | 17A7 | 34A13 | 34A9 | 2A | 34A9 | $ \left[ \left(\begin{array}{rr} 4 & 5 \\ 101 & 58 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 34A9 | $34$ | $18906$ | not computed | 17A8 | 34A7 | 34A3 | 2A | 34A3 | $ \left[ \left(\begin{array}{rr} 132 & 43 \\ 74 & 21 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 34A11 | $34$ | $18906$ | not computed | 17A6 | 34A1 | 34A15 | 2A | 34A15 | $ \left[ \left(\begin{array}{rr} 69 & 131 \\ 98 & 59 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 34A13 | $34$ | $18906$ | not computed | 17A4 | 34A5 | 34A7 | 2A | 34A7 | $ \left[ \left(\begin{array}{rr} 70 & 102 \\ 115 & 103 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 34A15 | $34$ | $18906$ | not computed | 17A2 | 34A11 | 34A5 | 2A | 34A5 | $ \left[ \left(\begin{array}{rr} 19 & 99 \\ 27 & 47 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A1 | $68$ | $18906$ | not computed | 34A1 | 68A3 | 68A11 | 4A | 68A23 | $ \left[ \left(\begin{array}{rr} 60 & 126 \\ 134 & 133 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A3 | $68$ | $18906$ | not computed | 34A3 | 68A9 | 68A33 | 4A | 68A1 | $ \left[ \left(\begin{array}{rr} 80 & 39 \\ 48 & 8 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A5 | $68$ | $18906$ | not computed | 34A5 | 68A15 | 68A13 | 4A | 68A21 | $ \left[ \left(\begin{array}{rr} 87 & 33 \\ 9 & 5 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A7 | $68$ | $18906$ | not computed | 34A7 | 68A21 | 68A9 | 4A | 68A25 | $ \left[ \left(\begin{array}{rr} 85 & 85 \\ 73 & 44 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A9 | $68$ | $18906$ | not computed | 34A9 | 68A27 | 68A31 | 4A | 68A3 | $ \left[ \left(\begin{array}{rr} 112 & 29 \\ 120 & 69 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A11 | $68$ | $18906$ | not computed | 34A11 | 68A33 | 68A15 | 4A | 68A19 | $ \left[ \left(\begin{array}{rr} 71 & 30 \\ 58 & 121 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A13 | $68$ | $18906$ | not computed | 34A13 | 68A29 | 68A7 | 4A | 68A27 | $ \left[ \left(\begin{array}{rr} 136 & 70 \\ 44 & 70 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A15 | $68$ | $18906$ | not computed | 34A15 | 68A23 | 68A29 | 4A | 68A5 | $ \left[ \left(\begin{array}{rr} 88 & 73 \\ 132 & 27 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A19 | $68$ | $18906$ | not computed | 34A15 | 68A11 | 68A5 | 4A | 68A29 | $ \left[ \left(\begin{array}{rr} 18 & 117 \\ 7 & 76 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A21 | $68$ | $18906$ | not computed | 34A13 | 68A5 | 68A27 | 4A | 68A7 | $ \left[ \left(\begin{array}{rr} 20 & 12 \\ 78 & 40 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A23 | $68$ | $18906$ | not computed | 34A11 | 68A1 | 68A19 | 4A | 68A15 | $ \left[ \left(\begin{array}{rr} 89 & 50 \\ 51 & 81 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A25 | $68$ | $18906$ | not computed | 34A9 | 68A7 | 68A3 | 4A | 68A31 | $ \left[ \left(\begin{array}{rr} 111 & 97 \\ 14 & 90 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A27 | $68$ | $18906$ | not computed | 34A7 | 68A13 | 68A25 | 4A | 68A9 | $ \left[ \left(\begin{array}{rr} 79 & 82 \\ 122 & 33 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A29 | $68$ | $18906$ | not computed | 34A5 | 68A19 | 68A21 | 4A | 68A13 | $ \left[ \left(\begin{array}{rr} 84 & 121 \\ 33 & 103 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A31 | $68$ | $18906$ | not computed | 34A3 | 68A25 | 68A1 | 4A | 68A33 | $ \left[ \left(\begin{array}{rr} 116 & 57 \\ 28 & 74 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 68A33 | $68$ | $18906$ | not computed | 34A1 | 68A31 | 68A23 | 4A | 68A11 | $ \left[ \left(\begin{array}{rr} 107 & 26 \\ 32 & 59 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 69A1 | $69$ | $18632$ | not computed | 69A2 | 23A1 | 69A11 | 69A17 | 3A | $ \left[ \left(\begin{array}{rr} 21 & 113 \\ 11 & 131 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 69A2 | $69$ | $18632$ | not computed | 69A4 | 23A2 | 69A22 | 69A34 | 3A | $ \left[ \left(\begin{array}{rr} 40 & 51 \\ 28 & 46 \end{array}\right) \right] $ |
| $\PSL(2,137)$ | 69A4 | $69$ | $18632$ | not computed | 69A8 | 23A4 | 69A25 | 69A1 | 3A | $ \left[ \left(\begin{array}{rr} 123 & 135 \\ 58 & 18 \end{array}\right) \right] $ |