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Results (34 matches)

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

Group Label Order Size Centralizer Powers Representative
2P 3P 5P
$\Sp(4,3)$ 1A $1$ $1$ $\Sp(4,3)$ 1A 1A 1A $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right) $
$\Sp(4,3)$ 2A $2$ $1$ $\Sp(4,3)$ 1A 2A 2A $ \left(\begin{array}{rrrr} 2 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 2 \end{array}\right) $
$\Sp(4,3)$ 2B $2$ $90$ $\SL(2,3)^2$ 1A 2B 2B $ \left(\begin{array}{rrrr} 2 & 0 & 2 & 0 \\ 2 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 2 & 2 \end{array}\right) $
$\Sp(4,3)$ 3A1 $3$ $40$ $C_2\times \Unitary(3,2)$ 3A-1 1A 3A-1 $ \left(\begin{array}{rrrr} 0 & 2 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 2 & 2 & 1 & 1 \\ 2 & 2 & 0 & 2 \end{array}\right) $
$\Sp(4,3)$ 3A-1 $3$ $40$ $C_2\times \Unitary(3,2)$ 3A1 1A 3A1 $ \left(\begin{array}{rrrr} 2 & 1 & 0 & 2 \\ 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 2 \\ 1 & 1 & 0 & 0 \end{array}\right) $
$\Sp(4,3)$ 3B $3$ $240$ $C_3^3:D_4$ 3B 1A 3B $ \left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 0 & 0 & 2 & 2 \\ 2 & 2 & 2 & 1 \\ 1 & 2 & 0 & 1 \end{array}\right) $
$\Sp(4,3)$ 3C $3$ $480$ $C_3^2\times D_6$ 3C 1A 3C $ \left(\begin{array}{rrrr} 2 & 1 & 1 & 2 \\ 0 & 2 & 0 & 1 \\ 2 & 0 & 0 & 2 \\ 0 & 2 & 0 & 0 \end{array}\right) $
$\Sp(4,3)$ 4A $4$ $540$ $C_4\times \SL(2,3)$ 2B 4A 4A $ \left(\begin{array}{rrrr} 1 & 0 & 2 & 1 \\ 1 & 1 & 2 & 0 \\ 0 & 0 & 1 & 0 \\ 1 & 0 & 1 & 2 \end{array}\right) $
$\Sp(4,3)$ 4B $4$ $540$ $C_4\times \SL(2,3)$ 2B 4B 4B $ \left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 2 & 2 \\ 1 & 1 & 1 & 2 \\ 1 & 1 & 2 & 1 \end{array}\right) $
$\Sp(4,3)$ 4C $4$ $540$ $\Unitary(2,3)$ 2A 4C 4C $ \left(\begin{array}{rrrr} 2 & 1 & 1 & 0 \\ 0 & 2 & 0 & 1 \\ 1 & 2 & 1 & 2 \\ 0 & 1 & 0 & 1 \end{array}\right) $
$\Sp(4,3)$ 5A $5$ $5184$ $C_{10}$ 5A 5A 1A $ \left(\begin{array}{rrrr} 0 & 1 & 0 & 1 \\ 2 & 0 & 2 & 1 \\ 1 & 1 & 1 & 2 \\ 2 & 0 & 0 & 1 \end{array}\right) $
$\Sp(4,3)$ 6A1 $6$ $40$ $C_2\times \Unitary(3,2)$ 3A-1 2A 6A-1 $ \left(\begin{array}{rrrr} 0 & 0 & 0 & 2 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 2 & 0 \\ 1 & 0 & 0 & 1 \end{array}\right) $
$\Sp(4,3)$ 6A-1 $6$ $40$ $C_2\times \Unitary(3,2)$ 3A1 2A 6A1 $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 1 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 2 & 0 \\ 2 & 0 & 0 & 0 \end{array}\right) $
$\Sp(4,3)$ 6B $6$ $240$ $C_3^3:D_4$ 3B 2A 6B $ \left(\begin{array}{rrrr} 1 & 1 & 1 & 2 \\ 2 & 1 & 1 & 1 \\ 2 & 1 & 0 & 2 \\ 2 & 2 & 1 & 0 \end{array}\right) $
$\Sp(4,3)$ 6C1 $6$ $360$ $C_6\times \SL(2,3)$ 3A1 2B 6C-1 $ \left(\begin{array}{rrrr} 0 & 1 & 2 & 2 \\ 2 & 1 & 0 & 1 \\ 1 & 1 & 1 & 2 \\ 1 & 1 & 2 & 1 \end{array}\right) $
$\Sp(4,3)$ 6C-1 $6$ $360$ $C_6\times \SL(2,3)$ 3A-1 2B 6C1 $ \left(\begin{array}{rrrr} 1 & 2 & 2 & 1 \\ 2 & 1 & 0 & 1 \\ 2 & 2 & 1 & 1 \\ 2 & 2 & 2 & 0 \end{array}\right) $
$\Sp(4,3)$ 6D1 $6$ $360$ $C_6\times \SL(2,3)$ 3A-1 2B 6D-1 $ \left(\begin{array}{rrrr} 1 & 1 & 1 & 2 \\ 2 & 1 & 2 & 0 \\ 0 & 1 & 2 & 2 \\ 1 & 2 & 0 & 2 \end{array}\right) $
$\Sp(4,3)$ 6D-1 $6$ $360$ $C_6\times \SL(2,3)$ 3A1 2B 6D1 $ \left(\begin{array}{rrrr} 2 & 2 & 0 & 1 \\ 0 & 2 & 1 & 2 \\ 1 & 2 & 1 & 1 \\ 2 & 0 & 2 & 1 \end{array}\right) $
$\Sp(4,3)$ 6E $6$ $480$ $C_3^2\times D_6$ 3C 2A 6E $ \left(\begin{array}{rrrr} 1 & 1 & 2 & 0 \\ 1 & 0 & 1 & 2 \\ 2 & 0 & 1 & 2 \\ 2 & 2 & 2 & 0 \end{array}\right) $
$\Sp(4,3)$ 6F1 $6$ $1440$ $C_6^2$ 3B 2B 6F-1 $ \left(\begin{array}{rrrr} 0 & 1 & 2 & 2 \\ 2 & 2 & 2 & 2 \\ 2 & 0 & 1 & 0 \\ 2 & 0 & 2 & 0 \end{array}\right) $
$\Sp(4,3)$ 6F-1 $6$ $1440$ $C_6^2$ 3B 2B 6F1 $ \left(\begin{array}{rrrr} 0 & 0 & 1 & 1 \\ 2 & 1 & 1 & 1 \\ 0 & 0 & 2 & 1 \\ 1 & 1 & 2 & 0 \end{array}\right) $
$\Sp(4,3)$ 6G1 $6$ $1440$ $C_6^2$ 3C 2B 6G-1 $ \left(\begin{array}{rrrr} 0 & 2 & 2 & 1 \\ 0 & 2 & 2 & 2 \\ 2 & 1 & 2 & 1 \\ 1 & 1 & 2 & 2 \end{array}\right) $
$\Sp(4,3)$ 6G-1 $6$ $1440$ $C_6^2$ 3C 2B 6G1 $ \left(\begin{array}{rrrr} 2 & 1 & 1 & 2 \\ 2 & 2 & 1 & 1 \\ 2 & 2 & 2 & 2 \\ 2 & 1 & 0 & 0 \end{array}\right) $
$\Sp(4,3)$ 8A $8$ $6480$ $C_8$ 4C 8A 8A $ \left(\begin{array}{rrrr} 0 & 0 & 0 & 1 \\ 0 & 2 & 2 & 0 \\ 0 & 2 & 1 & 2 \\ 2 & 1 & 1 & 0 \end{array}\right) $
$\Sp(4,3)$ 9A1 $9$ $2880$ $C_{18}$ 9A-1 3A-1 9A-1 $ \left(\begin{array}{rrrr} 2 & 1 & 0 & 2 \\ 1 & 1 & 1 & 2 \\ 1 & 0 & 1 & 2 \\ 1 & 1 & 0 & 0 \end{array}\right) $
$\Sp(4,3)$ 9A-1 $9$ $2880$ $C_{18}$ 9A1 3A1 9A1 $ \left(\begin{array}{rrrr} 0 & 2 & 1 & 1 \\ 0 & 1 & 2 & 0 \\ 2 & 0 & 1 & 1 \\ 2 & 2 & 1 & 2 \end{array}\right) $
$\Sp(4,3)$ 10A $10$ $5184$ $C_{10}$ 5A 10A 2A $ \left(\begin{array}{rrrr} 0 & 0 & 1 & 2 \\ 0 & 0 & 2 & 2 \\ 2 & 2 & 2 & 0 \\ 2 & 1 & 2 & 2 \end{array}\right) $
$\Sp(4,3)$ 12A1 $12$ $2160$ $C_2\times C_{12}$ 6C1 4A 12A-1 $ \left(\begin{array}{rrrr} 1 & 2 & 0 & 0 \\ 1 & 1 & 1 & 1 \\ 2 & 2 & 1 & 1 \\ 1 & 2 & 1 & 2 \end{array}\right) $
$\Sp(4,3)$ 12A-1 $12$ $2160$ $C_2\times C_{12}$ 6C-1 4A 12A1 $ \left(\begin{array}{rrrr} 2 & 1 & 2 & 0 \\ 1 & 1 & 2 & 0 \\ 1 & 1 & 1 & 2 \\ 2 & 1 & 1 & 1 \end{array}\right) $
$\Sp(4,3)$ 12B1 $12$ $2160$ $C_2\times C_{12}$ 6C1 4B 12B-1 $ \left(\begin{array}{rrrr} 1 & 2 & 2 & 0 \\ 2 & 1 & 0 & 2 \\ 2 & 2 & 1 & 2 \\ 2 & 2 & 2 & 1 \end{array}\right) $
$\Sp(4,3)$ 12B-1 $12$ $2160$ $C_2\times C_{12}$ 6C-1 4B 12B1 $ \left(\begin{array}{rrrr} 1 & 2 & 1 & 0 \\ 2 & 1 & 0 & 1 \\ 1 & 1 & 1 & 2 \\ 1 & 1 & 2 & 1 \end{array}\right) $
$\Sp(4,3)$ 12C $12$ $4320$ $C_{12}$ 6B 4C 12C $ \left(\begin{array}{rrrr} 1 & 1 & 1 & 1 \\ 1 & 2 & 1 & 2 \\ 2 & 0 & 0 & 2 \\ 0 & 1 & 2 & 0 \end{array}\right) $
$\Sp(4,3)$ 18A1 $18$ $2880$ $C_{18}$ 9A1 6A1 18A-1 $ \left(\begin{array}{rrrr} 1 & 1 & 2 & 1 \\ 0 & 2 & 1 & 0 \\ 1 & 0 & 2 & 2 \\ 2 & 1 & 2 & 0 \end{array}\right) $
$\Sp(4,3)$ 18A-1 $18$ $2880$ $C_{18}$ 9A-1 6A-1 18A1 $ \left(\begin{array}{rrrr} 0 & 2 & 0 & 2 \\ 2 & 2 & 2 & 1 \\ 2 & 0 & 2 & 1 \\ 1 & 2 & 0 & 1 \end{array}\right) $
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