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Elements of the group are displayed as matrices in $\GL_{2}(\Z/{32}\Z)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_8^2.(C_4\times D_4^2)$ | 1A | $1$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2A | $2$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 1A | $ \left(\begin{array}{rr} 17 & 0 \\ 0 & 17 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2B | $2$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 1A | $ \left(\begin{array}{rr} 17 & 16 \\ 0 & 17 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2C | $2$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 1A | $ \left(\begin{array}{rr} 1 & 16 \\ 0 & 1 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2D | $2$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 1A | $ \left(\begin{array}{rr} 15 & 0 \\ 0 & 15 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2E | $2$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 1A | $ \left(\begin{array}{rr} 31 & 16 \\ 0 & 31 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2F | $2$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 1A | $ \left(\begin{array}{rr} 31 & 0 \\ 0 & 31 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2G | $2$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 1A | $ \left(\begin{array}{rr} 15 & 16 \\ 0 & 15 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2H | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 15 & 0 \\ 16 & 15 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2I | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 31 & 0 \\ 16 & 31 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2J | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 15 & 16 \\ 16 & 31 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2K | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 31 & 16 \\ 0 & 15 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2L | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 31 & 0 \\ 16 & 15 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2M | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 15 & 16 \\ 0 & 31 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2N | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 1 & 16 \\ 16 & 17 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2O | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 17 & 0 \\ 16 & 1 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2P | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 17 & 16 \\ 16 & 17 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2Q | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 1 & 16 \\ 16 & 1 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2R | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 17 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2S | $2$ | $2$ | $(C_4^3\times C_8).D_8$ | 1A | $ \left(\begin{array}{rr} 1 & 16 \\ 0 & 17 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2T | $2$ | $32$ | not computed | 1A | $ \left(\begin{array}{rr} 19 & 12 \\ 2 & 29 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2U | $2$ | $32$ | not computed | 1A | $ \left(\begin{array}{rr} 5 & 12 \\ 14 & 27 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2V | $2$ | $32$ | not computed | 1A | $ \left(\begin{array}{rr} 3 & 12 \\ 2 & 13 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2W | $2$ | $32$ | not computed | 1A | $ \left(\begin{array}{rr} 23 & 8 \\ 26 & 25 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2X | $2$ | $32$ | not computed | 1A | $ \left(\begin{array}{rr} 21 & 12 \\ 14 & 11 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2Y | $2$ | $32$ | not computed | 1A | $ \left(\begin{array}{rr} 1 & 16 \\ 22 & 31 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2Z | $2$ | $32$ | not computed | 1A | $ \left(\begin{array}{rr} 7 & 8 \\ 26 & 9 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2AA | $2$ | $32$ | not computed | 1A | $ \left(\begin{array}{rr} 17 & 16 \\ 22 & 15 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2AB | $2$ | $64$ | not computed | 1A | $ \left(\begin{array}{rr} 7 & 9 \\ 16 & 25 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2AC | $2$ | $64$ | not computed | 1A | $ \left(\begin{array}{rr} 17 & 23 \\ 0 & 15 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2AD | $2$ | $64$ | not computed | 1A | $ \left(\begin{array}{rr} 11 & 27 \\ 24 & 21 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 2AE | $2$ | $64$ | not computed | 1A | $ \left(\begin{array}{rr} 17 & 9 \\ 0 & 15 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4A1 | $4$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 2A | $ \left(\begin{array}{rr} 9 & 0 \\ 0 & 9 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4A-1 | $4$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 2A | $ \left(\begin{array}{rr} 25 & 0 \\ 0 & 25 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4B1 | $4$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 2A | $ \left(\begin{array}{rr} 9 & 16 \\ 0 & 9 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4B-1 | $4$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 2A | $ \left(\begin{array}{rr} 25 & 16 \\ 0 & 25 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4C1 | $4$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 2A | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4C-1 | $4$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 2A | $ \left(\begin{array}{rr} 7 & 0 \\ 0 & 7 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4D1 | $4$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 2A | $ \left(\begin{array}{rr} 7 & 16 \\ 0 & 7 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4D-1 | $4$ | $1$ | $C_8^2.(C_4\times D_4^2)$ | 2A | $ \left(\begin{array}{rr} 23 & 16 \\ 0 & 23 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4E | $4$ | $2$ | $(C_4^3\times C_8).D_8$ | 2A | $ \left(\begin{array}{rr} 7 & 0 \\ 16 & 23 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4F | $4$ | $2$ | $(C_4^3\times C_8).D_8$ | 2A | $ \left(\begin{array}{rr} 23 & 16 \\ 16 & 7 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4G | $4$ | $2$ | $C_8^2.(D_4\times C_4^2)$ | 2B | $ \left(\begin{array}{rr} 7 & 24 \\ 0 & 23 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4H | $4$ | $2$ | $C_8^2.(D_4\times C_4^2)$ | 2B | $ \left(\begin{array}{rr} 23 & 24 \\ 0 & 7 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4I | $4$ | $2$ | $(C_4^2\times C_8^2).D_4$ | 2B | $ \left(\begin{array}{rr} 25 & 24 \\ 16 & 9 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4J | $4$ | $2$ | $(C_4^3\times C_8).D_8$ | 2A | $ \left(\begin{array}{rr} 25 & 0 \\ 16 & 9 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4K | $4$ | $2$ | $C_8^2.(D_4\times C_4^2)$ | 2B | $ \left(\begin{array}{rr} 9 & 8 \\ 0 & 25 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4L | $4$ | $2$ | $(C_4^3\times C_8).D_8$ | 2A | $ \left(\begin{array}{rr} 9 & 16 \\ 16 & 25 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4M | $4$ | $2$ | $C_8^2.(D_4\times C_4^2)$ | 2B | $ \left(\begin{array}{rr} 9 & 24 \\ 0 & 25 \end{array}\right) $ |
| $C_8^2.(C_4\times D_4^2)$ | 4N | $4$ | $2$ | $(C_4^2\times C_8^2).D_4$ | 2B | $ \left(\begin{array}{rr} 9 & 24 \\ 16 & 25 \end{array}\right) $ |