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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 | ||||||
| $\PSL(2,125)$ | 21A1 | $21$ | $15500$ | $C_{63}$ | 21A2 | 7A1 | 21A5 | 3A | 21A10 | $ \left[ \left(\begin{array}{rr} 89 & 39 \\ 88 & 45 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 21A2 | $21$ | $15500$ | $C_{63}$ | 21A4 | 7A2 | 21A10 | 3A | 21A1 | $ \left[ \left(\begin{array}{rr} 15 & 0 \\ 49 & 36 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 21A4 | $21$ | $15500$ | $C_{63}$ | 21A8 | 7A3 | 21A1 | 3A | 21A2 | $ \left[ \left(\begin{array}{rr} 35 & 37 \\ 86 & 60 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 21A5 | $21$ | $15500$ | $C_{63}$ | 21A10 | 7A2 | 21A4 | 3A | 21A8 | $ \left[ \left(\begin{array}{rr} 34 & 111 \\ 36 & 101 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 21A8 | $21$ | $15500$ | $C_{63}$ | 21A5 | 7A1 | 21A2 | 3A | 21A4 | $ \left[ \left(\begin{array}{rr} 117 & 54 \\ 103 & 68 \end{array}\right) \right] $ |
| $\PSL(2,125)$ | 21A10 | $21$ | $15500$ | $C_{63}$ | 21A1 | 7A3 | 21A8 | 3A | 21A5 | $ \left[ \left(\begin{array}{rr} 95 & 102 \\ 27 & 13 \end{array}\right) \right] $ |