Refine search
Elements of the group are displayed as matrices in $\SL(2,64)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 7P | 13P | ||||||
| $\SL(2,64)$ | 1A | $1$ | $1$ | $\SL(2,64)$ | 1A | 1A | 1A | 1A | 1A | $\left(\begin{array}{ll}1 & 0 \\ 0 & 1 \\ \end{array}\right)$ |
| $\SL(2,64)$ | 2A | $2$ | $4095$ | $C_2^6$ | 1A | 2A | 2A | 2A | 2A | $\left(\begin{array}{ll}\alpha^{42} & \alpha^{40} \\ \alpha^{2} & \alpha^{42} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 3A | $3$ | $4160$ | $C_{63}$ | 3A | 1A | 3A | 3A | 3A | $\left(\begin{array}{ll}\alpha^{51} & \alpha^{39} \\ \alpha^{56} & \alpha^{40} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 5A1 | $5$ | $4032$ | $C_{65}$ | 5A2 | 5A2 | 1A | 5A2 | 5A2 | $\left(\begin{array}{ll}\alpha^{14} & \alpha^{61} \\ \alpha^{47} & \alpha^{22} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 5A2 | $5$ | $4032$ | $C_{65}$ | 5A1 | 5A1 | 1A | 5A1 | 5A1 | $\left(\begin{array}{ll}\alpha^{4} & \alpha^{19} \\ \alpha^{5} & \alpha^{37} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 7A1 | $7$ | $4160$ | $C_{63}$ | 7A2 | 7A3 | 7A2 | 1A | 7A1 | $\left(\begin{array}{ll}\alpha^{22} & \alpha^{3} \\ \alpha^{20} & \alpha^{52} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 7A2 | $7$ | $4160$ | $C_{63}$ | 7A3 | 7A1 | 7A3 | 1A | 7A2 | $\left(\begin{array}{ll}\alpha^{2} & \alpha^{30} \\ \alpha^{47} & \alpha^{14} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 7A3 | $7$ | $4160$ | $C_{63}$ | 7A1 | 7A2 | 7A1 | 1A | 7A3 | $\left(\begin{array}{ll}\alpha^{30} & \alpha^{21} \\ \alpha^{38} & \alpha \\ \end{array}\right)$ |
| $\SL(2,64)$ | 9A1 | $9$ | $4160$ | $C_{63}$ | 9A2 | 3A | 9A4 | 9A2 | 9A4 | $\left(\begin{array}{ll}\alpha^{11} & \alpha^{57} \\ \alpha^{11} & \alpha^{19} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 9A2 | $9$ | $4160$ | $C_{63}$ | 9A4 | 3A | 9A1 | 9A4 | 9A1 | $\left(\begin{array}{ll}\alpha^{44} & \alpha^{12} \\ \alpha^{29} & \alpha^{43} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 9A4 | $9$ | $4160$ | $C_{63}$ | 9A1 | 3A | 9A2 | 9A1 | 9A2 | $\left(\begin{array}{ll}\alpha^{39} & \alpha^{48} \\ \alpha^{2} & \alpha^{14} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 13A1 | $13$ | $4032$ | $C_{65}$ | 13A2 | 13A3 | 13A5 | 13A6 | 1A | $\left(\begin{array}{ll}\alpha^{7} & \alpha^{3} \\ \alpha^{52} & \alpha^{55} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 13A2 | $13$ | $4032$ | $C_{65}$ | 13A4 | 13A6 | 13A3 | 13A1 | 1A | $\left(\begin{array}{ll}\alpha^{38} & \alpha^{29} \\ \alpha^{15} & \alpha^{54} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 13A3 | $13$ | $4032$ | $C_{65}$ | 13A6 | 13A4 | 13A2 | 13A5 | 1A | $\left(\begin{array}{ll}\alpha^{27} & \alpha^{15} \\ \alpha & \alpha^{50} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 13A4 | $13$ | $4032$ | $C_{65}$ | 13A5 | 13A1 | 13A6 | 13A2 | 1A | $\left(\begin{array}{ll}\alpha^{9} & \alpha^{18} \\ \alpha^{4} & \alpha^{37} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 13A5 | $13$ | $4032$ | $C_{65}$ | 13A3 | 13A2 | 13A1 | 13A4 | 1A | $\left(\begin{array}{ll}\alpha^{34} & \alpha^{59} \\ \alpha^{45} & \alpha^{53} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 13A6 | $13$ | $4032$ | $C_{65}$ | 13A1 | 13A5 | 13A4 | 13A3 | 1A | $\left(\begin{array}{ll}\alpha^{49} & \alpha^{53} \\ \alpha^{39} & \alpha^{58} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 21A1 | $21$ | $4160$ | $C_{63}$ | 21A2 | 7A1 | 21A5 | 3A | 21A8 | $\left(\begin{array}{ll}\alpha^{44} & \alpha^{29} \\ \alpha^{46} & \alpha^{8} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 21A2 | $21$ | $4160$ | $C_{63}$ | 21A4 | 7A2 | 21A10 | 3A | 21A5 | $\left(\begin{array}{ll}\alpha^{15} & \alpha^{19} \\ \alpha^{36} & \alpha^{47} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 21A4 | $21$ | $4160$ | $C_{63}$ | 21A8 | 7A3 | 21A1 | 3A | 21A10 | $\left(\begin{array}{ll}\alpha^{25} & \alpha^{62} \\ \alpha^{16} & \alpha^{9} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 21A5 | $21$ | $4160$ | $C_{63}$ | 21A10 | 7A2 | 21A4 | 3A | 21A2 | $\left(\begin{array}{ll}\alpha^{23} & \alpha^{5} \\ \alpha^{22} & \alpha^{49} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 21A8 | $21$ | $4160$ | $C_{63}$ | 21A5 | 7A1 | 21A2 | 3A | 21A1 | $\left(\begin{array}{ll}\alpha^{19} & \alpha^{22} \\ \alpha^{39} & \alpha^{28} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 21A10 | $21$ | $4160$ | $C_{63}$ | 21A1 | 7A3 | 21A8 | 3A | 21A4 | $\left(\begin{array}{ll}\alpha^{12} & \alpha^{34} \\ \alpha^{51} & \alpha^{34} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A1 | $63$ | $4160$ | $C_{63}$ | 63A2 | 21A1 | 63A5 | 9A1 | 63A13 | $\left(\begin{array}{ll}\alpha^{62} & \alpha^{51} \\ \alpha^{5} & \alpha^{2} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A2 | $63$ | $4160$ | $C_{63}$ | 63A4 | 21A2 | 63A10 | 9A2 | 63A26 | $\left(\begin{array}{ll}\alpha^{23} & 1 \\ \alpha^{17} & \alpha^{16} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A4 | $63$ | $4160$ | $C_{63}$ | 63A8 | 21A4 | 63A20 | 9A4 | 63A11 | $\left(\begin{array}{ll}\alpha^{61} & \alpha^{24} \\ \alpha^{41} & \alpha^{51} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A5 | $63$ | $4160$ | $C_{63}$ | 63A10 | 21A5 | 63A25 | 9A4 | 63A2 | $\left(\begin{array}{ll}\alpha^{25} & \alpha^{37} \\ \alpha^{54} & \alpha^{7} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A8 | $63$ | $4160$ | $C_{63}$ | 63A16 | 21A8 | 63A23 | 9A1 | 63A22 | $\left(\begin{array}{ll}\alpha^{22} & \alpha^{9} \\ \alpha^{26} & \alpha^{45} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A10 | $63$ | $4160$ | $C_{63}$ | 63A20 | 21A10 | 63A13 | 9A1 | 63A4 | $\left(\begin{array}{ll}\alpha^{11} & \alpha^{35} \\ \alpha^{52} & \alpha^{30} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A11 | $63$ | $4160$ | $C_{63}$ | 63A22 | 21A10 | 63A8 | 9A2 | 63A17 | $\left(\begin{array}{ll}\alpha^{15} & \alpha^{32} \\ \alpha^{49} & \alpha^{39} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A13 | $63$ | $4160$ | $C_{63}$ | 63A26 | 21A8 | 63A2 | 9A4 | 63A20 | $\left(\begin{array}{ll}\alpha^{61} & \alpha^{53} \\ \alpha^{7} & \alpha^{12} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A16 | $63$ | $4160$ | $C_{63}$ | 63A31 | 21A5 | 63A17 | 9A2 | 63A19 | $\left(\begin{array}{ll}\alpha^{62} & \alpha^{42} \\ \alpha^{59} & \alpha^{34} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A17 | $63$ | $4160$ | $C_{63}$ | 63A29 | 21A4 | 63A22 | 9A1 | 63A31 | $\left(\begin{array}{ll}1 & \alpha^{7} \\ \alpha^{24} & \alpha^{59} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A19 | $63$ | $4160$ | $C_{63}$ | 63A25 | 21A2 | 63A31 | 9A1 | 63A5 | $\left(\begin{array}{ll}\alpha^{16} & \alpha^{11} \\ \alpha^{28} & \alpha \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A20 | $63$ | $4160$ | $C_{63}$ | 63A23 | 21A1 | 63A26 | 9A2 | 63A8 | $\left(\begin{array}{ll}\alpha^{8} & \alpha^{31} \\ \alpha^{48} & \alpha^{6} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A22 | $63$ | $4160$ | $C_{63}$ | 63A19 | 21A1 | 63A16 | 9A4 | 63A29 | $\left(\begin{array}{ll}\alpha^{7} & \alpha^{25} \\ \alpha^{42} & \alpha^{28} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A23 | $63$ | $4160$ | $C_{63}$ | 63A17 | 21A2 | 63A11 | 9A4 | 63A16 | $\left(\begin{array}{ll}\alpha^{47} & \alpha^{23} \\ \alpha^{40} & 0 \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A25 | $63$ | $4160$ | $C_{63}$ | 63A13 | 21A4 | 63A1 | 9A2 | 63A10 | $\left(\begin{array}{ll}\alpha^{45} & \alpha^{46} \\ 1 & \alpha^{40} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A26 | $63$ | $4160$ | $C_{63}$ | 63A11 | 21A5 | 63A4 | 9A1 | 63A23 | $\left(\begin{array}{ll}\alpha^{52} & \alpha^{4} \\ \alpha^{21} & \alpha^{6} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A29 | $63$ | $4160$ | $C_{63}$ | 63A5 | 21A8 | 63A19 | 9A2 | 63A1 | $\left(\begin{array}{ll}\alpha^{9} & \alpha^{38} \\ \alpha^{55} & \alpha^{59} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 63A31 | $63$ | $4160$ | $C_{63}$ | 63A1 | 21A10 | 63A29 | 9A4 | 63A25 | $\left(\begin{array}{ll}\alpha^{43} & \alpha^{45} \\ \alpha^{62} & \alpha^{49} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 65A1 | $65$ | $4032$ | $C_{65}$ | 65A2 | 65A3 | 13A1 | 65A7 | 5A1 | $\left(\begin{array}{ll}\alpha^{2} & \alpha^{50} \\ \alpha^{36} & \alpha^{9} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 65A2 | $65$ | $4032$ | $C_{65}$ | 65A4 | 65A6 | 13A2 | 65A14 | 5A2 | $\left(\begin{array}{ll}\alpha^{52} & \alpha^{60} \\ \alpha^{46} & \alpha^{48} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 65A3 | $65$ | $4032$ | $C_{65}$ | 65A6 | 65A9 | 13A3 | 65A21 | 5A2 | $\left(\begin{array}{ll}\alpha^{12} & \alpha^{44} \\ \alpha^{30} & \alpha^{11} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 65A4 | $65$ | $4032$ | $C_{65}$ | 65A8 | 65A12 | 13A4 | 65A28 | 5A1 | $\left(\begin{array}{ll}\alpha^{27} & \alpha^{17} \\ \alpha^{3} & \alpha^{30} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 65A6 | $65$ | $4032$ | $C_{65}$ | 65A12 | 65A18 | 13A6 | 65A23 | 5A1 | $\left(\begin{array}{ll}\alpha^{14} & \alpha^{48} \\ \alpha^{34} & \alpha^{34} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 65A7 | $65$ | $4032$ | $C_{65}$ | 65A14 | 65A21 | 13A6 | 65A16 | 5A2 | $\left(\begin{array}{ll}\alpha^{46} & \alpha^{2} \\ \alpha^{51} & \alpha^{4} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 65A8 | $65$ | $4032$ | $C_{65}$ | 65A16 | 65A24 | 13A5 | 65A9 | 5A2 | $\left(\begin{array}{ll}\alpha^{35} & \alpha^{57} \\ \alpha^{43} & \alpha^{8} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 65A9 | $65$ | $4032$ | $C_{65}$ | 65A18 | 65A27 | 13A4 | 65A2 | 5A1 | $\left(\begin{array}{ll}\alpha^{38} & \alpha^{51} \\ \alpha^{37} & \alpha^{20} \\ \end{array}\right)$ |
| $\SL(2,64)$ | 65A11 | $65$ | $4032$ | $C_{65}$ | 65A22 | 65A32 | 13A2 | 65A12 | 5A1 | $\left(\begin{array}{ll}\alpha^{35} & \alpha^{28} \\ \alpha^{14} & \alpha^{49} \\ \end{array}\right)$ |