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Elements of the group are displayed as equivalence classes (represented by square brackets) of matrices in $\SL(2,47)$.

Group Label Order Size Centralizer Powers Representative
2P 3P 23P 47P
$\PSL(2,47)$ 1A $1$ $1$ $\PSL(2,47)$ 1A 1A 1A 1A $ \left[ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) \right] $
$\PSL(2,47)$ 2A $2$ $1081$ $D_{24}$ 1A 2A 2A 2A $ \left[ \left(\begin{array}{rr} 16 & 39 \\ 38 & 31 \end{array}\right) \right] $
$\PSL(2,47)$ 3A $3$ $2162$ $C_{24}$ 3A 1A 3A 3A $ \left[ \left(\begin{array}{rr} 25 & 46 \\ 40 & 21 \end{array}\right) \right] $
$\PSL(2,47)$ 4A $4$ $2162$ $C_{24}$ 2A 4A 4A 4A $ \left[ \left(\begin{array}{rr} 29 & 19 \\ 39 & 11 \end{array}\right) \right] $
$\PSL(2,47)$ 6A $6$ $2162$ $C_{24}$ 3A 2A 6A 6A $ \left[ \left(\begin{array}{rr} 2 & 43 \\ 19 & 33 \end{array}\right) \right] $
$\PSL(2,47)$ 8A1 $8$ $2162$ $C_{24}$ 4A 8A3 8A3 8A1 $ \left[ \left(\begin{array}{rr} 22 & 25 \\ 34 & 28 \end{array}\right) \right] $
$\PSL(2,47)$ 8A3 $8$ $2162$ $C_{24}$ 4A 8A1 8A1 8A3 $ \left[ \left(\begin{array}{rr} 15 & 35 \\ 10 & 14 \end{array}\right) \right] $
$\PSL(2,47)$ 12A1 $12$ $2162$ $C_{24}$ 6A 4A 12A1 12A1 $ \left[ \left(\begin{array}{rr} 15 & 34 \\ 3 & 10 \end{array}\right) \right] $
$\PSL(2,47)$ 12A5 $12$ $2162$ $C_{24}$ 6A 4A 12A5 12A5 $ \left[ \left(\begin{array}{rr} 4 & 6 \\ 42 & 28 \end{array}\right) \right] $
$\PSL(2,47)$ 23A1 $23$ $2256$ $C_{23}$ 23A2 23A3 23A11 1A $ \left[ \left(\begin{array}{rr} 34 & 6 \\ 22 & 44 \end{array}\right) \right] $
$\PSL(2,47)$ 23A2 $23$ $2256$ $C_{23}$ 23A4 23A6 23A1 1A $ \left[ \left(\begin{array}{rr} 28 & 2 \\ 23 & 0 \end{array}\right) \right] $
$\PSL(2,47)$ 23A3 $23$ $2256$ $C_{23}$ 23A6 23A9 23A10 1A $ \left[ \left(\begin{array}{rr} 38 & 26 \\ 17 & 3 \end{array}\right) \right] $
$\PSL(2,47)$ 23A4 $23$ $2256$ $C_{23}$ 23A8 23A11 23A2 1A $ \left[ \left(\begin{array}{rr} 31 & 9 \\ 33 & 46 \end{array}\right) \right] $
$\PSL(2,47)$ 23A5 $23$ $2256$ $C_{23}$ 23A10 23A8 23A9 1A $ \left[ \left(\begin{array}{rr} 17 & 29 \\ 28 & 34 \end{array}\right) \right] $
$\PSL(2,47)$ 23A6 $23$ $2256$ $C_{23}$ 23A11 23A5 23A3 1A $ \left[ \left(\begin{array}{rr} 41 & 15 \\ 8 & 19 \end{array}\right) \right] $
$\PSL(2,47)$ 23A7 $23$ $2256$ $C_{23}$ 23A9 23A2 23A8 1A $ \left[ \left(\begin{array}{rr} 32 & 13 \\ 32 & 38 \end{array}\right) \right] $
$\PSL(2,47)$ 23A8 $23$ $2256$ $C_{23}$ 23A7 23A1 23A4 1A $ \left[ \left(\begin{array}{rr} 11 & 12 \\ 44 & 31 \end{array}\right) \right] $
$\PSL(2,47)$ 23A9 $23$ $2256$ $C_{23}$ 23A5 23A4 23A7 1A $ \left[ \left(\begin{array}{rr} 27 & 30 \\ 16 & 30 \end{array}\right) \right] $
$\PSL(2,47)$ 23A10 $23$ $2256$ $C_{23}$ 23A3 23A7 23A5 1A $ \left[ \left(\begin{array}{rr} 20 & 22 \\ 18 & 41 \end{array}\right) \right] $
$\PSL(2,47)$ 23A11 $23$ $2256$ $C_{23}$ 23A1 23A10 23A6 1A $ \left[ \left(\begin{array}{rr} 36 & 7 \\ 10 & 32 \end{array}\right) \right] $
$\PSL(2,47)$ 24A1 $24$ $2162$ $C_{24}$ 12A1 8A1 24A11 24A1 $ \left[ \left(\begin{array}{rr} 4 & 3 \\ 21 & 16 \end{array}\right) \right] $
$\PSL(2,47)$ 24A5 $24$ $2162$ $C_{24}$ 12A5 8A3 24A7 24A5 $ \left[ \left(\begin{array}{rr} 29 & 11 \\ 30 & 26 \end{array}\right) \right] $
$\PSL(2,47)$ 24A7 $24$ $2162$ $C_{24}$ 12A5 8A1 24A5 24A7 $ \left[ \left(\begin{array}{rr} 2 & 32 \\ 36 & 36 \end{array}\right) \right] $
$\PSL(2,47)$ 24A11 $24$ $2162$ $C_{24}$ 12A1 8A3 24A1 24A11 $ \left[ \left(\begin{array}{rr} 46 & 33 \\ 43 & 37 \end{array}\right) \right] $
$\PSL(2,47)$ 47A1 $47$ $1104$ $C_{47}$ 47A1 47A1 47A-1 47A-1 $ \left[ \left(\begin{array}{rr} 14 & 15 \\ 32 & 31 \end{array}\right) \right] $
$\PSL(2,47)$ 47A-1 $47$ $1104$ $C_{47}$ 47A-1 47A-1 47A1 47A1 $ \left[ \left(\begin{array}{rr} 16 & 15 \\ 32 & 33 \end{array}\right) \right] $
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