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Elements of the group are displayed as matrices in $\SU(4,8)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 7P | 13P | 19P | ||||||
| $\SU(4,8)$ | 1A | $1$ | $1$ | not computed | 1A | 1A | 1A | 1A | 1A | 1A | $\left(\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array}\right)$ |
| $\SU(4,8)$ | 2A | $2$ | $233415$ | not computed | 1A | 2A | 2A | 2A | 2A | 2A | $\left(\begin{array}{llll}\alpha^{6} & \alpha^{13} & \alpha^{44} & \alpha^{27} \\ \alpha^{36} & \alpha^{11} & \alpha^{54} & \alpha^{37} \\ \alpha^{40} & \alpha^{27} & \alpha^{25} & \alpha^{41} \\ \alpha^{18} & \alpha^{5} & \alpha^{36} & \alpha^{48} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 2B | $2$ | $16805880$ | not computed | 1A | 2B | 2B | 2B | 2B | 2B | $\left(\begin{array}{llll}\alpha^{44} & \alpha^{17} & \alpha^{54} & \alpha^{27} \\ \alpha^{9} & \alpha^{44} & 0 & \alpha^{54} \\ 1 & \alpha^{36} & \alpha^{37} & \alpha^{10} \\ 0 & 1 & \alpha^{9} & \alpha^{37} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 3A1 | $3$ | $232960$ | not computed | 3A-1 | 1A | 3A-1 | 3A1 | 3A1 | 3A1 | $\left(\begin{array}{llll}\alpha^{60} & \alpha^{4} & \alpha^{4} & \alpha^{6} \\ \alpha^{22} & \alpha^{26} & \alpha^{51} & \alpha^{53} \\ \alpha^{22} & \alpha^{51} & \alpha^{26} & \alpha^{53} \\ \alpha^{42} & \alpha^{8} & \alpha^{8} & \alpha^{33} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 3A-1 | $3$ | $232960$ | not computed | 3A1 | 1A | 3A1 | 3A-1 | 3A-1 | 3A-1 | $\left(\begin{array}{llll}\alpha^{12} & \alpha^{46} & \alpha^{46} & \alpha^{48} \\ \alpha & \alpha^{19} & \alpha^{30} & \alpha^{32} \\ \alpha & \alpha^{30} & \alpha^{19} & \alpha^{32} \\ \alpha^{21} & \alpha^{50} & \alpha^{50} & \alpha^{39} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 3B | $3$ | $15175680$ | not computed | 3B | 1A | 3B | 3B | 3B | 3B | $\left(\begin{array}{llll}\alpha^{24} & \alpha^{24} & \alpha^{59} & \alpha^{18} \\ \alpha^{59} & \alpha^{43} & \alpha^{18} & \alpha^{31} \\ \alpha^{5} & 1 & \alpha^{44} & \alpha^{3} \\ 0 & \alpha^{40} & \alpha^{31} & \alpha^{13} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 3C | $3$ | $849838080$ | not computed | 3C | 1A | 3C | 3C | 3C | 3C | $\left(\begin{array}{llll}\alpha^{62} & \alpha^{52} & \alpha^{38} & \alpha^{51} \\ \alpha^{25} & \alpha^{11} & \alpha^{37} & \alpha^{10} \\ \alpha^{59} & \alpha^{7} & \alpha^{16} & \alpha^{59} \\ \alpha & \alpha^{60} & \alpha^{21} & \alpha^{57} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 4A | $4$ | $941129280$ | not computed | 2A | 4A | 4A | 4A | 4A | 4A | $\left(\begin{array}{llll}\alpha^{53} & \alpha^{53} & \alpha^{38} & \alpha^{48} \\ \alpha^{24} & \alpha^{12} & \alpha^{57} & \alpha^{24} \\ \alpha^{19} & \alpha^{55} & \alpha^{42} & \alpha^{61} \\ \alpha^{7} & \alpha^{2} & \alpha^{46} & \alpha^{62} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 4B | $4$ | $67761308160$ | not computed | 2B | 4B | 4B | 4B | 4B | 4B | $\left(\begin{array}{llll}\alpha^{37} & \alpha^{17} & \alpha^{58} & \alpha^{59} \\ \alpha^{3} & \alpha^{54} & \alpha^{10} & \alpha^{16} \\ \alpha^{37} & \alpha^{35} & \alpha^{54} & \alpha^{38} \\ \alpha^{15} & \alpha^{16} & \alpha^{45} & \alpha^{37} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 5A | $5$ | $76250087424$ | not computed | 5A | 5A | 1A | 5A | 5A | 5A | $\left(\begin{array}{llll}\alpha^{40} & \alpha^{7} & \alpha^{3} & \alpha^{57} \\ \alpha^{54} & \alpha^{15} & \alpha^{17} & \alpha^{20} \\ \alpha^{42} & \alpha^{20} & \alpha^{41} & \alpha^{32} \\ \alpha^{7} & \alpha^{21} & \alpha^{46} & \alpha^{26} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 6A1 | $6$ | $836559360$ | not computed | 3A-1 | 2A | 6A-1 | 6A1 | 6A1 | 6A1 | $\left(\begin{array}{llll}\alpha^{57} & \alpha^{27} & \alpha^{61} & \alpha^{4} \\ \alpha^{53} & \alpha^{20} & \alpha^{36} & \alpha^{10} \\ \alpha & 1 & \alpha^{2} & \alpha^{8} \\ \alpha^{47} & \alpha^{30} & \alpha^{38} & \alpha^{50} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 6A-1 | $6$ | $836559360$ | not computed | 3A1 | 2A | 6A1 | 6A-1 | 6A-1 | 6A-1 | $\left(\begin{array}{llll}\alpha^{22} & \alpha & \alpha^{17} & \alpha^{32} \\ \alpha^{52} & \alpha^{16} & \alpha^{36} & \alpha^{47} \\ \alpha^{51} & 1 & \alpha^{34} & \alpha^{27} \\ \alpha^{61} & \alpha^{8} & \alpha^{46} & \alpha^{15} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 6B1 | $6$ | $956067840$ | not computed | 3B | 2A | 6B-1 | 6B1 | 6B1 | 6B1 | $\left(\begin{array}{llll}\alpha^{50} & \alpha^{20} & \alpha^{5} & \alpha^{58} \\ \alpha^{44} & \alpha^{6} & \alpha^{52} & \alpha^{50} \\ \alpha^{21} & \alpha^{26} & \alpha^{36} & \alpha^{42} \\ \alpha^{60} & \alpha^{48} & \alpha^{29} & \alpha^{28} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 6B-1 | $6$ | $956067840$ | not computed | 3B | 2A | 6B1 | 6B-1 | 6B-1 | 6B-1 | $\left(\begin{array}{llll}\alpha^{35} & \alpha^{21} & \alpha^{22} & \alpha^{23} \\ \alpha^{43} & \alpha^{36} & \alpha^{38} & \alpha^{40} \\ \alpha^{6} & \alpha^{19} & \alpha^{48} & \alpha^{34} \\ \alpha^{39} & \alpha^{42} & \alpha^{37} & \alpha^{22} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 6C | $6$ | $53539799040$ | not computed | 3C | 2A | 6C | 6C | 6C | 6C | $\left(\begin{array}{llll}\alpha^{16} & 1 & \alpha^{12} & \alpha^{51} \\ \alpha^{3} & \alpha^{28} & \alpha^{41} & \alpha^{17} \\ \alpha^{57} & \alpha^{51} & \alpha^{42} & \alpha^{39} \\ \alpha^{7} & \alpha^{25} & \alpha^{22} & \alpha^{19} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 6D | $6$ | $60232273920$ | not computed | 3B | 2B | 6D | 6D | 6D | 6D | $\left(\begin{array}{llll}\alpha^{44} & \alpha^{7} & \alpha^{37} & \alpha^{34} \\ \alpha^{13} & \alpha^{23} & \alpha^{8} & \alpha^{25} \\ \alpha^{24} & \alpha^{40} & \alpha^{15} & \alpha^{12} \\ \alpha^{36} & \alpha^{42} & \alpha^{16} & \alpha^{5} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 7A1 | $7$ | $18911232$ | not computed | 7A2 | 7A3 | 7A2 | 1A | 7A1 | 7A2 | $\left(\begin{array}{llll}\alpha^{45} & \alpha^{8} & \alpha^{53} & \alpha^{27} \\ \alpha^{37} & 0 & \alpha^{9} & \alpha^{46} \\ 0 & \alpha^{27} & \alpha^{54} & \alpha \\ 1 & 0 & \alpha^{44} & \alpha^{9} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 7A2 | $7$ | $18911232$ | not computed | 7A3 | 7A1 | 7A3 | 1A | 7A2 | 7A3 | $\left(\begin{array}{llll}\alpha^{45} & \alpha^{62} & \alpha^{44} & \alpha^{18} \\ \alpha^{28} & 1 & 1 & \alpha^{37} \\ 0 & \alpha^{18} & \alpha^{36} & \alpha^{55} \\ \alpha^{54} & 0 & \alpha^{35} & 0 \\ \end{array}\right)$ |
| $\SU(4,8)$ | 7A3 | $7$ | $18911232$ | not computed | 7A1 | 7A2 | 7A1 | 1A | 7A3 | 7A1 | $\left(\begin{array}{llll}1 & \alpha^{44} & \alpha^{26} & 1 \\ \alpha^{10} & \alpha^{54} & \alpha^{45} & \alpha^{19} \\ 0 & 1 & \alpha^{36} & \alpha^{37} \\ \alpha^{36} & 0 & \alpha^{17} & \alpha^{9} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 7B1 | $7$ | $1092648960$ | not computed | 7B2 | 7B3 | 7B2 | 1A | 7B1 | 7B2 | $\left(\begin{array}{llll}\alpha^{17} & \alpha^{48} & \alpha^{34} & \alpha^{60} \\ \alpha^{11} & \alpha^{38} & \alpha^{55} & \alpha^{19} \\ \alpha^{41} & \alpha^{57} & \alpha^{29} & \alpha^{24} \\ \alpha^{34} & \alpha^{16} & \alpha^{58} & \alpha^{57} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 7B2 | $7$ | $1092648960$ | not computed | 7B3 | 7B1 | 7B3 | 1A | 7B2 | 7B3 | $\left(\begin{array}{llll}\alpha^{25} & \alpha^{57} & \alpha^{55} & \alpha^{59} \\ \alpha & \alpha^{49} & \alpha^{43} & \alpha^{24} \\ \alpha^{54} & \alpha^{49} & \alpha^{21} & \alpha^{24} \\ \alpha^{10} & \alpha^{30} & \alpha^{51} & \alpha^{32} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 7B3 | $7$ | $1092648960$ | not computed | 7B1 | 7B2 | 7B1 | 1A | 7B3 | 7B1 | $\left(\begin{array}{llll}\alpha^{10} & \alpha^{48} & \alpha^{49} & \alpha^{25} \\ \alpha^{34} & \alpha^{15} & \alpha^{5} & \alpha^{22} \\ \alpha^{17} & \alpha^{29} & \alpha^{56} & 0 \\ \alpha^{24} & \alpha^{5} & \alpha^{32} & 0 \\ \end{array}\right)$ |
| $\SU(4,8)$ | 7C1 | $7$ | $78670725120$ | not computed | 7C2 | 7C3 | 7C2 | 1A | 7C1 | 7C2 | $\left(\begin{array}{llll}\alpha^{18} & \alpha^{9} & \alpha^{13} & \alpha^{15} \\ \alpha^{30} & \alpha^{31} & \alpha^{23} & \alpha^{37} \\ \alpha^{36} & \alpha^{9} & \alpha^{55} & \alpha^{57} \\ \alpha^{23} & \alpha^{42} & \alpha^{55} & \alpha^{18} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 7C2 | $7$ | $78670725120$ | not computed | 7C3 | 7C1 | 7C3 | 1A | 7C2 | 7C3 | $\left(\begin{array}{llll}\alpha^{38} & \alpha^{61} & \alpha^{29} & \alpha^{24} \\ \alpha^{44} & \alpha^{24} & \alpha^{35} & \alpha^{13} \\ \alpha^{15} & \alpha^{54} & \alpha^{3} & \alpha^{34} \\ \alpha^{57} & \alpha^{10} & \alpha^{62} & \alpha^{50} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 7C3 | $7$ | $78670725120$ | not computed | 7C1 | 7C2 | 7C1 | 1A | 7C3 | 7C1 | $\left(\begin{array}{llll}\alpha^{21} & \alpha^{10} & \alpha^{20} & \alpha^{62} \\ \alpha^{19} & \alpha^{8} & \alpha^{52} & \alpha^{20} \\ \alpha^{4} & \alpha^{18} & \alpha^{8} & \alpha^{50} \\ \alpha^{22} & \alpha^{52} & \alpha^{4} & \alpha^{55} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9A1 | $9$ | $232960$ | not computed | 9A2 | 3A1 | 9A-4 | 9A-2 | 9A4 | 9A1 | $\left(\begin{array}{llll}\alpha^{59} & \alpha^{12} & \alpha^{12} & \alpha^{14} \\ \alpha^{30} & \alpha^{46} & \alpha^{59} & \alpha^{61} \\ \alpha^{30} & \alpha^{59} & \alpha^{46} & \alpha^{61} \\ \alpha^{50} & \alpha^{16} & \alpha^{16} & \alpha^{14} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9A-1 | $9$ | $232960$ | not computed | 9A-2 | 3A-1 | 9A4 | 9A2 | 9A-4 | 9A-1 | $\left(\begin{array}{llll}\alpha^{49} & \alpha^{47} & \alpha^{47} & \alpha^{49} \\ \alpha^{2} & \alpha^{53} & \alpha^{31} & \alpha^{33} \\ \alpha^{2} & \alpha^{31} & \alpha^{53} & \alpha^{33} \\ \alpha^{22} & \alpha^{51} & \alpha^{51} & \alpha^{31} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9A2 | $9$ | $232960$ | not computed | 9A4 | 3A-1 | 9A1 | 9A-4 | 9A-1 | 9A2 | $\left(\begin{array}{llll}\alpha^{19} & \alpha^{62} & \alpha^{62} & \alpha \\ \alpha^{17} & \alpha^{58} & \alpha^{46} & \alpha^{48} \\ \alpha^{17} & \alpha^{46} & \alpha^{58} & \alpha^{48} \\ \alpha^{37} & \alpha^{3} & \alpha^{3} & \alpha^{10} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9A-2 | $9$ | $232960$ | not computed | 9A-4 | 3A1 | 9A-1 | 9A4 | 9A1 | 9A-2 | $\left(\begin{array}{llll}\alpha^{17} & \alpha^{6} & \alpha^{6} & \alpha^{8} \\ \alpha^{24} & \alpha^{23} & \alpha^{53} & \alpha^{55} \\ \alpha^{24} & \alpha^{53} & \alpha^{23} & \alpha^{55} \\ \alpha^{44} & \alpha^{10} & \alpha^{10} & \alpha^{26} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9A4 | $9$ | $232960$ | not computed | 9A-1 | 3A1 | 9A2 | 9A1 | 9A-2 | 9A4 | $\left(\begin{array}{llll}0 & \alpha^{36} & \alpha^{36} & \alpha^{38} \\ \alpha^{54} & \alpha^{10} & \alpha^{20} & \alpha^{22} \\ \alpha^{54} & \alpha^{20} & \alpha^{10} & \alpha^{22} \\ \alpha^{11} & \alpha^{40} & \alpha^{40} & \alpha^{11} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9A-4 | $9$ | $232960$ | not computed | 9A1 | 3A-1 | 9A-2 | 9A-1 | 9A2 | 9A-4 | $\left(\begin{array}{llll}\alpha^{25} & \alpha^{50} & \alpha^{50} & \alpha^{52} \\ \alpha^{5} & \alpha^{17} & \alpha^{34} & \alpha^{36} \\ \alpha^{5} & \alpha^{34} & \alpha^{17} & \alpha^{36} \\ \alpha^{25} & \alpha^{54} & \alpha^{54} & 0 \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9B1 | $9$ | $15175680$ | not computed | 9B2 | 3B | 9B4 | 9B2 | 9B4 | 9B1 | $\left(\begin{array}{llll}\alpha^{49} & \alpha^{60} & \alpha^{32} & \alpha^{54} \\ \alpha^{32} & \alpha^{17} & \alpha^{54} & \alpha^{4} \\ \alpha^{41} & \alpha^{36} & \alpha^{16} & \alpha^{39} \\ 0 & \alpha^{13} & \alpha^{4} & \alpha^{60} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9B2 | $9$ | $15175680$ | not computed | 9B4 | 3B | 9B1 | 9B4 | 9B1 | 9B2 | $\left(\begin{array}{llll}\alpha^{46} & \alpha^{33} & \alpha^{5} & \alpha^{27} \\ \alpha^{5} & \alpha^{50} & \alpha^{27} & \alpha^{40} \\ \alpha^{14} & \alpha^{9} & \alpha^{12} & \alpha^{12} \\ 0 & \alpha^{49} & \alpha^{40} & \alpha^{38} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9B4 | $9$ | $15175680$ | not computed | 9B1 | 3B | 9B2 | 9B1 | 9B2 | 9B4 | $\left(\begin{array}{llll}\alpha^{62} & \alpha^{42} & \alpha^{14} & \alpha^{36} \\ \alpha^{14} & \alpha^{31} & \alpha^{36} & \alpha^{49} \\ \alpha^{23} & \alpha^{18} & \alpha^{42} & \alpha^{21} \\ 0 & \alpha^{58} & \alpha^{49} & \alpha^{61} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9C1 | $9$ | $849838080$ | not computed | 9C2 | 3C | 9C4 | 9C2 | 9C4 | 9C1 | $\left(\begin{array}{llll}\alpha^{4} & \alpha^{26} & \alpha^{32} & \alpha^{39} \\ \alpha^{14} & \alpha^{60} & \alpha^{34} & \alpha^{28} \\ \alpha^{12} & \alpha^{18} & \alpha^{37} & \alpha^{9} \\ \alpha^{52} & \alpha^{59} & \alpha^{11} & \alpha^{46} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9C2 | $9$ | $849838080$ | not computed | 9C4 | 3C | 9C1 | 9C4 | 9C1 | 9C2 | $\left(\begin{array}{llll}\alpha^{62} & \alpha & \alpha^{56} & \alpha^{38} \\ \alpha^{40} & \alpha^{4} & \alpha^{51} & \alpha^{30} \\ \alpha^{37} & \alpha^{54} & \alpha^{41} & \alpha^{23} \\ \alpha^{6} & \alpha^{40} & \alpha^{57} & \alpha^{36} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9C4 | $9$ | $849838080$ | not computed | 9C1 | 3C | 9C2 | 9C1 | 9C2 | 9C4 | $\left(\begin{array}{llll}\alpha^{58} & \alpha^{33} & \alpha^{16} & \alpha^{55} \\ \alpha^{27} & \alpha^{15} & \alpha^{49} & \alpha^{60} \\ \alpha^{36} & 1 & \alpha^{17} & \alpha^{29} \\ \alpha^{4} & \alpha^{55} & \alpha^{19} & \alpha^{31} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9D1 | $9$ | $849838080$ | not computed | 9D2 | 3C | 9D-4 | 9D-2 | 9D4 | 9D1 | $\left(\begin{array}{llll}\alpha^{21} & \alpha^{60} & \alpha^{46} & \alpha^{59} \\ \alpha^{34} & \alpha^{38} & \alpha^{44} & \alpha^{18} \\ \alpha^{18} & \alpha^{11} & \alpha^{50} & \alpha^{4} \\ \alpha^{8} & \alpha^{51} & \alpha^{51} & \alpha^{44} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9D-1 | $9$ | $849838080$ | not computed | 9D-2 | 3C | 9D4 | 9D2 | 9D-4 | 9D-1 | $\left(\begin{array}{llll}\alpha^{37} & \alpha^{32} & \alpha^{18} & \alpha^{31} \\ \alpha^{30} & \alpha^{22} & \alpha^{37} & \alpha^{53} \\ \alpha^{30} & \alpha^{25} & \alpha^{52} & \alpha^{39} \\ \alpha & \alpha^{18} & \alpha^{20} & \alpha^{42} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9D2 | $9$ | $849838080$ | not computed | 9D4 | 3C | 9D1 | 9D-4 | 9D-1 | 9D2 | $\left(\begin{array}{llll}\alpha^{2} & \alpha^{47} & \alpha^{33} & \alpha^{46} \\ \alpha^{19} & \alpha^{39} & \alpha^{50} & \alpha^{5} \\ \alpha^{25} & \alpha^{7} & \alpha^{46} & \alpha^{54} \\ \alpha^{14} & \alpha^{34} & \alpha^{52} & \alpha^{41} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9D-2 | $9$ | $849838080$ | not computed | 9D-4 | 3C | 9D-1 | 9D4 | 9D1 | 9D-2 | $\left(\begin{array}{llll}\alpha^{13} & \alpha^{54} & \alpha^{40} & \alpha^{53} \\ \alpha^{38} & \alpha^{53} & \alpha^{22} & \alpha^{12} \\ \alpha^{20} & \alpha^{56} & \alpha^{60} & \alpha^{61} \\ \alpha^{49} & \alpha^{11} & \alpha^{26} & \alpha^{16} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9D4 | $9$ | $849838080$ | not computed | 9D-1 | 3C | 9D2 | 9D1 | 9D-2 | 9D4 | $\left(\begin{array}{llll}\alpha^{15} & \alpha^{21} & \alpha^{7} & \alpha^{20} \\ \alpha^{49} & \alpha^{25} & \alpha^{53} & \alpha^{42} \\ \alpha^{11} & \alpha^{19} & \alpha^{12} & \alpha^{28} \\ \alpha^{17} & \alpha^{61} & \alpha^{2} & \alpha^{39} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9D-4 | $9$ | $849838080$ | not computed | 9D1 | 3C | 9D-2 | 9D-1 | 9D2 | 9D-4 | $\left(\begin{array}{llll}\alpha^{60} & \alpha^{35} & \alpha^{21} & \alpha^{34} \\ \alpha^{16} & \alpha^{33} & \alpha^{46} & \alpha^{56} \\ \alpha^{47} & \alpha^{26} & \alpha^{11} & \alpha^{42} \\ \alpha^{10} & \alpha^{25} & \alpha^{14} & \alpha^{57} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9E1 | $9$ | $849838080$ | not computed | 9E2 | 3B | 9E-4 | 9E-2 | 9E4 | 9E1 | $\left(\begin{array}{llll}\alpha^{57} & \alpha^{6} & \alpha^{48} & \alpha^{23} \\ \alpha^{53} & \alpha^{37} & \alpha^{28} & \alpha^{8} \\ \alpha^{9} & 1 & 1 & 1 \\ \alpha^{32} & \alpha^{58} & \alpha^{26} & \alpha^{6} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9E-1 | $9$ | $849838080$ | not computed | 9E-2 | 3B | 9E4 | 9E2 | 9E-4 | 9E-1 | $\left(\begin{array}{llll}\alpha^{48} & 1 & \alpha & \alpha^{58} \\ \alpha^{19} & 1 & \alpha^{35} & \alpha^{6} \\ \alpha^{23} & 1 & \alpha^{44} & \alpha^{48} \\ \alpha^{4} & \alpha^{9} & \alpha^{46} & \alpha^{15} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9E2 | $9$ | $849838080$ | not computed | 9E4 | 3B | 9E1 | 9E-4 | 9E-1 | 9E2 | $\left(\begin{array}{llll}\alpha^{17} & \alpha^{39} & 0 & \alpha^{17} \\ \alpha^{2} & \alpha^{26} & \alpha^{55} & \alpha^{53} \\ \alpha^{2} & \alpha^{7} & \alpha^{19} & \alpha^{37} \\ \alpha^{26} & \alpha^{51} & \alpha^{7} & \alpha^{18} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9E-2 | $9$ | $849838080$ | not computed | 9E-4 | 3B | 9E-1 | 9E4 | 9E1 | 9E-2 | $\left(\begin{array}{llll}\alpha^{18} & \alpha^{44} & \alpha^{46} & \alpha^{10} \\ \alpha^{56} & \alpha^{26} & \alpha^{62} & 0 \\ \alpha^{30} & \alpha^{56} & \alpha^{19} & \alpha^{60} \\ \alpha^{19} & \alpha^{16} & \alpha^{16} & \alpha^{10} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9E4 | $9$ | $849838080$ | not computed | 9E-1 | 3B | 9E2 | 9E1 | 9E-2 | 9E4 | $\left(\begin{array}{llll}\alpha^{35} & \alpha^{39} & \alpha^{32} & \alpha^{13} \\ \alpha^{3} & \alpha^{49} & \alpha^{43} & \alpha^{8} \\ \alpha^{51} & \alpha & \alpha^{48} & \alpha^{10} \\ \alpha^{22} & \alpha^{37} & \alpha^{13} & \alpha^{41} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9E-4 | $9$ | $849838080$ | not computed | 9E1 | 3B | 9E-2 | 9E-1 | 9E2 | 9E-4 | $\left(\begin{array}{llll}\alpha^{13} & \alpha^{17} & \alpha & \alpha^{41} \\ \alpha^{41} & \alpha^{6} & \alpha^{29} & \alpha^{4} \\ \alpha^{44} & \alpha^{8} & \alpha^{14} & \alpha^{60} \\ \alpha^{50} & \alpha^{30} & \alpha^{24} & \alpha^{28} \\ \end{array}\right)$ |
| $\SU(4,8)$ | 9F1 | $9$ | $849838080$ | not computed | 9F2 | 3A1 | 9F-4 | 9F-2 | 9F4 | 9F1 | $\left(\begin{array}{llll}\alpha^{51} & \alpha^{11} & \alpha^{37} & \alpha^{54} \\ \alpha^{15} & \alpha^{38} & \alpha^{34} & \alpha^{32} \\ \alpha^{14} & \alpha^{18} & \alpha^{52} & \alpha^{7} \\ \alpha^{21} & \alpha^{46} & \alpha^{46} & \alpha^{57} \\ \end{array}\right)$ |