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Elements of the group are displayed as matrices in $\COPlus(2,29)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 7P | ||||||
| $C_{28}\wr C_2$ | 1A | $1$ | $1$ | $C_{28}\wr C_2$ | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 2A | $2$ | $1$ | $C_{28}\wr C_2$ | 1A | 2A | $ \left(\begin{array}{rr} 28 & 0 \\ 0 & 28 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 2B | $2$ | $2$ | $C_{28}^2$ | 1A | 2B | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 28 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 2C | $2$ | $28$ | $C_2\times C_{28}$ | 1A | 2C | $ \left(\begin{array}{rr} 0 & 24 \\ 23 & 0 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 4A1 | $4$ | $1$ | $C_{28}\wr C_2$ | 2A | 4A-1 | $ \left(\begin{array}{rr} 12 & 0 \\ 0 & 12 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 4A-1 | $4$ | $1$ | $C_{28}\wr C_2$ | 2A | 4A1 | $ \left(\begin{array}{rr} 17 & 0 \\ 0 & 17 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 4B | $4$ | $2$ | $C_{28}^2$ | 2A | 4B | $ \left(\begin{array}{rr} 12 & 0 \\ 0 & 17 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 4C1 | $4$ | $2$ | $C_{28}^2$ | 2B | 4C-1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 12 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 4C-1 | $4$ | $2$ | $C_{28}^2$ | 2B | 4C1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 17 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 4D1 | $4$ | $2$ | $C_{28}^2$ | 2B | 4D-1 | $ \left(\begin{array}{rr} 12 & 0 \\ 0 & 28 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 4D-1 | $4$ | $2$ | $C_{28}^2$ | 2B | 4D1 | $ \left(\begin{array}{rr} 17 & 0 \\ 0 & 28 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 4E | $4$ | $28$ | $C_2\times C_{28}$ | 2A | 4E | $ \left(\begin{array}{rr} 0 & 6 \\ 24 & 0 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7A1 | $7$ | $1$ | $C_{28}\wr C_2$ | 7A2 | 7A3 | $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 7 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7A-1 | $7$ | $1$ | $C_{28}\wr C_2$ | 7A-2 | 7A-3 | $ \left(\begin{array}{rr} 25 & 0 \\ 0 & 25 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7A2 | $7$ | $1$ | $C_{28}\wr C_2$ | 7A-3 | 7A-1 | $ \left(\begin{array}{rr} 20 & 0 \\ 0 & 20 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7A-2 | $7$ | $1$ | $C_{28}\wr C_2$ | 7A3 | 7A1 | $ \left(\begin{array}{rr} 16 & 0 \\ 0 & 16 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7A3 | $7$ | $1$ | $C_{28}\wr C_2$ | 7A-1 | 7A2 | $ \left(\begin{array}{rr} 24 & 0 \\ 0 & 24 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7A-3 | $7$ | $1$ | $C_{28}\wr C_2$ | 7A1 | 7A-2 | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7B1 | $7$ | $2$ | $C_{28}^2$ | 7B2 | 7B3 | $ \left(\begin{array}{rr} 16 & 0 \\ 0 & 20 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7B2 | $7$ | $2$ | $C_{28}^2$ | 7B3 | 7B1 | $ \left(\begin{array}{rr} 24 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7B3 | $7$ | $2$ | $C_{28}^2$ | 7B1 | 7B2 | $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 25 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7C1 | $7$ | $2$ | $C_{28}^2$ | 7C2 | 7C3 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 16 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7C-1 | $7$ | $2$ | $C_{28}^2$ | 7C-2 | 7C-3 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 20 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7C2 | $7$ | $2$ | $C_{28}^2$ | 7C-3 | 7C-1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 24 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7C-2 | $7$ | $2$ | $C_{28}^2$ | 7C3 | 7C1 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7C3 | $7$ | $2$ | $C_{28}^2$ | 7C-1 | 7C2 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 7 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7C-3 | $7$ | $2$ | $C_{28}^2$ | 7C1 | 7C-2 | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 25 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7D1 | $7$ | $2$ | $C_{28}^2$ | 7D2 | 7D3 | $ \left(\begin{array}{rr} 16 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7D-1 | $7$ | $2$ | $C_{28}^2$ | 7D-2 | 7D-3 | $ \left(\begin{array}{rr} 20 & 0 \\ 0 & 24 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7D2 | $7$ | $2$ | $C_{28}^2$ | 7D-3 | 7D-1 | $ \left(\begin{array}{rr} 24 & 0 \\ 0 & 7 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7D-2 | $7$ | $2$ | $C_{28}^2$ | 7D3 | 7D1 | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 25 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7D3 | $7$ | $2$ | $C_{28}^2$ | 7D-1 | 7D2 | $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 16 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7D-3 | $7$ | $2$ | $C_{28}^2$ | 7D1 | 7D-2 | $ \left(\begin{array}{rr} 25 & 0 \\ 0 & 20 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7E1 | $7$ | $2$ | $C_{28}^2$ | 7E2 | 7E3 | $ \left(\begin{array}{rr} 16 & 0 \\ 0 & 24 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7E-1 | $7$ | $2$ | $C_{28}^2$ | 7E-2 | 7E-3 | $ \left(\begin{array}{rr} 20 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7E2 | $7$ | $2$ | $C_{28}^2$ | 7E-3 | 7E-1 | $ \left(\begin{array}{rr} 24 & 0 \\ 0 & 25 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7E-2 | $7$ | $2$ | $C_{28}^2$ | 7E3 | 7E1 | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 7 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7E3 | $7$ | $2$ | $C_{28}^2$ | 7E-1 | 7E2 | $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 20 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 7E-3 | $7$ | $2$ | $C_{28}^2$ | 7E1 | 7E-2 | $ \left(\begin{array}{rr} 25 & 0 \\ 0 & 16 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 8A1 | $8$ | $28$ | $C_{56}$ | 4A1 | 8A-1 | $ \left(\begin{array}{rr} 0 & 8 \\ 16 & 0 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 8A-1 | $8$ | $28$ | $C_{56}$ | 4A-1 | 8A1 | $ \left(\begin{array}{rr} 0 & 20 \\ 11 & 0 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 14A1 | $14$ | $1$ | $C_{28}\wr C_2$ | 7A-2 | 14A3 | $ \left(\begin{array}{rr} 4 & 0 \\ 0 & 4 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 14A-1 | $14$ | $1$ | $C_{28}\wr C_2$ | 7A2 | 14A-3 | $ \left(\begin{array}{rr} 22 & 0 \\ 0 & 22 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 14A3 | $14$ | $1$ | $C_{28}\wr C_2$ | 7A1 | 14A-5 | $ \left(\begin{array}{rr} 6 & 0 \\ 0 & 6 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 14A-3 | $14$ | $1$ | $C_{28}\wr C_2$ | 7A-1 | 14A5 | $ \left(\begin{array}{rr} 5 & 0 \\ 0 & 5 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 14A5 | $14$ | $1$ | $C_{28}\wr C_2$ | 7A-3 | 14A1 | $ \left(\begin{array}{rr} 9 & 0 \\ 0 & 9 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 14A-5 | $14$ | $1$ | $C_{28}\wr C_2$ | 7A3 | 14A-1 | $ \left(\begin{array}{rr} 13 & 0 \\ 0 & 13 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 14B1 | $14$ | $2$ | $C_{28}^2$ | 7B1 | 14B3 | $ \left(\begin{array}{rr} 4 & 0 \\ 0 & 22 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 14B3 | $14$ | $2$ | $C_{28}^2$ | 7B3 | 14B5 | $ \left(\begin{array}{rr} 6 & 0 \\ 0 & 5 \end{array}\right) $ |
| $C_{28}\wr C_2$ | 14B5 | $14$ | $2$ | $C_{28}^2$ | 7B2 | 14B1 | $ \left(\begin{array}{rr} 9 & 0 \\ 0 & 13 \end{array}\right) $ |