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Elements of the group are displayed as matrices in $\GL_{2}(\Z/{40}\Z)$.

Group Label Order Size Centralizer Powers Representative
2P 5P
$D_{10}.C_2^6$ 1A $1$ $1$ $D_{10}.C_2^6$ 1A 1A $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $
$D_{10}.C_2^6$ 2A $2$ $1$ $D_{10}.C_2^6$ 1A 2A $ \left(\begin{array}{rr} 1 & 20 \\ 0 & 1 \end{array}\right) $
$D_{10}.C_2^6$ 2B $2$ $1$ $D_{10}.C_2^6$ 1A 2B $ \left(\begin{array}{rr} 29 & 20 \\ 20 & 29 \end{array}\right) $
$D_{10}.C_2^6$ 2C $2$ $1$ $D_{10}.C_2^6$ 1A 2C $ \left(\begin{array}{rr} 21 & 0 \\ 0 & 21 \end{array}\right) $
$D_{10}.C_2^6$ 2D $2$ $1$ $D_{10}.C_2^6$ 1A 2D $ \left(\begin{array}{rr} 19 & 0 \\ 20 & 19 \end{array}\right) $
$D_{10}.C_2^6$ 2E $2$ $1$ $D_{10}.C_2^6$ 1A 2E $ \left(\begin{array}{rr} 9 & 20 \\ 20 & 9 \end{array}\right) $
$D_{10}.C_2^6$ 2F $2$ $1$ $D_{10}.C_2^6$ 1A 2F $ \left(\begin{array}{rr} 31 & 20 \\ 0 & 31 \end{array}\right) $
$D_{10}.C_2^6$ 2G $2$ $1$ $D_{10}.C_2^6$ 1A 2G $ \left(\begin{array}{rr} 39 & 0 \\ 20 & 39 \end{array}\right) $
$D_{10}.C_2^6$ 2H $2$ $1$ $D_{10}.C_2^6$ 1A 2H $ \left(\begin{array}{rr} 29 & 0 \\ 20 & 29 \end{array}\right) $
$D_{10}.C_2^6$ 2I $2$ $1$ $D_{10}.C_2^6$ 1A 2I $ \left(\begin{array}{rr} 21 & 20 \\ 0 & 21 \end{array}\right) $
$D_{10}.C_2^6$ 2J $2$ $1$ $D_{10}.C_2^6$ 1A 2J $ \left(\begin{array}{rr} 19 & 20 \\ 20 & 19 \end{array}\right) $
$D_{10}.C_2^6$ 2K $2$ $1$ $D_{10}.C_2^6$ 1A 2K $ \left(\begin{array}{rr} 11 & 20 \\ 0 & 11 \end{array}\right) $
$D_{10}.C_2^6$ 2L $2$ $1$ $D_{10}.C_2^6$ 1A 2L $ \left(\begin{array}{rr} 9 & 0 \\ 20 & 9 \end{array}\right) $
$D_{10}.C_2^6$ 2M $2$ $1$ $D_{10}.C_2^6$ 1A 2M $ \left(\begin{array}{rr} 31 & 0 \\ 0 & 31 \end{array}\right) $
$D_{10}.C_2^6$ 2N $2$ $1$ $D_{10}.C_2^6$ 1A 2N $ \left(\begin{array}{rr} 39 & 20 \\ 20 & 39 \end{array}\right) $
$D_{10}.C_2^6$ 2O $2$ $1$ $D_{10}.C_2^6$ 1A 2O $ \left(\begin{array}{rr} 11 & 0 \\ 0 & 11 \end{array}\right) $
$D_{10}.C_2^6$ 2P $2$ $2$ $F_5\times C_2^5$ 1A 2P $ \left(\begin{array}{rr} 31 & 20 \\ 0 & 1 \end{array}\right) $
$D_{10}.C_2^6$ 2Q $2$ $2$ $F_5\times C_2^5$ 1A 2Q $ \left(\begin{array}{rr} 19 & 0 \\ 20 & 29 \end{array}\right) $
$D_{10}.C_2^6$ 2R $2$ $2$ $F_5\times C_2^5$ 1A 2R $ \left(\begin{array}{rr} 11 & 20 \\ 0 & 21 \end{array}\right) $
$D_{10}.C_2^6$ 2S $2$ $2$ $F_5\times C_2^5$ 1A 2S $ \left(\begin{array}{rr} 29 & 20 \\ 20 & 19 \end{array}\right) $
$D_{10}.C_2^6$ 2T $2$ $2$ $F_5\times C_2^5$ 1A 2T $ \left(\begin{array}{rr} 19 & 10 \\ 0 & 9 \end{array}\right) $
$D_{10}.C_2^6$ 2U $2$ $2$ $F_5\times C_2^5$ 1A 2U $ \left(\begin{array}{rr} 39 & 0 \\ 20 & 9 \end{array}\right) $
$D_{10}.C_2^6$ 2V $2$ $2$ $F_5\times C_2^5$ 1A 2V $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 31 \end{array}\right) $
$D_{10}.C_2^6$ 2W $2$ $2$ $F_5\times C_2^5$ 1A 2W $ \left(\begin{array}{rr} 9 & 20 \\ 20 & 39 \end{array}\right) $
$D_{10}.C_2^6$ 2X $2$ $2$ $F_5\times C_2^5$ 1A 2X $ \left(\begin{array}{rr} 31 & 30 \\ 20 & 21 \end{array}\right) $
$D_{10}.C_2^6$ 2Y $2$ $2$ $F_5\times C_2^5$ 1A 2Y $ \left(\begin{array}{rr} 39 & 10 \\ 0 & 29 \end{array}\right) $
$D_{10}.C_2^6$ 2Z $2$ $2$ $F_5\times C_2^5$ 1A 2Z $ \left(\begin{array}{rr} 1 & 30 \\ 20 & 11 \end{array}\right) $
$D_{10}.C_2^6$ 2AA $2$ $2$ $F_5\times C_2^5$ 1A 2AA $ \left(\begin{array}{rr} 21 & 0 \\ 0 & 11 \end{array}\right) $
$D_{10}.C_2^6$ 2AB $2$ $2$ $F_5\times C_2^5$ 1A 2AB $ \left(\begin{array}{rr} 11 & 30 \\ 20 & 1 \end{array}\right) $
$D_{10}.C_2^6$ 2AC $2$ $2$ $F_5\times C_2^5$ 1A 2AC $ \left(\begin{array}{rr} 29 & 10 \\ 0 & 39 \end{array}\right) $
$D_{10}.C_2^6$ 2AD $2$ $2$ $F_5\times C_2^5$ 1A 2AD $ \left(\begin{array}{rr} 21 & 30 \\ 20 & 31 \end{array}\right) $
$D_{10}.C_2^6$ 2AE $2$ $2$ $F_5\times C_2^5$ 1A 2AE $ \left(\begin{array}{rr} 9 & 10 \\ 0 & 19 \end{array}\right) $
$D_{10}.C_2^6$ 2AF $2$ $5$ $C_4^2:C_2^4$ 1A 2AF $ \left(\begin{array}{rr} 29 & 20 \\ 20 & 21 \end{array}\right) $
$D_{10}.C_2^6$ 2AG $2$ $5$ $C_4^2:C_2^4$ 1A 2AG $ \left(\begin{array}{rr} 21 & 0 \\ 0 & 29 \end{array}\right) $
$D_{10}.C_2^6$ 2AH $2$ $5$ $C_4^2:C_2^4$ 1A 2AH $ \left(\begin{array}{rr} 19 & 0 \\ 20 & 11 \end{array}\right) $
$D_{10}.C_2^6$ 2AI $2$ $5$ $C_4^2:C_2^4$ 1A 2AI $ \left(\begin{array}{rr} 9 & 20 \\ 20 & 1 \end{array}\right) $
$D_{10}.C_2^6$ 2AJ $2$ $5$ $C_4^2:C_2^4$ 1A 2AJ $ \left(\begin{array}{rr} 31 & 20 \\ 0 & 39 \end{array}\right) $
$D_{10}.C_2^6$ 2AK $2$ $5$ $C_4^2:C_2^4$ 1A 2AK $ \left(\begin{array}{rr} 39 & 0 \\ 20 & 31 \end{array}\right) $
$D_{10}.C_2^6$ 2AL $2$ $5$ $C_4^2:C_2^4$ 1A 2AL $ \left(\begin{array}{rr} 29 & 0 \\ 20 & 21 \end{array}\right) $
$D_{10}.C_2^6$ 2AM $2$ $5$ $C_4^2:C_2^4$ 1A 2AM $ \left(\begin{array}{rr} 21 & 20 \\ 0 & 29 \end{array}\right) $
$D_{10}.C_2^6$ 2AN $2$ $5$ $C_4^2:C_2^4$ 1A 2AN $ \left(\begin{array}{rr} 19 & 20 \\ 20 & 11 \end{array}\right) $
$D_{10}.C_2^6$ 2AO $2$ $5$ $C_4^2:C_2^4$ 1A 2AO $ \left(\begin{array}{rr} 11 & 20 \\ 0 & 19 \end{array}\right) $
$D_{10}.C_2^6$ 2AP $2$ $5$ $C_4^2:C_2^4$ 1A 2AP $ \left(\begin{array}{rr} 9 & 0 \\ 20 & 1 \end{array}\right) $
$D_{10}.C_2^6$ 2AQ $2$ $5$ $C_4^2:C_2^4$ 1A 2AQ $ \left(\begin{array}{rr} 31 & 0 \\ 0 & 39 \end{array}\right) $
$D_{10}.C_2^6$ 2AR $2$ $5$ $C_4^2:C_2^4$ 1A 2AR $ \left(\begin{array}{rr} 39 & 20 \\ 20 & 31 \end{array}\right) $
$D_{10}.C_2^6$ 2AS $2$ $5$ $C_4^2:C_2^4$ 1A 2AS $ \left(\begin{array}{rr} 11 & 0 \\ 0 & 19 \end{array}\right) $
$D_{10}.C_2^6$ 2AT $2$ $5$ $C_4^2:C_2^4$ 1A 2AT $ \left(\begin{array}{rr} 1 & 24 \\ 0 & 9 \end{array}\right) $
$D_{10}.C_2^6$ 2AU $2$ $5$ $C_4^2:C_2^4$ 1A 2AU $ \left(\begin{array}{rr} 1 & 4 \\ 0 & 9 \end{array}\right) $
$D_{10}.C_2^6$ 2AV $2$ $10$ $C_2^5\times C_4$ 1A 2AV $ \left(\begin{array}{rr} 31 & 28 \\ 0 & 9 \end{array}\right) $
$D_{10}.C_2^6$ 2AW $2$ $10$ $C_2^5\times C_4$ 1A 2AW $ \left(\begin{array}{rr} 19 & 32 \\ 20 & 21 \end{array}\right) $
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