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Results (13 matches)

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Elements of the group are displayed as matrices in $\SL(2,9)$.

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$\SL(2,9)$ 1A $1$ $1$ $\SL(2,9)$ 1A 1A 1A $\left(\begin{array}{ll}1 & 0 \\ 0 & 1 \\ \end{array}\right)$
$\SL(2,9)$ 2A $2$ $1$ $\SL(2,9)$ 1A 2A 2A $\left(\begin{array}{ll}\alpha^{4} & 0 \\ 0 & \alpha^{4} \\ \end{array}\right)$
$\SL(2,9)$ 3A $3$ $40$ $C_3\times C_6$ 3A 1A 3A $\left(\begin{array}{ll}\alpha & \alpha^{6} \\ \alpha^{4} & \alpha^{6} \\ \end{array}\right)$
$\SL(2,9)$ 3B $3$ $40$ $C_3\times C_6$ 3B 1A 3B $\left(\begin{array}{ll}\alpha^{6} & \alpha \\ \alpha & \alpha \\ \end{array}\right)$
$\SL(2,9)$ 4A $4$ $90$ $C_8$ 2A 4A 4A $\left(\begin{array}{ll}\alpha^{6} & 0 \\ 0 & \alpha^{2} \\ \end{array}\right)$
$\SL(2,9)$ 5A1 $5$ $72$ $C_{10}$ 5A2 5A2 1A $\left(\begin{array}{ll}\alpha^{5} & \alpha^{7} \\ \alpha^{5} & 0 \\ \end{array}\right)$
$\SL(2,9)$ 5A2 $5$ $72$ $C_{10}$ 5A1 5A1 1A $\left(\begin{array}{ll}\alpha & \alpha^{4} \\ \alpha^{2} & \alpha^{4} \\ \end{array}\right)$
$\SL(2,9)$ 6A $6$ $40$ $C_3\times C_6$ 3A 2A 6A $\left(\begin{array}{ll}\alpha^{2} & \alpha^{6} \\ \alpha^{4} & \alpha^{5} \\ \end{array}\right)$
$\SL(2,9)$ 6B $6$ $40$ $C_3\times C_6$ 3B 2A 6B $\left(\begin{array}{ll}\alpha^{5} & \alpha \\ \alpha & \alpha^{2} \\ \end{array}\right)$
$\SL(2,9)$ 8A1 $8$ $90$ $C_8$ 4A 8A3 8A3 $\left(\begin{array}{ll}\alpha^{3} & 0 \\ 0 & \alpha^{5} \\ \end{array}\right)$
$\SL(2,9)$ 8A3 $8$ $90$ $C_8$ 4A 8A1 8A1 $\left(\begin{array}{ll}\alpha & 0 \\ 0 & \alpha^{7} \\ \end{array}\right)$
$\SL(2,9)$ 10A1 $10$ $72$ $C_{10}$ 5A1 10A3 2A $\left(\begin{array}{ll}1 & \alpha^{4} \\ \alpha^{2} & \alpha^{5} \\ \end{array}\right)$
$\SL(2,9)$ 10A3 $10$ $72$ $C_{10}$ 5A2 10A1 2A $\left(\begin{array}{ll}0 & \alpha^{7} \\ \alpha^{5} & \alpha \\ \end{array}\right)$
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