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Elements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\GL(2,151)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 19P | 151P | ||||||
| $\PGL(2,151)$ | 1A | $1$ | $1$ | $\PGL(2,151)$ | 1A | 1A | 1A | 1A | 1A | $ \left[ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 2A | $2$ | $11325$ | $D_{152}$ | 1A | 2A | 2A | 2A | 2A | $ \left[ \left(\begin{array}{rr} 1 & 94 \\ 113 & 150 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 2B | $2$ | $11476$ | $D_{150}$ | 1A | 2B | 2B | 2B | 2B | $ \left[ \left(\begin{array}{rr} 118 & 111 \\ 23 & 33 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 3A | $3$ | $22952$ | $C_{150}$ | 3A | 1A | 3A | 3A | 3A | $ \left[ \left(\begin{array}{rr} 48 & 36 \\ 85 & 49 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 4A | $4$ | $22650$ | $C_{152}$ | 2A | 4A | 4A | 4A | 4A | $ \left[ \left(\begin{array}{rr} 116 & 95 \\ 13 & 69 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 5A1 | $5$ | $22952$ | $C_{150}$ | 5A2 | 5A2 | 1A | 5A1 | 5A1 | $ \left[ \left(\begin{array}{rr} 1 & 98 \\ 72 & 96 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 5A2 | $5$ | $22952$ | $C_{150}$ | 5A1 | 5A1 | 1A | 5A2 | 5A2 | $ \left[ \left(\begin{array}{rr} 134 & 31 \\ 69 & 30 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 6A | $6$ | $22952$ | $C_{150}$ | 3A | 2B | 6A | 6A | 6A | $ \left[ \left(\begin{array}{rr} 84 & 100 \\ 18 & 70 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 8A1 | $8$ | $22650$ | $C_{152}$ | 4A | 8A3 | 8A3 | 8A3 | 8A1 | $ \left[ \left(\begin{array}{rr} 14 & 37 \\ 75 & 10 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 8A3 | $8$ | $22650$ | $C_{152}$ | 4A | 8A1 | 8A1 | 8A1 | 8A3 | $ \left[ \left(\begin{array}{rr} 99 & 20 \\ 114 & 105 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 10A1 | $10$ | $22952$ | $C_{150}$ | 5A1 | 10A3 | 2B | 10A1 | 10A1 | $ \left[ \left(\begin{array}{rr} 22 & 129 \\ 141 & 13 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 10A3 | $10$ | $22952$ | $C_{150}$ | 5A2 | 10A1 | 2B | 10A3 | 10A3 | $ \left[ \left(\begin{array}{rr} 16 & 91 \\ 110 & 115 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 15A1 | $15$ | $22952$ | $C_{150}$ | 15A2 | 5A1 | 3A | 15A4 | 15A1 | $ \left[ \left(\begin{array}{rr} 15 & 109 \\ 77 & 39 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 15A2 | $15$ | $22952$ | $C_{150}$ | 15A4 | 5A2 | 3A | 15A7 | 15A2 | $ \left[ \left(\begin{array}{rr} 85 & 18 \\ 118 & 10 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 15A4 | $15$ | $22952$ | $C_{150}$ | 15A7 | 5A1 | 3A | 15A1 | 15A4 | $ \left[ \left(\begin{array}{rr} 7 & 113 \\ 120 & 115 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 15A7 | $15$ | $22952$ | $C_{150}$ | 15A1 | 5A2 | 3A | 15A2 | 15A7 | $ \left[ \left(\begin{array}{rr} 62 & 30 \\ 96 & 88 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 19A1 | $19$ | $22650$ | $C_{152}$ | 19A2 | 19A3 | 19A5 | 1A | 19A1 | $ \left[ \left(\begin{array}{rr} 19 & 27 \\ 18 & 12 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 19A2 | $19$ | $22650$ | $C_{152}$ | 19A4 | 19A6 | 19A9 | 1A | 19A2 | $ \left[ \left(\begin{array}{rr} 113 & 104 \\ 19 & 114 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 19A3 | $19$ | $22650$ | $C_{152}$ | 19A6 | 19A9 | 19A4 | 1A | 19A3 | $ \left[ \left(\begin{array}{rr} 11 & 36 \\ 24 & 52 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 19A4 | $19$ | $22650$ | $C_{152}$ | 19A8 | 19A7 | 19A1 | 1A | 19A4 | $ \left[ \left(\begin{array}{rr} 21 & 119 \\ 29 & 102 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 19A5 | $19$ | $22650$ | $C_{152}$ | 19A9 | 19A4 | 19A6 | 1A | 19A5 | $ \left[ \left(\begin{array}{rr} 75 & 140 \\ 43 & 117 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 19A6 | $19$ | $22650$ | $C_{152}$ | 19A7 | 19A1 | 19A8 | 1A | 19A6 | $ \left[ \left(\begin{array}{rr} 26 & 87 \\ 58 & 37 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 19A7 | $19$ | $22650$ | $C_{152}$ | 19A5 | 19A2 | 19A3 | 1A | 19A7 | $ \left[ \left(\begin{array}{rr} 133 & 129 \\ 86 & 66 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 19A8 | $19$ | $22650$ | $C_{152}$ | 19A3 | 19A5 | 19A2 | 1A | 19A8 | $ \left[ \left(\begin{array}{rr} 34 & 10 \\ 57 & 37 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 19A9 | $19$ | $22650$ | $C_{152}$ | 19A1 | 19A8 | 19A7 | 1A | 19A9 | $ \left[ \left(\begin{array}{rr} 87 & 15 \\ 10 & 16 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 25A1 | $25$ | $22952$ | $C_{150}$ | 25A2 | 25A3 | 5A1 | 25A6 | 25A1 | $ \left[ \left(\begin{array}{rr} 7 & 42 \\ 74 & 134 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 25A2 | $25$ | $22952$ | $C_{150}$ | 25A4 | 25A6 | 5A2 | 25A12 | 25A2 | $ \left[ \left(\begin{array}{rr} 5 & 150 \\ 27 & 135 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 25A3 | $25$ | $22952$ | $C_{150}$ | 25A6 | 25A9 | 5A2 | 25A7 | 25A3 | $ \left[ \left(\begin{array}{rr} 45 & 133 \\ 33 & 120 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 25A4 | $25$ | $22952$ | $C_{150}$ | 25A8 | 25A12 | 5A1 | 25A1 | 25A4 | $ \left[ \left(\begin{array}{rr} 126 & 62 \\ 138 & 69 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 25A6 | $25$ | $22952$ | $C_{150}$ | 25A12 | 25A7 | 5A1 | 25A11 | 25A6 | $ \left[ \left(\begin{array}{rr} 15 & 23 \\ 134 & 45 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 25A7 | $25$ | $22952$ | $C_{150}$ | 25A11 | 25A4 | 5A2 | 25A8 | 25A7 | $ \left[ \left(\begin{array}{rr} 35 & 139 \\ 22 & 85 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 25A8 | $25$ | $22952$ | $C_{150}$ | 25A9 | 25A1 | 5A2 | 25A2 | 25A8 | $ \left[ \left(\begin{array}{rr} 72 & 127 \\ 44 & 21 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 25A9 | $25$ | $22952$ | $C_{150}$ | 25A7 | 25A2 | 5A1 | 25A4 | 25A9 | $ \left[ \left(\begin{array}{rr} 89 & 116 \\ 39 & 109 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 25A11 | $25$ | $22952$ | $C_{150}$ | 25A3 | 25A8 | 5A1 | 25A9 | 25A11 | $ \left[ \left(\begin{array}{rr} 29 & 66 \\ 30 & 56 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 25A12 | $25$ | $22952$ | $C_{150}$ | 25A1 | 25A11 | 5A2 | 25A3 | 25A12 | $ \left[ \left(\begin{array}{rr} 113 & 23 \\ 134 & 143 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 30A1 | $30$ | $22952$ | $C_{150}$ | 15A1 | 10A1 | 6A | 30A11 | 30A1 | $ \left[ \left(\begin{array}{rr} 112 & 125 \\ 98 & 19 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 30A7 | $30$ | $22952$ | $C_{150}$ | 15A7 | 10A3 | 6A | 30A13 | 30A7 | $ \left[ \left(\begin{array}{rr} 105 & 2 \\ 97 & 147 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 30A11 | $30$ | $22952$ | $C_{150}$ | 15A4 | 10A1 | 6A | 30A1 | 30A11 | $ \left[ \left(\begin{array}{rr} 101 & 98 \\ 72 & 45 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 30A13 | $30$ | $22952$ | $C_{150}$ | 15A2 | 10A3 | 6A | 30A7 | 30A13 | $ \left[ \left(\begin{array}{rr} 23 & 4 \\ 43 & 107 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 38A1 | $38$ | $22650$ | $C_{152}$ | 19A1 | 38A3 | 38A5 | 2A | 38A1 | $ \left[ \left(\begin{array}{rr} 16 & 143 \\ 45 & 74 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 38A3 | $38$ | $22650$ | $C_{152}$ | 19A3 | 38A9 | 38A15 | 2A | 38A3 | $ \left[ \left(\begin{array}{rr} 27 & 102 \\ 68 & 118 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 38A5 | $38$ | $22650$ | $C_{152}$ | 19A5 | 38A15 | 38A13 | 2A | 38A5 | $ \left[ \left(\begin{array}{rr} 79 & 138 \\ 92 & 60 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 38A7 | $38$ | $22650$ | $C_{152}$ | 19A7 | 38A17 | 38A3 | 2A | 38A7 | $ \left[ \left(\begin{array}{rr} 103 & 27 \\ 18 & 96 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 38A9 | $38$ | $22650$ | $C_{152}$ | 19A9 | 38A11 | 38A7 | 2A | 38A9 | $ \left[ \left(\begin{array}{rr} 73 & 90 \\ 60 & 100 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 38A11 | $38$ | $22650$ | $C_{152}$ | 19A8 | 38A5 | 38A17 | 2A | 38A11 | $ \left[ \left(\begin{array}{rr} 45 & 125 \\ 33 & 7 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 38A13 | $38$ | $22650$ | $C_{152}$ | 19A6 | 38A1 | 38A11 | 2A | 38A13 | $ \left[ \left(\begin{array}{rr} 49 & 64 \\ 93 & 38 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 38A15 | $38$ | $22650$ | $C_{152}$ | 19A4 | 38A7 | 38A1 | 2A | 38A15 | $ \left[ \left(\begin{array}{rr} 110 & 67 \\ 95 & 115 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 38A17 | $38$ | $22650$ | $C_{152}$ | 19A2 | 38A13 | 38A9 | 2A | 38A17 | $ \left[ \left(\begin{array}{rr} 43 & 112 \\ 125 & 137 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 50A1 | $50$ | $22952$ | $C_{150}$ | 25A1 | 50A3 | 10A1 | 50A19 | 50A1 | $ \left[ \left(\begin{array}{rr} 118 & 12 \\ 129 & 68 \end{array}\right) \right] $ |
| $\PGL(2,151)$ | 50A3 | $50$ | $22952$ | $C_{150}$ | 25A3 | 50A9 | 10A3 | 50A7 | 50A3 | $ \left[ \left(\begin{array}{rr} 125 & 25 \\ 80 & 46 \end{array}\right) \right] $ |