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Results (36 matches)

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Elements of the group are displayed as matrices in $\CSU(2,17)$.

Group Label Order Size Centralizer Powers Representative
2P 3P 17P
$C_2.\PGL(2,17)$ 1A $1$ $1$ $C_2.\PGL(2,17)$ 1A 1A 1A $\left(\begin{array}{ll}1 & 0 \\ 0 & 1 \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 2A $2$ $1$ $C_2.\PGL(2,17)$ 1A 2A 2A $\left(\begin{array}{ll}\alpha^{144} & 0 \\ 0 & \alpha^{144} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 3A $3$ $272$ $C_{36}$ 3A 1A 3A $\left(\begin{array}{ll}\alpha^{90} & \alpha^{117} \\ \alpha^{189} & \alpha^{126} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 4A $4$ $272$ $C_{36}$ 2A 4A 4A $\left(\begin{array}{ll}\alpha^{117} & \alpha^{72} \\ \alpha^{144} & \alpha^{261} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 4B $4$ $306$ $C_{32}$ 2A 4B 4B $\left(\begin{array}{ll}\alpha^{108} & \alpha^{117} \\ \alpha^{117} & \alpha^{252} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 6A $6$ $272$ $C_{36}$ 3A 2A 6A $\left(\begin{array}{ll}\alpha^{270} & \alpha^{117} \\ \alpha^{189} & \alpha^{234} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 8A1 $8$ $306$ $C_{32}$ 4B 8A3 8A1 $\left(\begin{array}{ll}\alpha^{18} & \alpha^{279} \\ \alpha^{279} & \alpha^{180} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 8A3 $8$ $306$ $C_{32}$ 4B 8A1 8A3 $\left(\begin{array}{ll}\alpha^{36} & \alpha^{279} \\ \alpha^{279} & \alpha^{162} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 9A1 $9$ $272$ $C_{36}$ 9A2 3A 9A1 $\left(\begin{array}{ll}\alpha^{72} & \alpha^{225} \\ \alpha^{9} & 1 \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 9A2 $9$ $272$ $C_{36}$ 9A4 3A 9A2 $\left(\begin{array}{ll}\alpha^{126} & \alpha^{99} \\ \alpha^{171} & \alpha^{72} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 9A4 $9$ $272$ $C_{36}$ 9A1 3A 9A4 $\left(\begin{array}{ll}\alpha^{180} & \alpha^{9} \\ \alpha^{81} & \alpha^{90} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 12A1 $12$ $272$ $C_{36}$ 6A 4A 12A5 $\left(\begin{array}{ll}\alpha^{189} & \alpha^{108} \\ \alpha^{180} & \alpha^{63} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 12A5 $12$ $272$ $C_{36}$ 6A 4A 12A1 $\left(\begin{array}{ll}\alpha^{207} & \alpha^{108} \\ \alpha^{180} & \alpha^{45} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 16A1 $16$ $306$ $C_{32}$ 8A1 16A3 16A1 $\left(\begin{array}{ll}\alpha^{180} & \alpha^{243} \\ \alpha^{243} & 1 \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 16A3 $16$ $306$ $C_{32}$ 8A3 16A7 16A3 $\left(\begin{array}{ll}\alpha^{252} & \alpha^{189} \\ \alpha^{189} & \alpha^{18} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 16A5 $16$ $306$ $C_{32}$ 8A3 16A1 16A5 $\left(\begin{array}{ll}\alpha^{162} & \alpha^{189} \\ \alpha^{189} & \alpha^{108} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 16A7 $16$ $306$ $C_{32}$ 8A1 16A5 16A7 $\left(\begin{array}{ll}\alpha^{144} & \alpha^{243} \\ \alpha^{243} & \alpha^{36} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 17A $17$ $288$ $C_{34}$ 17A 17A 1A $\left(\begin{array}{ll}1 & 0 \\ \alpha^{243} & 1 \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 18A1 $18$ $272$ $C_{36}$ 9A1 6A 18A1 $\left(\begin{array}{ll}\alpha^{234} & \alpha^{9} \\ \alpha^{81} & \alpha^{36} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 18A5 $18$ $272$ $C_{36}$ 9A4 6A 18A5 $\left(\begin{array}{ll}\alpha^{216} & \alpha^{99} \\ \alpha^{171} & \alpha^{270} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 18A7 $18$ $272$ $C_{36}$ 9A2 6A 18A7 $\left(\begin{array}{ll}\alpha^{144} & \alpha^{225} \\ \alpha^{9} & \alpha^{216} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 32A1 $32$ $306$ $C_{32}$ 16A1 32A3 32A15 $\left(\begin{array}{ll}\alpha^{261} & \alpha^{180} \\ \alpha^{180} & \alpha^{189} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 32A3 $32$ $306$ $C_{32}$ 16A3 32A9 32A13 $\left(\begin{array}{ll}\alpha^{63} & \alpha^{234} \\ \alpha^{234} & \alpha^{261} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 32A5 $32$ $306$ $C_{32}$ 16A5 32A15 32A11 $\left(\begin{array}{ll}\alpha^{27} & \alpha^{108} \\ \alpha^{108} & \alpha^{63} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 32A7 $32$ $306$ $C_{32}$ 16A7 32A11 32A9 $\left(\begin{array}{ll}0 & \alpha^{216} \\ \alpha^{216} & \alpha^{27} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 32A9 $32$ $306$ $C_{32}$ 16A7 32A5 32A7 $\left(\begin{array}{ll}\alpha^{171} & \alpha^{216} \\ \alpha^{216} & 0 \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 32A11 $32$ $306$ $C_{32}$ 16A5 32A1 32A5 $\left(\begin{array}{ll}\alpha^{207} & \alpha^{108} \\ \alpha^{108} & \alpha^{171} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 32A13 $32$ $306$ $C_{32}$ 16A3 32A7 32A3 $\left(\begin{array}{ll}\alpha^{117} & \alpha^{234} \\ \alpha^{234} & \alpha^{207} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 32A15 $32$ $306$ $C_{32}$ 16A1 32A13 32A1 $\left(\begin{array}{ll}\alpha^{45} & \alpha^{180} \\ \alpha^{180} & \alpha^{117} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 34A $34$ $288$ $C_{34}$ 17A 34A 2A $\left(\begin{array}{ll}\alpha^{144} & 0 \\ \alpha^{135} & \alpha^{144} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 36A1 $36$ $272$ $C_{36}$ 18A1 12A1 36A17 $\left(\begin{array}{ll}\alpha^{81} & \alpha^{18} \\ \alpha^{90} & \alpha^{63} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 36A5 $36$ $272$ $C_{36}$ 18A5 12A5 36A13 $\left(\begin{array}{ll}\alpha^{261} & \alpha^{270} \\ \alpha^{54} & \alpha^{81} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 36A7 $36$ $272$ $C_{36}$ 18A7 12A5 36A11 $\left(\begin{array}{ll}0 & \alpha^{36} \\ \alpha^{108} & \alpha^{189} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 36A11 $36$ $272$ $C_{36}$ 18A7 12A1 36A7 $\left(\begin{array}{ll}\alpha^{45} & \alpha^{36} \\ \alpha^{108} & 0 \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 36A13 $36$ $272$ $C_{36}$ 18A5 12A1 36A5 $\left(\begin{array}{ll}\alpha^{225} & \alpha^{270} \\ \alpha^{54} & \alpha^{117} \\ \end{array}\right)$
$C_2.\PGL(2,17)$ 36A17 $36$ $272$ $C_{36}$ 18A1 12A5 36A1 $\left(\begin{array}{ll}\alpha^{207} & \alpha^{18} \\ \alpha^{90} & \alpha^{225} \\ \end{array}\right)$
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