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Elements of the group are displayed as matrices in $\GL_{2}(\Z/{16}\Z)$.

Group Label Order Size Centralizer Powers Representative
2P
$\OD_{16}:C_2^2$ 1A $1$ $1$ $\OD_{16}:C_2^2$ 1A $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $
$\OD_{16}:C_2^2$ 2A $2$ $1$ $\OD_{16}:C_2^2$ 1A $ \left(\begin{array}{rr} 15 & 0 \\ 8 & 15 \end{array}\right) $
$\OD_{16}:C_2^2$ 2B $2$ $1$ $\OD_{16}:C_2^2$ 1A $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 7 \end{array}\right) $
$\OD_{16}:C_2^2$ 2C $2$ $1$ $\OD_{16}:C_2^2$ 1A $ \left(\begin{array}{rr} 9 & 0 \\ 8 & 9 \end{array}\right) $
$\OD_{16}:C_2^2$ 2D $2$ $2$ $C_2^2\times D_4$ 1A $ \left(\begin{array}{rr} 7 & 8 \\ 0 & 7 \end{array}\right) $
$\OD_{16}:C_2^2$ 2E $2$ $2$ $C_2^2\times D_4$ 1A $ \left(\begin{array}{rr} 9 & 8 \\ 8 & 9 \end{array}\right) $
$\OD_{16}:C_2^2$ 2F $2$ $4$ $C_2^4$ 1A $ \left(\begin{array}{rr} 7 & 2 \\ 0 & 1 \end{array}\right) $
$\OD_{16}:C_2^2$ 2G $2$ $4$ $C_2^4$ 1A $ \left(\begin{array}{rr} 5 & 14 \\ 4 & 3 \end{array}\right) $
$\OD_{16}:C_2^2$ 2H $2$ $4$ $C_2^4$ 1A $ \left(\begin{array}{rr} 9 & 14 \\ 8 & 15 \end{array}\right) $
$\OD_{16}:C_2^2$ 2I $2$ $4$ $C_2^4$ 1A $ \left(\begin{array}{rr} 11 & 2 \\ 4 & 13 \end{array}\right) $
$\OD_{16}:C_2^2$ 4A $4$ $2$ $C_2\times \OD_{16}$ 2C $ \left(\begin{array}{rr} 5 & 8 \\ 4 & 13 \end{array}\right) $
$\OD_{16}:C_2^2$ 4B $4$ $2$ $C_2\times \OD_{16}$ 2C $ \left(\begin{array}{rr} 3 & 0 \\ 12 & 11 \end{array}\right) $
$\OD_{16}:C_2^2$ 4C $4$ $2$ $C_2\times \OD_{16}$ 2C $ \left(\begin{array}{rr} 11 & 8 \\ 4 & 3 \end{array}\right) $
$\OD_{16}:C_2^2$ 4D $4$ $2$ $C_2\times \OD_{16}$ 2C $ \left(\begin{array}{rr} 13 & 0 \\ 12 & 5 \end{array}\right) $
$\OD_{16}:C_2^2$ 8A1 $8$ $4$ $C_2\times C_8$ 4C $ \left(\begin{array}{rr} 13 & 10 \\ 5 & 7 \end{array}\right) $
$\OD_{16}:C_2^2$ 8A-1 $8$ $4$ $C_2\times C_8$ 4C $ \left(\begin{array}{rr} 7 & 6 \\ 3 & 13 \end{array}\right) $
$\OD_{16}:C_2^2$ 8B1 $8$ $4$ $C_2\times C_8$ 4D $ \left(\begin{array}{rr} 5 & 4 \\ 5 & 7 \end{array}\right) $
$\OD_{16}:C_2^2$ 8B-1 $8$ $4$ $C_2\times C_8$ 4D $ \left(\begin{array}{rr} 7 & 4 \\ 3 & 13 \end{array}\right) $
$\OD_{16}:C_2^2$ 8C1 $8$ $4$ $C_2\times C_8$ 4C $ \left(\begin{array}{rr} 3 & 6 \\ 3 & 9 \end{array}\right) $
$\OD_{16}:C_2^2$ 8C-1 $8$ $4$ $C_2\times C_8$ 4C $ \left(\begin{array}{rr} 9 & 10 \\ 5 & 3 \end{array}\right) $
$\OD_{16}:C_2^2$ 8D1 $8$ $4$ $C_2\times C_8$ 4D $ \left(\begin{array}{rr} 11 & 12 \\ 3 & 9 \end{array}\right) $
$\OD_{16}:C_2^2$ 8D-1 $8$ $4$ $C_2\times C_8$ 4D $ \left(\begin{array}{rr} 9 & 12 \\ 5 & 3 \end{array}\right) $
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