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Elements of the group are displayed as matrices in $\GL_{2}(\F_{103})$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 17P | ||||||
| $C_{102}\wr C_2$ | 1A | $1$ | $1$ | not computed | 1A | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 2A | $2$ | $1$ | not computed | 1A | 2A | 2A | $ \left(\begin{array}{rr} 102 & 0 \\ 0 & 102 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 2B | $2$ | $2$ | not computed | 1A | 2B | 2B | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 102 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 2C | $2$ | $102$ | not computed | 1A | 2C | 2C | $ \left(\begin{array}{rr} 0 & 19 \\ 38 & 0 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 3A1 | $3$ | $1$ | not computed | 3A-1 | 1A | 3A-1 | $ \left(\begin{array}{rr} 56 & 0 \\ 0 & 56 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 3A-1 | $3$ | $1$ | not computed | 3A1 | 1A | 3A1 | $ \left(\begin{array}{rr} 46 & 0 \\ 0 & 46 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 3B | $3$ | $2$ | not computed | 3B | 1A | 3B | $ \left(\begin{array}{rr} 56 & 0 \\ 0 & 46 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 3C1 | $3$ | $2$ | not computed | 3C-1 | 1A | 3C-1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 56 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 3C-1 | $3$ | $2$ | not computed | 3C1 | 1A | 3C1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 46 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 4A | $4$ | $102$ | not computed | 2A | 4A | 4A | $ \left(\begin{array}{rr} 0 & 12 \\ 60 & 0 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6A1 | $6$ | $1$ | not computed | 3A1 | 2A | 6A-1 | $ \left(\begin{array}{rr} 57 & 0 \\ 0 & 57 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6A-1 | $6$ | $1$ | not computed | 3A-1 | 2A | 6A1 | $ \left(\begin{array}{rr} 47 & 0 \\ 0 & 47 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6B | $6$ | $2$ | not computed | 3B | 2A | 6B | $ \left(\begin{array}{rr} 57 & 0 \\ 0 & 47 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6C1 | $6$ | $2$ | not computed | 3C1 | 2B | 6C-1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 57 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6C-1 | $6$ | $2$ | not computed | 3C-1 | 2B | 6C1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 47 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6D1 | $6$ | $2$ | not computed | 3C-1 | 2B | 6D-1 | $ \left(\begin{array}{rr} 56 & 0 \\ 0 & 102 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6D-1 | $6$ | $2$ | not computed | 3C1 | 2B | 6D1 | $ \left(\begin{array}{rr} 46 & 0 \\ 0 & 102 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6E1 | $6$ | $2$ | not computed | 3B | 2B | 6E-1 | $ \left(\begin{array}{rr} 56 & 0 \\ 0 & 57 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6E-1 | $6$ | $2$ | not computed | 3B | 2B | 6E1 | $ \left(\begin{array}{rr} 46 & 0 \\ 0 & 47 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6F1 | $6$ | $2$ | not computed | 3A-1 | 2B | 6F-1 | $ \left(\begin{array}{rr} 56 & 0 \\ 0 & 47 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6F-1 | $6$ | $2$ | not computed | 3A1 | 2B | 6F1 | $ \left(\begin{array}{rr} 46 & 0 \\ 0 & 57 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6G1 | $6$ | $2$ | not computed | 3C1 | 2A | 6G-1 | $ \left(\begin{array}{rr} 102 & 0 \\ 0 & 57 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6G-1 | $6$ | $2$ | not computed | 3C-1 | 2A | 6G1 | $ \left(\begin{array}{rr} 102 & 0 \\ 0 & 47 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6H1 | $6$ | $102$ | not computed | 3A1 | 2C | 6H-1 | $ \left(\begin{array}{rr} 0 & 50 \\ 100 & 0 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 6H-1 | $6$ | $102$ | not computed | 3A-1 | 2C | 6H1 | $ \left(\begin{array}{rr} 0 & 34 \\ 68 & 0 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 12A1 | $12$ | $102$ | not computed | 6A1 | 4A | 12A-1 | $ \left(\begin{array}{rr} 0 & 49 \\ 39 & 0 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 12A-1 | $12$ | $102$ | not computed | 6A-1 | 4A | 12A1 | $ \left(\begin{array}{rr} 0 & 37 \\ 82 & 0 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A1 | $17$ | $1$ | not computed | 17A2 | 17A3 | 1A | $ \left(\begin{array}{rr} 72 & 0 \\ 0 & 72 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A-1 | $17$ | $1$ | not computed | 17A-2 | 17A-3 | 1A | $ \left(\begin{array}{rr} 93 & 0 \\ 0 & 93 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A2 | $17$ | $1$ | not computed | 17A4 | 17A6 | 1A | $ \left(\begin{array}{rr} 34 & 0 \\ 0 & 34 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A-2 | $17$ | $1$ | not computed | 17A-4 | 17A-6 | 1A | $ \left(\begin{array}{rr} 100 & 0 \\ 0 & 100 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A3 | $17$ | $1$ | not computed | 17A6 | 17A-8 | 1A | $ \left(\begin{array}{rr} 79 & 0 \\ 0 & 79 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A-3 | $17$ | $1$ | not computed | 17A-6 | 17A8 | 1A | $ \left(\begin{array}{rr} 30 & 0 \\ 0 & 30 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A4 | $17$ | $1$ | not computed | 17A8 | 17A-5 | 1A | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A-4 | $17$ | $1$ | not computed | 17A-8 | 17A5 | 1A | $ \left(\begin{array}{rr} 9 & 0 \\ 0 & 9 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A5 | $17$ | $1$ | not computed | 17A-7 | 17A-2 | 1A | $ \left(\begin{array}{rr} 8 & 0 \\ 0 & 8 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A-5 | $17$ | $1$ | not computed | 17A7 | 17A2 | 1A | $ \left(\begin{array}{rr} 13 & 0 \\ 0 & 13 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A6 | $17$ | $1$ | not computed | 17A-5 | 17A1 | 1A | $ \left(\begin{array}{rr} 61 & 0 \\ 0 & 61 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A-6 | $17$ | $1$ | not computed | 17A5 | 17A-1 | 1A | $ \left(\begin{array}{rr} 76 & 0 \\ 0 & 76 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A7 | $17$ | $1$ | not computed | 17A-3 | 17A4 | 1A | $ \left(\begin{array}{rr} 66 & 0 \\ 0 & 66 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A-7 | $17$ | $1$ | not computed | 17A3 | 17A-4 | 1A | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 64 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A8 | $17$ | $1$ | not computed | 17A-1 | 17A7 | 1A | $ \left(\begin{array}{rr} 14 & 0 \\ 0 & 14 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17A-8 | $17$ | $1$ | not computed | 17A1 | 17A-7 | 1A | $ \left(\begin{array}{rr} 81 & 0 \\ 0 & 81 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17B1 | $17$ | $2$ | not computed | 17B2 | 17B3 | 1A | $ \left(\begin{array}{rr} 72 & 0 \\ 0 & 93 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17B2 | $17$ | $2$ | not computed | 17B4 | 17B6 | 1A | $ \left(\begin{array}{rr} 34 & 0 \\ 0 & 100 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17B3 | $17$ | $2$ | not computed | 17B6 | 17B8 | 1A | $ \left(\begin{array}{rr} 79 & 0 \\ 0 & 30 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17B4 | $17$ | $2$ | not computed | 17B8 | 17B5 | 1A | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 9 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17B5 | $17$ | $2$ | not computed | 17B7 | 17B2 | 1A | $ \left(\begin{array}{rr} 8 & 0 \\ 0 & 13 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17B6 | $17$ | $2$ | not computed | 17B5 | 17B1 | 1A | $ \left(\begin{array}{rr} 61 & 0 \\ 0 & 76 \end{array}\right) $ |
| $C_{102}\wr C_2$ | 17B7 | $17$ | $2$ | not computed | 17B3 | 17B4 | 1A | $ \left(\begin{array}{rr} 66 & 0 \\ 0 & 64 \end{array}\right) $ |