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Download displayed columns for resultsElements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SL(2,61)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 31P | 61P | ||||||
| $\PSL(2,61)$ | 31A1 | $31$ | $3660$ | $C_{31}$ | 31A2 | 31A3 | 31A5 | 1A | 31A1 | $ \left[ \left(\begin{array}{rr} 19 & 42 \\ 59 & 47 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A2 | $31$ | $3660$ | $C_{31}$ | 31A4 | 31A6 | 31A10 | 1A | 31A2 | $ \left[ \left(\begin{array}{rr} 33 & 27 \\ 51 & 51 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A3 | $31$ | $3660$ | $C_{31}$ | 31A6 | 31A9 | 31A15 | 1A | 31A3 | $ \left[ \left(\begin{array}{rr} 37 & 29 \\ 48 & 36 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A4 | $31$ | $3660$ | $C_{31}$ | 31A8 | 31A12 | 31A11 | 1A | 31A4 | $ \left[ \left(\begin{array}{rr} 26 & 11 \\ 14 & 13 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A5 | $31$ | $3660$ | $C_{31}$ | 31A10 | 31A15 | 31A6 | 1A | 31A5 | $ \left[ \left(\begin{array}{rr} 45 & 23 \\ 57 & 40 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A6 | $31$ | $3660$ | $C_{31}$ | 31A12 | 31A13 | 31A1 | 1A | 31A6 | $ \left[ \left(\begin{array}{rr} 45 & 18 \\ 34 & 57 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A7 | $31$ | $3660$ | $C_{31}$ | 31A14 | 31A10 | 31A4 | 1A | 31A7 | $ \left[ \left(\begin{array}{rr} 35 & 9 \\ 17 & 41 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A8 | $31$ | $3660$ | $C_{31}$ | 31A15 | 31A7 | 31A9 | 1A | 31A8 | $ \left[ \left(\begin{array}{rr} 24 & 59 \\ 3 & 43 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A9 | $31$ | $3660$ | $C_{31}$ | 31A13 | 31A4 | 31A14 | 1A | 31A9 | $ \left[ \left(\begin{array}{rr} 33 & 60 \\ 32 & 12 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A10 | $31$ | $3660$ | $C_{31}$ | 31A11 | 31A1 | 31A12 | 1A | 31A10 | $ \left[ \left(\begin{array}{rr} 19 & 58 \\ 35 & 17 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A11 | $31$ | $3660$ | $C_{31}$ | 31A9 | 31A2 | 31A7 | 1A | 31A11 | $ \left[ \left(\begin{array}{rr} 1 & 47 \\ 21 & 12 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A12 | $31$ | $3660$ | $C_{31}$ | 31A7 | 31A5 | 31A2 | 1A | 31A12 | $ \left[ \left(\begin{array}{rr} 47 & 55 \\ 9 & 43 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A13 | $31$ | $3660$ | $C_{31}$ | 31A5 | 31A8 | 31A3 | 1A | 31A13 | $ \left[ \left(\begin{array}{rr} 10 & 16 \\ 37 & 41 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A14 | $31$ | $3660$ | $C_{31}$ | 31A3 | 31A11 | 31A8 | 1A | 31A14 | $ \left[ \left(\begin{array}{rr} 25 & 48 \\ 50 & 57 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 31A15 | $31$ | $3660$ | $C_{31}$ | 31A1 | 31A14 | 31A13 | 1A | 31A15 | $ \left[ \left(\begin{array}{rr} 13 & 12 \\ 43 & 21 \end{array}\right) \right] $ |