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Download displayed columns for resultsElements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SL(2,37)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||
|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 19P | 37P | ||||||
| $\PSL(2,37)$ | 19A1 | $19$ | $1332$ | $C_{19}$ | 19A2 | 19A3 | 1A | 19A1 | $ \left[ \left(\begin{array}{rr} 36 & 15 \\ 3 & 28 \end{array}\right) \right] $ |
| $\PSL(2,37)$ | 19A2 | $19$ | $1332$ | $C_{19}$ | 19A4 | 19A6 | 1A | 19A2 | $ \left[ \left(\begin{array}{rr} 9 & 35 \\ 7 & 15 \end{array}\right) \right] $ |
| $\PSL(2,37)$ | 19A3 | $19$ | $1332$ | $C_{19}$ | 19A6 | 19A9 | 1A | 19A3 | $ \left[ \left(\begin{array}{rr} 15 & 32 \\ 36 & 30 \end{array}\right) \right] $ |
| $\PSL(2,37)$ | 19A4 | $19$ | $1332$ | $C_{19}$ | 19A8 | 19A7 | 1A | 19A4 | $ \left[ \left(\begin{array}{rr} 30 & 26 \\ 20 & 26 \end{array}\right) \right] $ |
| $\PSL(2,37)$ | 19A5 | $19$ | $1332$ | $C_{19}$ | 19A9 | 19A4 | 1A | 19A5 | $ \left[ \left(\begin{array}{rr} 11 & 31 \\ 21 & 29 \end{array}\right) \right] $ |
| $\PSL(2,37)$ | 19A6 | $19$ | $1332$ | $C_{19}$ | 19A7 | 19A1 | 1A | 19A6 | $ \left[ \left(\begin{array}{rr} 8 & 34 \\ 29 & 17 \end{array}\right) \right] $ |
| $\PSL(2,37)$ | 19A7 | $19$ | $1332$ | $C_{19}$ | 19A5 | 19A2 | 1A | 19A7 | $ \left[ \left(\begin{array}{rr} 17 & 1 \\ 15 & 14 \end{array}\right) \right] $ |
| $\PSL(2,37)$ | 19A8 | $19$ | $1332$ | $C_{19}$ | 19A3 | 19A5 | 1A | 19A8 | $ \left[ \left(\begin{array}{rr} 14 & 13 \\ 10 & 12 \end{array}\right) \right] $ |
| $\PSL(2,37)$ | 19A9 | $19$ | $1332$ | $C_{19}$ | 19A1 | 19A8 | 1A | 19A9 | $ \left[ \left(\begin{array}{rr} 25 & 19 \\ 26 & 5 \end{array}\right) \right] $ |