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Results (22 matches)

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Elements of the group are displayed as matrices in $\SU(3,4)$.

Group Label Order Size Centralizer Powers Representative
2P 3P 5P 13P
$\SU(3,4)$ 1A $1$ $1$ $\SU(3,4)$ 1A 1A 1A 1A $\left(\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{array}\right)$
$\SU(3,4)$ 2A $2$ $195$ $C_2^2.C_2^4:C_5$ 1A 2A 2A 2A $\left(\begin{array}{lll}\alpha^{11} & \alpha^{2} & 1 \\ \alpha^{5} & \alpha^{5} & \alpha^{8} \\ 1 & \alpha^{5} & \alpha^{14} \\ \end{array}\right)$
$\SU(3,4)$ 3A $3$ $4160$ $C_{15}$ 3A 1A 3A 3A $\left(\begin{array}{lll}\alpha^{5} & 0 & 0 \\ \alpha^{14} & 1 & 0 \\ \alpha^{13} & \alpha^{6} & \alpha^{10} \\ \end{array}\right)$
$\SU(3,4)$ 4A $4$ $3900$ $C_4^2$ 2A 4A 4A 4A $\left(\begin{array}{lll}\alpha^{7} & \alpha^{3} & \alpha^{6} \\ \alpha^{3} & \alpha^{8} & \alpha \\ \alpha^{4} & \alpha^{10} & \alpha^{12} \\ \end{array}\right)$
$\SU(3,4)$ 5A1 $5$ $208$ $C_5\times A_5$ 5A2 5A-2 1A 5A-2 $\left(\begin{array}{lll}\alpha^{12} & 0 & 0 \\ \alpha^{8} & \alpha^{6} & 0 \\ \alpha^{9} & \alpha^{5} & \alpha^{12} \\ \end{array}\right)$
$\SU(3,4)$ 5A-1 $5$ $208$ $C_5\times A_5$ 5A-2 5A2 1A 5A2 $\left(\begin{array}{lll}\alpha^{3} & 0 & 0 \\ \alpha^{5} & \alpha^{9} & 0 \\ \alpha^{6} & \alpha^{2} & \alpha^{3} \\ \end{array}\right)$
$\SU(3,4)$ 5A2 $5$ $208$ $C_5\times A_5$ 5A-1 5A1 1A 5A1 $\left(\begin{array}{lll}\alpha^{9} & 0 & 0 \\ \alpha^{12} & \alpha^{12} & 0 \\ \alpha^{13} & \alpha^{9} & \alpha^{9} \\ \end{array}\right)$
$\SU(3,4)$ 5A-2 $5$ $208$ $C_5\times A_5$ 5A1 5A-1 1A 5A-1 $\left(\begin{array}{lll}\alpha^{6} & 0 & 0 \\ \alpha^{6} & \alpha^{3} & 0 \\ \alpha^{7} & \alpha^{3} & \alpha^{6} \\ \end{array}\right)$
$\SU(3,4)$ 5B1 $5$ $2496$ $C_5^2$ 5B2 5B2 1A 5B2 $\left(\begin{array}{lll}\alpha^{9} & \alpha & \alpha \\ \alpha^{2} & \alpha^{8} & \alpha^{13} \\ \alpha^{6} & \alpha^{2} & \alpha^{3} \\ \end{array}\right)$
$\SU(3,4)$ 5B2 $5$ $2496$ $C_5^2$ 5B1 5B1 1A 5B1 $\left(\begin{array}{lll}\alpha^{7} & \alpha^{8} & \alpha^{13} \\ \alpha^{9} & \alpha^{7} & \alpha^{5} \\ \alpha^{3} & \alpha^{9} & \alpha^{5} \\ \end{array}\right)$
$\SU(3,4)$ 10A1 $10$ $3120$ $C_2\times C_{10}$ 5A-2 10A3 2A 10A3 $\left(\begin{array}{lll}\alpha & \alpha^{13} & \alpha^{2} \\ \alpha^{7} & \alpha^{7} & \alpha^{14} \\ \alpha^{5} & \alpha^{7} & \alpha^{4} \\ \end{array}\right)$
$\SU(3,4)$ 10A-1 $10$ $3120$ $C_2\times C_{10}$ 5A2 10A-3 2A 10A-3 $\left(\begin{array}{lll}\alpha & \alpha^{11} & \alpha^{8} \\ \alpha^{13} & \alpha^{13} & \alpha^{7} \\ \alpha^{5} & \alpha^{13} & \alpha^{4} \\ \end{array}\right)$
$\SU(3,4)$ 10A3 $10$ $3120$ $C_2\times C_{10}$ 5A-1 10A-1 2A 10A-1 $\left(\begin{array}{lll}\alpha^{12} & \alpha^{10} & \alpha^{10} \\ 1 & 1 & 0 \\ \alpha & 1 & 1 \\ \end{array}\right)$
$\SU(3,4)$ 10A-3 $10$ $3120$ $C_2\times C_{10}$ 5A1 10A1 2A 10A1 $\left(\begin{array}{lll}1 & 0 & \alpha^{10} \\ 1 & 1 & \alpha^{10} \\ \alpha^{4} & 1 & \alpha^{3} \\ \end{array}\right)$
$\SU(3,4)$ 13A1 $13$ $4800$ $C_{13}$ 13A2 13A1 13A2 1A $\left(\begin{array}{lll}\alpha^{14} & \alpha^{5} & \alpha \\ \alpha^{4} & \alpha^{3} & 0 \\ \alpha^{13} & \alpha^{10} & \alpha^{6} \\ \end{array}\right)$
$\SU(3,4)$ 13A-1 $13$ $4800$ $C_{13}$ 13A-2 13A-1 13A-2 1A $\left(\begin{array}{lll}\alpha^{9} & 0 & \alpha^{4} \\ \alpha^{10} & \alpha^{12} & \alpha^{5} \\ \alpha^{7} & \alpha & \alpha^{11} \\ \end{array}\right)$
$\SU(3,4)$ 13A2 $13$ $4800$ $C_{13}$ 13A-1 13A2 13A-1 1A $\left(\begin{array}{lll}\alpha^{11} & \alpha^{3} & \alpha^{9} \\ \alpha^{4} & \alpha^{5} & \alpha^{5} \\ \alpha^{8} & \alpha^{10} & \alpha^{5} \\ \end{array}\right)$
$\SU(3,4)$ 13A-2 $13$ $4800$ $C_{13}$ 13A1 13A-2 13A1 1A $\left(\begin{array}{lll}\alpha^{5} & \alpha^{5} & \alpha^{6} \\ \alpha^{10} & \alpha^{5} & \alpha^{12} \\ \alpha^{2} & \alpha & \alpha^{14} \\ \end{array}\right)$
$\SU(3,4)$ 15A1 $15$ $4160$ $C_{15}$ 15A2 5A1 3A 15A-2 $\left(\begin{array}{lll}\alpha^{4} & 0 & 0 \\ \alpha^{10} & \alpha^{12} & 0 \\ \alpha^{12} & \alpha^{6} & \alpha^{14} \\ \end{array}\right)$
$\SU(3,4)$ 15A-1 $15$ $4160$ $C_{15}$ 15A-2 5A-1 3A 15A2 $\left(\begin{array}{lll}\alpha^{11} & 0 & 0 \\ \alpha^{9} & \alpha^{3} & 0 \\ \alpha^{3} & \alpha^{10} & \alpha \\ \end{array}\right)$
$\SU(3,4)$ 15A2 $15$ $4160$ $C_{15}$ 15A-1 5A2 3A 15A1 $\left(\begin{array}{lll}\alpha^{8} & 0 & 0 \\ \alpha & \alpha^{9} & 0 \\ \alpha^{11} & \alpha^{11} & \alpha^{13} \\ \end{array}\right)$
$\SU(3,4)$ 15A-2 $15$ $4160$ $C_{15}$ 15A1 5A-2 3A 15A-1 $\left(\begin{array}{lll}\alpha^{7} & 0 & 0 \\ \alpha^{14} & \alpha^{6} & 0 \\ \alpha^{14} & \alpha^{4} & \alpha^{2} \\ \end{array}\right)$
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