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Download displayed columns for resultsElements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SL(2,125)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 7P | 31P | ||||||
| $\PSL(2,125)$ | 31A1 | $31$ | $15750$ | $C_{62}$ | 31A2 | 31A3 | 31A5 | 31A7 | 1A | $ \left[ \left(\begin{array}{rr} 77 & 108 \\ 118 & 29 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A2 | $31$ | $15750$ | $C_{62}$ | 31A4 | 31A6 | 31A10 | 31A14 | 1A | $ \left[ \left(\begin{array}{rr} 95 & 56 \\ 66 & 98 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A3 | $31$ | $15750$ | $C_{62}$ | 31A6 | 31A9 | 31A15 | 31A10 | 1A | $ \left[ \left(\begin{array}{rr} 57 & 32 \\ 42 & 56 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A4 | $31$ | $15750$ | $C_{62}$ | 31A8 | 31A12 | 31A11 | 31A3 | 1A | $ \left[ \left(\begin{array}{rr} 34 & 99 \\ 109 & 49 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A5 | $31$ | $15750$ | $C_{62}$ | 31A10 | 31A15 | 31A6 | 31A4 | 1A | $ \left[ \left(\begin{array}{rr} 12 & 100 \\ 110 & 66 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A6 | $31$ | $15750$ | $C_{62}$ | 31A12 | 31A13 | 31A1 | 31A11 | 1A | $ \left[ \left(\begin{array}{rr} 73 & 60 \\ 70 & 66 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A7 | $31$ | $15750$ | $C_{62}$ | 31A14 | 31A10 | 31A4 | 31A13 | 1A | $ \left[ \left(\begin{array}{rr} 6 & 83 \\ 93 & 111 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A8 | $31$ | $15750$ | $C_{62}$ | 31A15 | 31A7 | 31A9 | 31A6 | 1A | $ \left[ \left(\begin{array}{rr} 92 & 59 \\ 69 & 118 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A9 | $31$ | $15750$ | $C_{62}$ | 31A13 | 31A4 | 31A14 | 31A1 | 1A | $ \left[ \left(\begin{array}{rr} 20 & 41 \\ 51 & 98 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A10 | $31$ | $15750$ | $C_{62}$ | 31A11 | 31A1 | 31A12 | 31A8 | 1A | $ \left[ \left(\begin{array}{rr} -1 & 26 \\ 36 & 91 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A11 | $31$ | $15750$ | $C_{62}$ | 31A9 | 31A2 | 31A7 | 31A15 | 1A | $ \left[ \left(\begin{array}{rr} 82 & 117 \\ 3 & 0 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A12 | $31$ | $15750$ | $C_{62}$ | 31A7 | 31A5 | 31A2 | 31A9 | 1A | $ \left[ \left(\begin{array}{rr} 92 & 0 \\ 10 & 15 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A13 | $31$ | $15750$ | $C_{62}$ | 31A5 | 31A8 | 31A3 | 31A2 | 1A | $ \left[ \left(\begin{array}{rr} 68 & 82 \\ 92 & 95 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A14 | $31$ | $15750$ | $C_{62}$ | 31A3 | 31A11 | 31A8 | 31A5 | 1A | $ \left[ \left(\begin{array}{rr} 11 & 75 \\ 85 & 119 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 31A15 | $31$ | $15750$ | $C_{62}$ | 31A1 | 31A14 | 31A13 | 31A12 | 1A | $ \left[ \left(\begin{array}{rr} 74 & 30 \\ 40 & 96 \end{array}\right) \right] $ |