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Elements of the group are displayed as matrices in $\GL_{2}(\Z/{78}\Z)$.

Group Label Order Size Centralizer Powers Representative
2P 3P
$C_{12}.D_6^2$ 1A $1$ $1$ $C_{12}.D_6^2$ 1A 1A $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $
$C_{12}.D_6^2$ 2A $2$ $1$ $C_{12}.D_6^2$ 1A 2A $ \left(\begin{array}{rr} 53 & 0 \\ 0 & 53 \end{array}\right) $
$C_{12}.D_6^2$ 2B $2$ $1$ $C_{12}.D_6^2$ 1A 2B $ \left(\begin{array}{rr} 77 & 0 \\ 0 & 77 \end{array}\right) $
$C_{12}.D_6^2$ 2C $2$ $1$ $C_{12}.D_6^2$ 1A 2C $ \left(\begin{array}{rr} 25 & 0 \\ 0 & 25 \end{array}\right) $
$C_{12}.D_6^2$ 2D $2$ $6$ $C_6^2.C_2^3$ 1A 2D $ \left(\begin{array}{rr} 25 & 33 \\ 0 & 1 \end{array}\right) $
$C_{12}.D_6^2$ 2E $2$ $6$ $C_6^2.C_2^3$ 1A 2E $ \left(\begin{array}{rr} 77 & 20 \\ 0 & 1 \end{array}\right) $
$C_{12}.D_6^2$ 2F $2$ $6$ $C_6^2.C_2^3$ 1A 2F $ \left(\begin{array}{rr} 38 & 33 \\ 39 & 14 \end{array}\right) $
$C_{12}.D_6^2$ 2G $2$ $6$ $C_6^2.C_2^3$ 1A 2G $ \left(\begin{array}{rr} 25 & 46 \\ 0 & 53 \end{array}\right) $
$C_{12}.D_6^2$ 2H $2$ $6$ $C_2.D_6^2$ 1A 2H $ \left(\begin{array}{rr} 61 & 18 \\ 36 & 43 \end{array}\right) $
$C_{12}.D_6^2$ 2I $2$ $6$ $C_2.D_6^2$ 1A 2I $ \left(\begin{array}{rr} 5 & 30 \\ 72 & 47 \end{array}\right) $
$C_{12}.D_6^2$ 2J $2$ $6$ $C_2.D_6^2$ 1A 2J $ \left(\begin{array}{rr} 35 & 18 \\ 36 & 17 \end{array}\right) $
$C_{12}.D_6^2$ 2K $2$ $6$ $C_2.D_6^2$ 1A 2K $ \left(\begin{array}{rr} 31 & 30 \\ 72 & 73 \end{array}\right) $
$C_{12}.D_6^2$ 2L $2$ $9$ $D_{12}:C_2^3$ 1A 2L $ \left(\begin{array}{rr} 53 & 65 \\ 0 & 1 \end{array}\right) $
$C_{12}.D_6^2$ 2M $2$ $9$ $D_{12}:C_2^3$ 1A 2M $ \left(\begin{array}{rr} 77 & 65 \\ 0 & 25 \end{array}\right) $
$C_{12}.D_6^2$ 2N $2$ $9$ $D_{12}:C_2^3$ 1A 2N $ \left(\begin{array}{rr} 40 & 13 \\ 39 & 14 \end{array}\right) $
$C_{12}.D_6^2$ 2O $2$ $9$ $D_{12}:C_2^3$ 1A 2O $ \left(\begin{array}{rr} 64 & 13 \\ 39 & 38 \end{array}\right) $
$C_{12}.D_6^2$ 2P $2$ $54$ $C_2^3\times C_4$ 1A 2P $ \left(\begin{array}{rr} 50 & 67 \\ 57 & 28 \end{array}\right) $
$C_{12}.D_6^2$ 2Q $2$ $54$ $C_2^3\times C_4$ 1A 2Q $ \left(\begin{array}{rr} 55 & 73 \\ 12 & 23 \end{array}\right) $
$C_{12}.D_6^2$ 2R $2$ $54$ $C_2^3\times C_4$ 1A 2R $ \left(\begin{array}{rr} 73 & 35 \\ 6 & 5 \end{array}\right) $
$C_{12}.D_6^2$ 2S $2$ $54$ $C_2^3\times C_4$ 1A 2S $ \left(\begin{array}{rr} 29 & 21 \\ 12 & 49 \end{array}\right) $
$C_{12}.D_6^2$ 3A $3$ $2$ $C_6.D_6^2$ 3A 1A $ \left(\begin{array}{rr} 40 & 39 \\ 39 & 1 \end{array}\right) $
$C_{12}.D_6^2$ 3B $3$ $2$ $C_6.D_6^2$ 3B 1A $ \left(\begin{array}{rr} 61 & 18 \\ 0 & 55 \end{array}\right) $
$C_{12}.D_6^2$ 3C $3$ $2$ $C_6.D_6^2$ 3C 1A $ \left(\begin{array}{rr} 1 & 52 \\ 0 & 1 \end{array}\right) $
$C_{12}.D_6^2$ 3D $3$ $4$ $C_{12}:C_6^2$ 3D 1A $ \left(\begin{array}{rr} 22 & 57 \\ 39 & 55 \end{array}\right) $
$C_{12}.D_6^2$ 3E $3$ $4$ $C_{12}:C_6^2$ 3E 1A $ \left(\begin{array}{rr} 40 & 13 \\ 39 & 1 \end{array}\right) $
$C_{12}.D_6^2$ 3F $3$ $4$ $C_{12}:C_6^2$ 3F 1A $ \left(\begin{array}{rr} 61 & 70 \\ 0 & 55 \end{array}\right) $
$C_{12}.D_6^2$ 3G $3$ $8$ $C_3\times C_6\times C_{12}$ 3G 1A $ \left(\begin{array}{rr} 22 & 31 \\ 39 & 55 \end{array}\right) $
$C_{12}.D_6^2$ 4A $4$ $2$ $C_6.D_6^2$ 2C 4A $ \left(\begin{array}{rr} 47 & 48 \\ 0 & 5 \end{array}\right) $
$C_{12}.D_6^2$ 4B $4$ $2$ $C_6.D_6^2$ 2C 4B $ \left(\begin{array}{rr} 73 & 48 \\ 0 & 31 \end{array}\right) $
$C_{12}.D_6^2$ 4C1 $4$ $3$ $C_4.D_6^2$ 2C 4C-1 $ \left(\begin{array}{rr} 5 & 39 \\ 0 & 5 \end{array}\right) $
$C_{12}.D_6^2$ 4C-1 $4$ $3$ $C_4.D_6^2$ 2C 4C1 $ \left(\begin{array}{rr} 47 & 39 \\ 0 & 47 \end{array}\right) $
$C_{12}.D_6^2$ 4D1 $4$ $3$ $C_4.D_6^2$ 2C 4D-1 $ \left(\begin{array}{rr} 31 & 52 \\ 0 & 5 \end{array}\right) $
$C_{12}.D_6^2$ 4D-1 $4$ $3$ $C_4.D_6^2$ 2C 4D1 $ \left(\begin{array}{rr} 73 & 52 \\ 0 & 47 \end{array}\right) $
$C_{12}.D_6^2$ 4E1 $4$ $3$ $C_4.D_6^2$ 2C 4E-1 $ \left(\begin{array}{rr} 70 & 39 \\ 39 & 70 \end{array}\right) $
$C_{12}.D_6^2$ 4E-1 $4$ $3$ $C_4.D_6^2$ 2C 4E1 $ \left(\begin{array}{rr} 34 & 39 \\ 39 & 34 \end{array}\right) $
$C_{12}.D_6^2$ 4F1 $4$ $3$ $C_4.D_6^2$ 2C 4F-1 $ \left(\begin{array}{rr} 47 & 26 \\ 0 & 73 \end{array}\right) $
$C_{12}.D_6^2$ 4F-1 $4$ $3$ $C_4.D_6^2$ 2C 4F1 $ \left(\begin{array}{rr} 5 & 26 \\ 0 & 31 \end{array}\right) $
$C_{12}.D_6^2$ 4G $4$ $18$ $C_2^3\times C_{12}$ 2C 4G $ \left(\begin{array}{rr} 73 & 61 \\ 0 & 5 \end{array}\right) $
$C_{12}.D_6^2$ 4H $4$ $18$ $C_2^3\times C_{12}$ 2C 4H $ \left(\begin{array}{rr} 8 & 35 \\ 39 & 70 \end{array}\right) $
$C_{12}.D_6^2$ 4I $4$ $18$ $C_{12}:C_2^3$ 2C 4I $ \left(\begin{array}{rr} 43 & 3 \\ 42 & 61 \end{array}\right) $
$C_{12}.D_6^2$ 4J $4$ $18$ $C_{12}:C_2^3$ 2C 4J $ \left(\begin{array}{rr} 47 & 39 \\ 6 & 5 \end{array}\right) $
$C_{12}.D_6^2$ 4K $4$ $18$ $C_{12}:C_2^3$ 2C 4K $ \left(\begin{array}{rr} 56 & 3 \\ 3 & 74 \end{array}\right) $
$C_{12}.D_6^2$ 4L $4$ $18$ $C_{12}:C_2^3$ 2C 4L $ \left(\begin{array}{rr} 17 & 16 \\ 42 & 61 \end{array}\right) $
$C_{12}.D_6^2$ 4M $4$ $18$ $C_{12}:C_2^3$ 2C 4M $ \left(\begin{array}{rr} 43 & 68 \\ 42 & 35 \end{array}\right) $
$C_{12}.D_6^2$ 4N $4$ $18$ $C_{12}:C_2^3$ 2C 4N $ \left(\begin{array}{rr} 34 & 39 \\ 45 & 70 \end{array}\right) $
$C_{12}.D_6^2$ 4O $4$ $18$ $C_{12}:C_2^3$ 2C 4O $ \left(\begin{array}{rr} 73 & 26 \\ 6 & 5 \end{array}\right) $
$C_{12}.D_6^2$ 4P $4$ $18$ $C_{12}:C_2^3$ 2C 4P $ \left(\begin{array}{rr} 47 & 52 \\ 6 & 31 \end{array}\right) $
$C_{12}.D_6^2$ 6A $6$ $2$ $C_6.D_6^2$ 3A 2A $ \left(\begin{array}{rr} 53 & 39 \\ 39 & 14 \end{array}\right) $
$C_{12}.D_6^2$ 6B $6$ $2$ $C_6.D_6^2$ 3A 2B $ \left(\begin{array}{rr} 77 & 39 \\ 39 & 38 \end{array}\right) $
$C_{12}.D_6^2$ 6C $6$ $2$ $C_6.D_6^2$ 3B 2A $ \left(\begin{array}{rr} 29 & 60 \\ 0 & 35 \end{array}\right) $
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