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Elements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SL(2,73)$.

Group Label Order Size Centralizer Powers Representative
2P 3P 37P 73P
$\PSL(2,73)$ 1A $1$ $1$ $\PSL(2,73)$ 1A 1A 1A 1A $ \left[ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) \right] $
$\PSL(2,73)$ 2A $2$ $2701$ $D_{36}$ 1A 2A 2A 2A $ \left[ \left(\begin{array}{rr} 67 & 27 \\ 50 & 6 \end{array}\right) \right] $
$\PSL(2,73)$ 3A $3$ $5402$ $C_{36}$ 3A 1A 3A 3A $ \left[ \left(\begin{array}{rr} 47 & 28 \\ 14 & 27 \end{array}\right) \right] $
$\PSL(2,73)$ 4A $4$ $5402$ $C_{36}$ 2A 4A 4A 4A $ \left[ \left(\begin{array}{rr} 34 & 67 \\ 70 & 7 \end{array}\right) \right] $
$\PSL(2,73)$ 6A $6$ $5402$ $C_{36}$ 3A 2A 6A 6A $ \left[ \left(\begin{array}{rr} 29 & 23 \\ 48 & 23 \end{array}\right) \right] $
$\PSL(2,73)$ 9A1 $9$ $5402$ $C_{36}$ 9A2 3A 9A1 9A1 $ \left[ \left(\begin{array}{rr} 5 & 54 \\ 27 & 29 \end{array}\right) \right] $
$\PSL(2,73)$ 9A2 $9$ $5402$ $C_{36}$ 9A4 3A 9A2 9A2 $ \left[ \left(\begin{array}{rr} 23 & 11 \\ 42 & 36 \end{array}\right) \right] $
$\PSL(2,73)$ 9A4 $9$ $5402$ $C_{36}$ 9A1 3A 9A4 9A4 $ \left[ \left(\begin{array}{rr} 31 & 8 \\ 4 & 67 \end{array}\right) \right] $
$\PSL(2,73)$ 12A1 $12$ $5402$ $C_{36}$ 6A 4A 12A1 12A1 $ \left[ \left(\begin{array}{rr} 48 & 66 \\ 33 & 53 \end{array}\right) \right] $
$\PSL(2,73)$ 12A5 $12$ $5402$ $C_{36}$ 6A 4A 12A5 12A5 $ \left[ \left(\begin{array}{rr} 41 & 60 \\ 30 & 19 \end{array}\right) \right] $
$\PSL(2,73)$ 18A1 $18$ $5402$ $C_{36}$ 9A1 6A 18A1 18A1 $ \left[ \left(\begin{array}{rr} 72 & 64 \\ 32 & 68 \end{array}\right) \right] $
$\PSL(2,73)$ 18A5 $18$ $5402$ $C_{36}$ 9A4 6A 18A5 18A5 $ \left[ \left(\begin{array}{rr} 37 & 30 \\ 15 & 26 \end{array}\right) \right] $
$\PSL(2,73)$ 18A7 $18$ $5402$ $C_{36}$ 9A2 6A 18A7 18A7 $ \left[ \left(\begin{array}{rr} 46 & 21 \\ 47 & 31 \end{array}\right) \right] $
$\PSL(2,73)$ 36A1 $36$ $5402$ $C_{36}$ 18A1 12A1 36A1 36A1 $ \left[ \left(\begin{array}{rr} 16 & 72 \\ 36 & 48 \end{array}\right) \right] $
$\PSL(2,73)$ 36A5 $36$ $5402$ $C_{36}$ 18A5 12A5 36A5 36A5 $ \left[ \left(\begin{array}{rr} 20 & 41 \\ 57 & 22 \end{array}\right) \right] $
$\PSL(2,73)$ 36A7 $36$ $5402$ $C_{36}$ 18A7 12A5 36A7 36A7 $ \left[ \left(\begin{array}{rr} 51 & 53 \\ 63 & 34 \end{array}\right) \right] $
$\PSL(2,73)$ 36A11 $36$ $5402$ $C_{36}$ 18A7 12A1 36A11 36A11 $ \left[ \left(\begin{array}{rr} 7 & 57 \\ 65 & 8 \end{array}\right) \right] $
$\PSL(2,73)$ 36A13 $36$ $5402$ $C_{36}$ 18A5 12A1 36A13 36A13 $ \left[ \left(\begin{array}{rr} 65 & 17 \\ 45 & 32 \end{array}\right) \right] $
$\PSL(2,73)$ 36A17 $36$ $5402$ $C_{36}$ 18A1 12A5 36A17 36A17 $ \left[ \left(\begin{array}{rr} 54 & 61 \\ 67 & 0 \end{array}\right) \right] $
$\PSL(2,73)$ 37A1 $37$ $5256$ $C_{37}$ 37A2 37A3 1A 37A1 $ \left[ \left(\begin{array}{rr} 40 & 69 \\ 25 & 3 \end{array}\right) \right] $
$\PSL(2,73)$ 37A2 $37$ $5256$ $C_{37}$ 37A4 37A6 1A 37A2 $ \left[ \left(\begin{array}{rr} 40 & 47 \\ 53 & 55 \end{array}\right) \right] $
$\PSL(2,73)$ 37A3 $37$ $5256$ $C_{37}$ 37A6 37A9 1A 37A3 $ \left[ \left(\begin{array}{rr} 1 & 54 \\ 64 & 26 \end{array}\right) \right] $
$\PSL(2,73)$ 37A4 $37$ $5256$ $C_{37}$ 37A8 37A12 1A 37A4 $ \left[ \left(\begin{array}{rr} 3 & 12 \\ 71 & 41 \end{array}\right) \right] $
$\PSL(2,73)$ 37A5 $37$ $5256$ $C_{37}$ 37A10 37A15 1A 37A5 $ \left[ \left(\begin{array}{rr} 18 & 49 \\ 4 & 15 \end{array}\right) \right] $
$\PSL(2,73)$ 37A6 $37$ $5256$ $C_{37}$ 37A12 37A18 1A 37A6 $ \left[ \left(\begin{array}{rr} 26 & 71 \\ 49 & 44 \end{array}\right) \right] $
$\PSL(2,73)$ 37A7 $37$ $5256$ $C_{37}$ 37A14 37A16 1A 37A7 $ \left[ \left(\begin{array}{rr} 32 & 37 \\ 6 & 64 \end{array}\right) \right] $
$\PSL(2,73)$ 37A8 $37$ $5256$ $C_{37}$ 37A16 37A13 1A 37A8 $ \left[ \left(\begin{array}{rr} 15 & 56 \\ 15 & 22 \end{array}\right) \right] $
$\PSL(2,73)$ 37A9 $37$ $5256$ $C_{37}$ 37A18 37A10 1A 37A9 $ \left[ \left(\begin{array}{rr} 44 & 38 \\ 18 & 67 \end{array}\right) \right] $
$\PSL(2,73)$ 37A10 $37$ $5256$ $C_{37}$ 37A17 37A7 1A 37A10 $ \left[ \left(\begin{array}{rr} 9 & 11 \\ 59 & 56 \end{array}\right) \right] $
$\PSL(2,73)$ 37A11 $37$ $5256$ $C_{37}$ 37A15 37A4 1A 37A11 $ \left[ \left(\begin{array}{rr} 51 & 70 \\ 37 & 5 \end{array}\right) \right] $
$\PSL(2,73)$ 37A12 $37$ $5256$ $C_{37}$ 37A13 37A1 1A 37A12 $ \left[ \left(\begin{array}{rr} 67 & 6 \\ 72 & 13 \end{array}\right) \right] $
$\PSL(2,73)$ 37A13 $37$ $5256$ $C_{37}$ 37A11 37A2 1A 37A13 $ \left[ \left(\begin{array}{rr} 17 & 31 \\ 7 & 30 \end{array}\right) \right] $
$\PSL(2,73)$ 37A14 $37$ $5256$ $C_{37}$ 37A9 37A5 1A 37A14 $ \left[ \left(\begin{array}{rr} 5 & 48 \\ 65 & 11 \end{array}\right) \right] $
$\PSL(2,73)$ 37A15 $37$ $5256$ $C_{37}$ 37A7 37A8 1A 37A15 $ \left[ \left(\begin{array}{rr} 13 & 51 \\ 28 & 65 \end{array}\right) \right] $
$\PSL(2,73)$ 37A16 $37$ $5256$ $C_{37}$ 37A5 37A11 1A 37A16 $ \left[ \left(\begin{array}{rr} 43 & 28 \\ 44 & 10 \end{array}\right) \right] $
$\PSL(2,73)$ 37A17 $37$ $5256$ $C_{37}$ 37A3 37A14 1A 37A17 $ \left[ \left(\begin{array}{rr} 11 & 58 \\ 39 & 0 \end{array}\right) \right] $
$\PSL(2,73)$ 37A18 $37$ $5256$ $C_{37}$ 37A1 37A17 1A 37A18 $ \left[ \left(\begin{array}{rr} 8 & 16 \\ 46 & 10 \end{array}\right) \right] $
$\PSL(2,73)$ 73A1 $73$ $2664$ $C_{73}$ 73A1 73A1 73A1 1A $ \left[ \left(\begin{array}{rr} 72 & 58 \\ 0 & 72 \end{array}\right) \right] $
$\PSL(2,73)$ 73A5 $73$ $2664$ $C_{73}$ 73A5 73A5 73A5 1A $ \left[ \left(\begin{array}{rr} 72 & 71 \\ 0 & 72 \end{array}\right) \right] $
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