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Results (34 matches)

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Elements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SOMinus(6,3)$.

Group Label Order Size Centralizer Powers Representative
2P 3P 5P 7P
$\PSOMinus(6,3)$ 1A $1$ $1$ $\PSOMinus(6,3)$ 1A 1A 1A 1A $ \left[ \left(\begin{array}{rrrrrr} 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 2A $2$ $540$ $C_2\times \SU(3,3)$ 1A 2A 2A 2A $ \left[ \left(\begin{array}{rrrrrr} 1 & 2 & 0 & 1 & 1 & 0 \\ 1 & 0 & 0 & 2 & 0 & 2 \\ 2 & 2 & 2 & 2 & 2 & 1 \\ 1 & 1 & 2 & 1 & 2 & 1 \\ 1 & 0 & 1 & 0 & 0 & 1 \\ 0 & 2 & 1 & 0 & 2 & 2 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 2B $2$ $2835$ $C_2^3:A_4.D_6.C_2$ 1A 2B 2B 2B $ \left[ \left(\begin{array}{rrrrrr} 0 & 2 & 0 & 2 & 1 & 1 \\ 1 & 0 & 1 & 0 & 2 & 1 \\ 2 & 2 & 1 & 2 & 1 & 1 \\ 1 & 2 & 1 & 1 & 2 & 1 \\ 1 & 1 & 0 & 1 & 0 & 2 \\ 2 & 1 & 2 & 0 & 1 & 0 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 2C $2$ $4536$ $C_2\times S_6$ 1A 2C 2C 2C $ \left[ \left(\begin{array}{rrrrrr} 0 & 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 0 & 1 \\ 0 & 0 & 2 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 \\ 1 & 0 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 & 0 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 3A $3$ $560$ $C_3^3:C_3^2.Q_8.C_6$ 3A 1A 3A 3A $ \left[ \left(\begin{array}{rrrrrr} 0 & 1 & 2 & 2 & 1 & 0 \\ 1 & 2 & 0 & 2 & 0 & 2 \\ 2 & 2 & 0 & 1 & 2 & 0 \\ 1 & 2 & 1 & 1 & 2 & 1 \\ 1 & 0 & 0 & 2 & 2 & 2 \\ 0 & 2 & 1 & 0 & 2 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 3B $3$ $3360$ $C_3^4:S_4$ 3B 1A 3B 3B $ \left[ \left(\begin{array}{rrrrrr} 0 & 2 & 0 & 1 & 1 & 0 \\ 2 & 0 & 2 & 2 & 2 & 2 \\ 0 & 0 & 2 & 2 & 2 & 1 \\ 2 & 2 & 1 & 1 & 0 & 1 \\ 2 & 2 & 1 & 0 & 1 & 1 \\ 2 & 2 & 1 & 0 & 0 & 2 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 3C $3$ $3360$ $C_3^4:S_4$ 3C 1A 3C 3C $ \left[ \left(\begin{array}{rrrrrr} 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 2 & 1 & 0 \\ 2 & 1 & 0 & 2 & 1 & 0 \\ 2 & 1 & 0 & 0 & 1 & 0 \\ 2 & 1 & 1 & 2 & 2 & 0 \\ 1 & 2 & 2 & 1 & 2 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 3D $3$ $40320$ $C_3^3:S_3$ 3D 1A 3D 3D $ \left[ \left(\begin{array}{rrrrrr} 0 & 0 & 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 2 & 1 & 1 & 0 & 2 \\ 0 & 0 & 0 & 2 & 0 & 2 \\ 0 & 2 & 2 & 1 & 1 & 0 \\ 2 & 0 & 0 & 2 & 0 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 4A $4$ $5670$ $Q_8.A_4.D_6$ 2B 4A 4A 4A $ \left[ \left(\begin{array}{rrrrrr} 0 & 1 & 0 & 2 & 2 & 2 \\ 1 & 1 & 1 & 0 & 1 & 0 \\ 2 & 0 & 0 & 2 & 0 & 2 \\ 2 & 1 & 2 & 2 & 2 & 0 \\ 2 & 1 & 2 & 0 & 1 & 0 \\ 2 & 0 & 1 & 2 & 0 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 4B $4$ $34020$ $C_2\times \Unitary(2,3)$ 2B 4B 4B 4B $ \left[ \left(\begin{array}{rrrrrr} 1 & 2 & 1 & 0 & 1 & 2 \\ 1 & 0 & 0 & 2 & 2 & 2 \\ 0 & 2 & 0 & 1 & 2 & 1 \\ 0 & 2 & 1 & 0 & 1 & 1 \\ 1 & 1 & 2 & 2 & 2 & 2 \\ 2 & 1 & 2 & 2 & 0 & 2 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 4C $4$ $51030$ $(C_2\times C_4^2):C_4$ 2B 4C 4C 4C $ \left[ \left(\begin{array}{rrrrrr} 0 & 2 & 2 & 1 & 1 & 1 \\ 2 & 1 & 0 & 1 & 0 & 1 \\ 2 & 1 & 2 & 1 & 2 & 1 \\ 0 & 0 & 0 & 2 & 0 & 1 \\ 1 & 0 & 0 & 2 & 1 & 2 \\ 2 & 1 & 0 & 1 & 2 & 0 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 4D $4$ $204120$ $C_4^2:C_2$ 2B 4D 4D 4D $ \left[ \left(\begin{array}{rrrrrr} 2 & 0 & 0 & 2 & 0 & 1 \\ 0 & 1 & 0 & 1 & 2 & 1 \\ 2 & 1 & 1 & 1 & 1 & 1 \\ 2 & 1 & 1 & 2 & 2 & 2 \\ 2 & 2 & 1 & 0 & 2 & 0 \\ 1 & 0 & 1 & 0 & 0 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 5A $5$ $653184$ $C_{10}$ 5A 5A 1A 5A $ \left[ \left(\begin{array}{rrrrrr} 1 & 2 & 0 & 1 & 0 & 2 \\ 1 & 1 & 0 & 1 & 0 & 2 \\ 0 & 1 & 1 & 1 & 0 & 2 \\ 0 & 1 & 1 & 2 & 0 & 0 \\ 2 & 2 & 2 & 0 & 2 & 0 \\ 1 & 0 & 1 & 0 & 1 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 6A $6$ $30240$ $C_2\times \He_3:C_4$ 3A 2A 6A 6A $ \left[ \left(\begin{array}{rrrrrr} 1 & 1 & 1 & 1 & 2 & 2 \\ 1 & 2 & 0 & 2 & 1 & 0 \\ 0 & 2 & 2 & 0 & 0 & 2 \\ 0 & 0 & 1 & 2 & 2 & 2 \\ 1 & 0 & 2 & 1 & 1 & 2 \\ 2 & 2 & 2 & 1 & 0 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 6B $6$ $45360$ $\SL(2,3):C_6$ 3A 2B 6B 6B $ \left[ \left(\begin{array}{rrrrrr} 1 & 0 & 2 & 2 & 1 & 1 \\ 0 & 0 & 0 & 0 & 2 & 0 \\ 2 & 0 & 2 & 2 & 2 & 0 \\ 1 & 0 & 2 & 1 & 2 & 0 \\ 1 & 2 & 0 & 2 & 0 & 2 \\ 1 & 0 & 0 & 0 & 2 & 0 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 6C $6$ $90720$ $C_3\times D_{12}$ 3B 2B 6C 6C $ \left[ \left(\begin{array}{rrrrrr} 1 & 2 & 0 & 1 & 1 & 0 \\ 1 & 2 & 0 & 1 & 0 & 2 \\ 2 & 1 & 1 & 0 & 1 & 1 \\ 1 & 2 & 0 & 0 & 0 & 1 \\ 2 & 0 & 0 & 1 & 0 & 1 \\ 2 & 2 & 1 & 1 & 2 & 0 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 6D $6$ $90720$ $C_3\times D_{12}$ 3C 2B 6D 6D $ \left[ \left(\begin{array}{rrrrrr} 2 & 2 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 2 & 2 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 2 & 1 & 2 \\ 1 & 2 & 2 & 0 & 1 & 2 \\ 1 & 1 & 1 & 2 & 0 & 2 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 6E $6$ $181440$ $C_6\times S_3$ 3C 2C 6E 6E $ \left[ \left(\begin{array}{rrrrrr} 0 & 1 & 1 & 1 & 1 & 1 \\ 2 & 0 & 1 & 2 & 2 & 1 \\ 2 & 1 & 1 & 2 & 1 & 0 \\ 1 & 1 & 2 & 0 & 1 & 1 \\ 2 & 2 & 1 & 2 & 0 & 1 \\ 0 & 2 & 1 & 0 & 2 & 0 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 6F $6$ $181440$ $C_6\times S_3$ 3B 2C 6F 6F $ \left[ \left(\begin{array}{rrrrrr} 1 & 2 & 2 & 0 & 0 & 1 \\ 1 & 1 & 1 & 0 & 2 & 2 \\ 0 & 1 & 0 & 0 & 2 & 2 \\ 0 & 2 & 2 & 2 & 1 & 1 \\ 1 & 1 & 0 & 0 & 2 & 1 \\ 2 & 0 & 1 & 0 & 2 & 2 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 6G $6$ $362880$ $C_3\times C_6$ 3D 2A 6G 6G $ \left[ \left(\begin{array}{rrrrrr} 2 & 1 & 1 & 2 & 1 & 2 \\ 1 & 0 & 0 & 2 & 0 & 2 \\ 2 & 2 & 1 & 0 & 2 & 1 \\ 0 & 1 & 1 & 0 & 2 & 2 \\ 1 & 1 & 1 & 2 & 0 & 2 \\ 2 & 1 & 0 & 2 & 2 & 0 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 7A1 $7$ $466560$ $C_{14}$ 7A1 7A-1 7A-1 1A $ \left[ \left(\begin{array}{rrrrrr} 2 & 0 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 2 & 0 & 2 \\ 1 & 0 & 1 & 0 & 2 & 0 \\ 2 & 2 & 2 & 0 & 2 & 2 \\ 1 & 2 & 1 & 1 & 1 & 2 \\ 1 & 0 & 2 & 1 & 2 & 2 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 7A-1 $7$ $466560$ $C_{14}$ 7A-1 7A1 7A1 1A $ \left[ \left(\begin{array}{rrrrrr} 1 & 1 & 1 & 1 & 1 & 0 \\ 1 & 2 & 0 & 2 & 0 & 2 \\ 2 & 0 & 2 & 0 & 0 & 0 \\ 0 & 2 & 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 0 \\ 2 & 2 & 2 & 0 & 1 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 8A $8$ $408240$ $C_2\times C_8$ 4B 8A 8A 8A $ \left[ \left(\begin{array}{rrrrrr} 1 & 1 & 1 & 0 & 1 & 0 \\ 2 & 1 & 2 & 2 & 0 & 2 \\ 2 & 2 & 0 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 & 0 & 2 \\ 2 & 1 & 1 & 1 & 0 & 2 \\ 0 & 1 & 0 & 0 & 0 & 0 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 8B $8$ $408240$ $C_2\times C_8$ 4B 8B 8B 8B $ \left[ \left(\begin{array}{rrrrrr} 1 & 1 & 1 & 1 & 0 & 1 \\ 1 & 2 & 1 & 0 & 2 & 0 \\ 1 & 1 & 0 & 1 & 1 & 0 \\ 2 & 2 & 2 & 1 & 1 & 2 \\ 1 & 1 & 1 & 1 & 1 & 0 \\ 0 & 2 & 1 & 1 & 2 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 9A $9$ $241920$ $C_3\times C_9$ 9A 3A 9A 9A $ \left[ \left(\begin{array}{rrrrrr} 0 & 1 & 0 & 0 & 0 & 1 \\ 1 & 1 & 0 & 1 & 2 & 0 \\ 2 & 0 & 2 & 1 & 1 & 2 \\ 2 & 2 & 2 & 0 & 1 & 0 \\ 2 & 1 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 2 & 0 & 2 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 9B $9$ $241920$ $C_3\times C_9$ 9B 3A 9B 9B $ \left[ \left(\begin{array}{rrrrrr} 2 & 2 & 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 2 & 1 & 0 & 0 \\ 2 & 0 & 1 & 0 & 0 & 2 \\ 2 & 2 & 2 & 1 & 2 & 2 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 10A $10$ $653184$ $C_{10}$ 5A 10A 2C 10A $ \left[ \left(\begin{array}{rrrrrr} 2 & 0 & 1 & 1 & 0 & 2 \\ 1 & 1 & 0 & 0 & 1 & 2 \\ 1 & 0 & 1 & 2 & 0 & 1 \\ 1 & 1 & 0 & 2 & 2 & 1 \\ 0 & 1 & 2 & 2 & 1 & 2 \\ 1 & 0 & 0 & 1 & 2 & 2 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 12A1 $12$ $45360$ $\SL(2,3):C_6$ 6B 4A 12A1 12A-1 $ \left[ \left(\begin{array}{rrrrrr} 1 & 2 & 0 & 2 & 2 & 1 \\ 2 & 2 & 1 & 2 & 2 & 2 \\ 2 & 2 & 0 & 1 & 0 & 2 \\ 2 & 0 & 1 & 1 & 2 & 1 \\ 2 & 2 & 2 & 0 & 2 & 0 \\ 1 & 2 & 2 & 2 & 0 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 12A-1 $12$ $45360$ $\SL(2,3):C_6$ 6B 4A 12A-1 12A1 $ \left[ \left(\begin{array}{rrrrrr} 2 & 0 & 1 & 0 & 1 & 2 \\ 0 & 1 & 1 & 1 & 1 & 1 \\ 0 & 1 & 2 & 1 & 1 & 2 \\ 1 & 2 & 1 & 0 & 0 & 2 \\ 1 & 1 & 2 & 1 & 1 & 1 \\ 2 & 1 & 0 & 2 & 1 & 2 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 12B $12$ $181440$ $C_3\times C_{12}$ 6C 4A 12B 12B $ \left[ \left(\begin{array}{rrrrrr} 0 & 1 & 0 & 2 & 2 & 0 \\ 1 & 2 & 2 & 1 & 2 & 1 \\ 1 & 2 & 0 & 1 & 1 & 2 \\ 0 & 2 & 0 & 2 & 0 & 2 \\ 2 & 2 & 2 & 0 & 0 & 2 \\ 0 & 1 & 1 & 0 & 1 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 12C $12$ $181440$ $C_3\times C_{12}$ 6D 4A 12C 12C $ \left[ \left(\begin{array}{rrrrrr} 1 & 1 & 2 & 1 & 1 & 1 \\ 0 & 2 & 2 & 2 & 2 & 0 \\ 0 & 0 & 1 & 0 & 0 & 2 \\ 2 & 1 & 0 & 2 & 0 & 0 \\ 1 & 0 & 0 & 2 & 0 & 2 \\ 1 & 1 & 0 & 2 & 0 & 2 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 12D $12$ $272160$ $C_2\times C_{12}$ 6B 4B 12D 12D $ \left[ \left(\begin{array}{rrrrrr} 2 & 0 & 0 & 0 & 2 & 0 \\ 0 & 1 & 0 & 2 & 2 & 2 \\ 2 & 0 & 1 & 1 & 0 & 0 \\ 1 & 2 & 1 & 0 & 2 & 1 \\ 2 & 1 & 2 & 2 & 0 & 2 \\ 2 & 2 & 2 & 0 & 2 & 0 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 14A1 $14$ $466560$ $C_{14}$ 7A1 14A-1 14A-1 2A $ \left[ \left(\begin{array}{rrrrrr} 1 & 0 & 1 & 2 & 2 & 2 \\ 0 & 2 & 2 & 2 & 2 & 1 \\ 2 & 0 & 0 & 1 & 1 & 2 \\ 1 & 1 & 2 & 1 & 2 & 1 \\ 0 & 2 & 0 & 0 & 0 & 2 \\ 1 & 0 & 2 & 2 & 2 & 1 \end{array}\right) \right] $
$\PSOMinus(6,3)$ 14A-1 $14$ $466560$ $C_{14}$ 7A-1 14A1 14A1 2A $ \left[ \left(\begin{array}{rrrrrr} 1 & 2 & 2 & 0 & 1 & 2 \\ 2 & 0 & 1 & 0 & 2 & 2 \\ 0 & 0 & 2 & 0 & 0 & 2 \\ 2 & 0 & 1 & 2 & 2 & 0 \\ 0 & 2 & 1 & 1 & 2 & 0 \\ 1 & 0 & 2 & 0 & 0 & 1 \end{array}\right) \right] $
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