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Results (33 matches)
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 | ||||||
| $\PSL(2,61)$ | 1A | $1$ | $1$ | $\PSL(2,61)$ | 1A | 1A | 1A | 1A | 1A | $ \left[ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 2A | $2$ | $1891$ | $D_{30}$ | 1A | 2A | 2A | 2A | 2A | $ \left[ \left(\begin{array}{rr} 30 & 34 \\ 4 & 31 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 3A | $3$ | $3782$ | $C_{30}$ | 3A | 1A | 3A | 3A | 3A | $ \left[ \left(\begin{array}{rr} 28 & 14 \\ 16 & 32 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 5A1 | $5$ | $3782$ | $C_{30}$ | 5A2 | 5A2 | 1A | 5A1 | 5A1 | $ \left[ \left(\begin{array}{rr} 52 & 31 \\ 18 & 26 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 5A2 | $5$ | $3782$ | $C_{30}$ | 5A1 | 5A1 | 1A | 5A2 | 5A2 | $ \left[ \left(\begin{array}{rr} 29 & 39 \\ 1 & 14 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 6A | $6$ | $3782$ | $C_{30}$ | 3A | 2A | 6A | 6A | 6A | $ \left[ \left(\begin{array}{rr} 11 & 17 \\ 2 & 42 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 10A1 | $10$ | $3782$ | $C_{30}$ | 5A1 | 10A3 | 2A | 10A1 | 10A1 | $ \left[ \left(\begin{array}{rr} 41 & 1 \\ 36 & 50 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 10A3 | $10$ | $3782$ | $C_{30}$ | 5A2 | 10A1 | 2A | 10A3 | 10A3 | $ \left[ \left(\begin{array}{rr} 46 & 45 \\ 34 & 24 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 15A1 | $15$ | $3782$ | $C_{30}$ | 15A2 | 5A1 | 3A | 15A1 | 15A1 | $ \left[ \left(\begin{array}{rr} 1 & 46 \\ 9 & 49 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 15A2 | $15$ | $3782$ | $C_{30}$ | 15A4 | 5A2 | 3A | 15A2 | 15A2 | $ \left[ \left(\begin{array}{rr} 12 & 18 \\ 38 & 52 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 15A4 | $15$ | $3782$ | $C_{30}$ | 15A7 | 5A1 | 3A | 15A4 | 15A4 | $ \left[ \left(\begin{array}{rr} 35 & 54 \\ 53 & 33 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 15A7 | $15$ | $3782$ | $C_{30}$ | 15A1 | 5A2 | 3A | 15A7 | 15A7 | $ \left[ \left(\begin{array}{rr} 14 & 12 \\ 5 & 0 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 30A1 | $30$ | $3782$ | $C_{30}$ | 15A1 | 10A1 | 6A | 30A1 | 30A1 | $ \left[ \left(\begin{array}{rr} 13 & 55 \\ 28 & 20 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 30A7 | $30$ | $3782$ | $C_{30}$ | 15A7 | 10A3 | 6A | 30A7 | 30A7 | $ \left[ \left(\begin{array}{rr} 42 & 58 \\ 14 & 15 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 30A11 | $30$ | $3782$ | $C_{30}$ | 15A4 | 10A1 | 6A | 30A11 | 30A11 | $ \left[ \left(\begin{array}{rr} 37 & 10 \\ 55 & 5 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 30A13 | $30$ | $3782$ | $C_{30}$ | 15A2 | 10A3 | 6A | 30A13 | 30A13 | $ \left[ \left(\begin{array}{rr} 56 & 4 \\ 22 & 31 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 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] $ |
| $\PSL(2,61)$ | 61A1 | $61$ | $1860$ | $C_{61}$ | 61A2 | 61A1 | 61A1 | 61A2 | 1A | $ \left[ \left(\begin{array}{rr} 12 & 16 \\ 42 & 51 \end{array}\right) \right] $ |
| $\PSL(2,61)$ | 61A2 | $61$ | $1860$ | $C_{61}$ | 61A1 | 61A2 | 61A2 | 61A1 | 1A | $ \left[ \left(\begin{array}{rr} 23 & 32 \\ 23 & 40 \end{array}\right) \right] $ |