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Elements of the group are displayed as matrices in $\GL_{2}(\Z/{28}\Z)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 7P | ||||||
| $C_2^5\times F_7$ | 1A | $1$ | $1$ | $C_2^5\times F_7$ | 1A | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2A | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2A | 2A | $ \left(\begin{array}{rr} 15 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2B | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2B | 2B | $ \left(\begin{array}{rr} 1 & 14 \\ 0 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2C | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2C | 2C | $ \left(\begin{array}{rr} 1 & 14 \\ 14 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2D | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2D | 2D | $ \left(\begin{array}{rr} 13 & 0 \\ 0 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2E | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2E | 2E | $ \left(\begin{array}{rr} 1 & 14 \\ 14 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2F | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2F | 2F | $ \left(\begin{array}{rr} 15 & 14 \\ 0 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2G | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2G | 2G | $ \left(\begin{array}{rr} 15 & 14 \\ 14 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2H | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2H | 2H | $ \left(\begin{array}{rr} 1 & 0 \\ 14 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2I | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2I | 2I | $ \left(\begin{array}{rr} 27 & 0 \\ 0 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2J | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2J | 2J | $ \left(\begin{array}{rr} 13 & 14 \\ 0 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2K | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2K | 2K | $ \left(\begin{array}{rr} 13 & 14 \\ 14 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2L | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2L | 2L | $ \left(\begin{array}{rr} 15 & 14 \\ 14 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2M | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2M | 2M | $ \left(\begin{array}{rr} 1 & 0 \\ 14 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2N | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2N | 2N | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2O | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2O | 2O | $ \left(\begin{array}{rr} 13 & 14 \\ 14 & 27 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2P | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2P | 2P | $ \left(\begin{array}{rr} 15 & 0 \\ 14 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2Q | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2Q | 2Q | $ \left(\begin{array}{rr} 27 & 14 \\ 0 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2R | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2R | 2R | $ \left(\begin{array}{rr} 27 & 14 \\ 14 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2S | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2S | 2S | $ \left(\begin{array}{rr} 13 & 0 \\ 14 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2T | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2T | 2T | $ \left(\begin{array}{rr} 15 & 0 \\ 14 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2U | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2U | 2U | $ \left(\begin{array}{rr} 15 & 0 \\ 0 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2V | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2V | 2V | $ \left(\begin{array}{rr} 1 & 14 \\ 0 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2W | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2W | 2W | $ \left(\begin{array}{rr} 27 & 14 \\ 14 & 27 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2X | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2X | 2X | $ \left(\begin{array}{rr} 13 & 0 \\ 14 & 27 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2Y | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2Y | 2Y | $ \left(\begin{array}{rr} 13 & 0 \\ 0 & 27 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2Z | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2Z | 2Z | $ \left(\begin{array}{rr} 27 & 0 \\ 14 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AA | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2AA | 2AA | $ \left(\begin{array}{rr} 15 & 14 \\ 0 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AB | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2AB | 2AB | $ \left(\begin{array}{rr} 27 & 0 \\ 14 & 27 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AC | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2AC | 2AC | $ \left(\begin{array}{rr} 27 & 0 \\ 0 & 27 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AD | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2AD | 2AD | $ \left(\begin{array}{rr} 13 & 14 \\ 0 & 27 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AE | $2$ | $1$ | $C_2^5\times F_7$ | 1A | 2AE | 2AE | $ \left(\begin{array}{rr} 27 & 14 \\ 0 & 27 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AF | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AF | 2AF | $ \left(\begin{array}{rr} 13 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AG | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AG | 2AG | $ \left(\begin{array}{rr} 27 & 24 \\ 0 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AH | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AH | 2AH | $ \left(\begin{array}{rr} 13 & 14 \\ 0 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AI | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AI | 2AI | $ \left(\begin{array}{rr} 13 & 14 \\ 14 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AJ | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AJ | 2AJ | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AK | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AK | 2AK | $ \left(\begin{array}{rr} 13 & 14 \\ 14 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AL | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AL | 2AL | $ \left(\begin{array}{rr} 27 & 10 \\ 0 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AM | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AM | 2AM | $ \left(\begin{array}{rr} 27 & 10 \\ 14 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AN | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AN | 2AN | $ \left(\begin{array}{rr} 13 & 0 \\ 14 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AO | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AO | 2AO | $ \left(\begin{array}{rr} 15 & 4 \\ 0 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AP | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AP | 2AP | $ \left(\begin{array}{rr} 1 & 14 \\ 0 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AQ | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AQ | 2AQ | $ \left(\begin{array}{rr} 1 & 14 \\ 14 & 13 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AR | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AR | 2AR | $ \left(\begin{array}{rr} 27 & 10 \\ 14 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AS | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AS | 2AS | $ \left(\begin{array}{rr} 13 & 0 \\ 14 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AT | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AT | 2AT | $ \left(\begin{array}{rr} 13 & 0 \\ 0 & 15 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AU | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AU | 2AU | $ \left(\begin{array}{rr} 1 & 14 \\ 14 & 27 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AV | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AV | 2AV | $ \left(\begin{array}{rr} 27 & 24 \\ 14 & 1 \end{array}\right) $ |
| $C_2^5\times F_7$ | 2AW | $2$ | $7$ | $C_2^5\times C_6$ | 1A | 2AW | 2AW | $ \left(\begin{array}{rr} 15 & 18 \\ 0 & 13 \end{array}\right) $ |