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Elements of the group are displayed as matrices in $\GL_{2}(\F_{113})$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 7P | ||||||
| $C_{16}.D_{28}$ | 1A | $1$ | $1$ | $C_{16}.D_{28}$ | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 2A | $2$ | $1$ | $C_{16}.D_{28}$ | 1A | 2A | $ \left(\begin{array}{rr} 112 & 0 \\ 0 & 112 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 2B | $2$ | $2$ | $C_4\times C_{112}$ | 1A | 2B | $ \left(\begin{array}{rr} 112 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 2C | $2$ | $28$ | $C_2\times C_{16}$ | 1A | 2C | $ \left(\begin{array}{rr} 0 & 1 \\ 1 & 0 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 2D | $2$ | $28$ | $C_2\times C_{16}$ | 1A | 2D | $ \left(\begin{array}{rr} 0 & 9 \\ 88 & 0 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 4A1 | $4$ | $1$ | $C_{16}.D_{28}$ | 2A | 4A-1 | $ \left(\begin{array}{rr} 15 & 0 \\ 0 & 15 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 4A-1 | $4$ | $1$ | $C_{16}.D_{28}$ | 2A | 4A1 | $ \left(\begin{array}{rr} 98 & 0 \\ 0 & 98 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 4B | $4$ | $2$ | $C_4\times C_{112}$ | 2A | 4B | $ \left(\begin{array}{rr} 98 & 0 \\ 0 & 15 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 4C1 | $4$ | $2$ | $C_4\times C_{112}$ | 2B | 4C-1 | $ \left(\begin{array}{rr} 15 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 4C-1 | $4$ | $2$ | $C_4\times C_{112}$ | 2B | 4C1 | $ \left(\begin{array}{rr} 98 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 4D1 | $4$ | $2$ | $C_4\times C_{112}$ | 2B | 4D-1 | $ \left(\begin{array}{rr} 15 & 0 \\ 0 & 112 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 4D-1 | $4$ | $2$ | $C_4\times C_{112}$ | 2B | 4D1 | $ \left(\begin{array}{rr} 98 & 0 \\ 0 & 112 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 4E | $4$ | $28$ | $C_2\times C_{16}$ | 2A | 4E | $ \left(\begin{array}{rr} 0 & 1 \\ 112 & 0 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 4F | $4$ | $28$ | $C_2\times C_{16}$ | 2A | 4F | $ \left(\begin{array}{rr} 0 & 9 \\ 25 & 0 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 7A1 | $7$ | $2$ | $C_4\times C_{112}$ | 7A2 | 7A3 | $ \left(\begin{array}{rr} 16 & 0 \\ 0 & 106 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 7A2 | $7$ | $2$ | $C_4\times C_{112}$ | 7A3 | 7A1 | $ \left(\begin{array}{rr} 30 & 0 \\ 0 & 49 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 7A3 | $7$ | $2$ | $C_4\times C_{112}$ | 7A1 | 7A2 | $ \left(\begin{array}{rr} 28 & 0 \\ 0 & 109 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8A1 | $8$ | $1$ | $C_{16}.D_{28}$ | 4A-1 | 8A3 | $ \left(\begin{array}{rr} 18 & 0 \\ 0 & 18 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8A-1 | $8$ | $1$ | $C_{16}.D_{28}$ | 4A1 | 8A-3 | $ \left(\begin{array}{rr} 44 & 0 \\ 0 & 44 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8A3 | $8$ | $1$ | $C_{16}.D_{28}$ | 4A1 | 8A1 | $ \left(\begin{array}{rr} 69 & 0 \\ 0 & 69 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8A-3 | $8$ | $1$ | $C_{16}.D_{28}$ | 4A-1 | 8A-1 | $ \left(\begin{array}{rr} 95 & 0 \\ 0 & 95 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8B1 | $8$ | $2$ | $C_4\times C_{112}$ | 4B | 8B1 | $ \left(\begin{array}{rr} 18 & 0 \\ 0 & 69 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8B-1 | $8$ | $2$ | $C_4\times C_{112}$ | 4B | 8B-1 | $ \left(\begin{array}{rr} 44 & 0 \\ 0 & 95 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8C1 | $8$ | $2$ | $C_4\times C_{112}$ | 4B | 8C3 | $ \left(\begin{array}{rr} 18 & 0 \\ 0 & 44 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8C3 | $8$ | $2$ | $C_4\times C_{112}$ | 4B | 8C1 | $ \left(\begin{array}{rr} 69 & 0 \\ 0 & 95 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8D1 | $8$ | $2$ | $C_4\times C_{112}$ | 4A-1 | 8D-1 | $ \left(\begin{array}{rr} 18 & 0 \\ 0 & 95 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8D-1 | $8$ | $2$ | $C_4\times C_{112}$ | 4A1 | 8D1 | $ \left(\begin{array}{rr} 44 & 0 \\ 0 & 69 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8E1 | $8$ | $28$ | $C_2\times C_{16}$ | 4A1 | 8E-1 | $ \left(\begin{array}{rr} 0 & 1 \\ 15 & 0 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8E-1 | $8$ | $28$ | $C_2\times C_{16}$ | 4A-1 | 8E1 | $ \left(\begin{array}{rr} 0 & 1 \\ 98 & 0 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8F1 | $8$ | $28$ | $C_2\times C_{16}$ | 4A-1 | 8F-1 | $ \left(\begin{array}{rr} 0 & 9 \\ 36 & 0 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 8F-1 | $8$ | $28$ | $C_2\times C_{16}$ | 4A1 | 8F1 | $ \left(\begin{array}{rr} 0 & 9 \\ 77 & 0 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 14A1 | $14$ | $2$ | $C_4\times C_{112}$ | 7A2 | 14A3 | $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 97 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 14A3 | $14$ | $2$ | $C_4\times C_{112}$ | 7A1 | 14A5 | $ \left(\begin{array}{rr} 4 & 0 \\ 0 & 85 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 14A5 | $14$ | $2$ | $C_4\times C_{112}$ | 7A3 | 14A1 | $ \left(\begin{array}{rr} 83 & 0 \\ 0 & 64 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 14B1 | $14$ | $2$ | $C_4\times C_{112}$ | 7A1 | 14B3 | $ \left(\begin{array}{rr} 4 & 0 \\ 0 & 28 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 14B-1 | $14$ | $2$ | $C_4\times C_{112}$ | 7A1 | 14B-3 | $ \left(\begin{array}{rr} 85 & 0 \\ 0 & 109 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 14B3 | $14$ | $2$ | $C_4\times C_{112}$ | 7A3 | 14B-5 | $ \left(\begin{array}{rr} 64 & 0 \\ 0 & 30 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 14B-3 | $14$ | $2$ | $C_4\times C_{112}$ | 7A3 | 14B5 | $ \left(\begin{array}{rr} 83 & 0 \\ 0 & 49 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 14B5 | $14$ | $2$ | $C_4\times C_{112}$ | 7A2 | 14B1 | $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 16 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 14B-5 | $14$ | $2$ | $C_4\times C_{112}$ | 7A2 | 14B-1 | $ \left(\begin{array}{rr} 97 & 0 \\ 0 & 106 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 16A1 | $16$ | $1$ | $C_{16}.D_{28}$ | 8A1 | 16A3 | $ \left(\begin{array}{rr} 40 & 0 \\ 0 & 40 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 16A-1 | $16$ | $1$ | $C_{16}.D_{28}$ | 8A-1 | 16A-3 | $ \left(\begin{array}{rr} 65 & 0 \\ 0 & 65 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 16A3 | $16$ | $1$ | $C_{16}.D_{28}$ | 8A3 | 16A-7 | $ \left(\begin{array}{rr} 42 & 0 \\ 0 & 42 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 16A-3 | $16$ | $1$ | $C_{16}.D_{28}$ | 8A-3 | 16A7 | $ \left(\begin{array}{rr} 35 & 0 \\ 0 & 35 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 16A5 | $16$ | $1$ | $C_{16}.D_{28}$ | 8A-3 | 16A-1 | $ \left(\begin{array}{rr} 78 & 0 \\ 0 & 78 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 16A-5 | $16$ | $1$ | $C_{16}.D_{28}$ | 8A3 | 16A1 | $ \left(\begin{array}{rr} 71 & 0 \\ 0 & 71 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 16A7 | $16$ | $1$ | $C_{16}.D_{28}$ | 8A-1 | 16A5 | $ \left(\begin{array}{rr} 48 & 0 \\ 0 & 48 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 16A-7 | $16$ | $1$ | $C_{16}.D_{28}$ | 8A1 | 16A-5 | $ \left(\begin{array}{rr} 73 & 0 \\ 0 & 73 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 16B1 | $16$ | $2$ | $C_4\times C_{112}$ | 8A1 | 16B3 | $ \left(\begin{array}{rr} 40 & 0 \\ 0 & 73 \end{array}\right) $ |
| $C_{16}.D_{28}$ | 16B-1 | $16$ | $2$ | $C_4\times C_{112}$ | 8A-1 | 16B-3 | $ \left(\begin{array}{rr} 65 & 0 \\ 0 & 48 \end{array}\right) $ |