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Results (20 matches)
Download displayed columns for resultsElements of the group are displayed as matrices in $\GL_{2}(\Z/{8}\Z)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_2^3:C_4$ | 1A | $1$ | $1$ | $C_2^3:C_4$ | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_2^3:C_4$ | 2A | $2$ | $1$ | $C_2^3:C_4$ | 1A | $ \left(\begin{array}{rr} 5 & 4 \\ 0 & 5 \end{array}\right) $ |
| $C_2^3:C_4$ | 2B | $2$ | $1$ | $C_2^3:C_4$ | 1A | $ \left(\begin{array}{rr} 3 & 4 \\ 4 & 3 \end{array}\right) $ |
| $C_2^3:C_4$ | 2C | $2$ | $1$ | $C_2^3:C_4$ | 1A | $ \left(\begin{array}{rr} 7 & 4 \\ 4 & 7 \end{array}\right) $ |
| $C_2^3:C_4$ | 2D | $2$ | $1$ | $C_2^3:C_4$ | 1A | $ \left(\begin{array}{rr} 7 & 0 \\ 4 & 7 \end{array}\right) $ |
| $C_2^3:C_4$ | 2E | $2$ | $1$ | $C_2^3:C_4$ | 1A | $ \left(\begin{array}{rr} 3 & 0 \\ 4 & 3 \end{array}\right) $ |
| $C_2^3:C_4$ | 2F | $2$ | $1$ | $C_2^3:C_4$ | 1A | $ \left(\begin{array}{rr} 5 & 0 \\ 0 & 5 \end{array}\right) $ |
| $C_2^3:C_4$ | 2G | $2$ | $1$ | $C_2^3:C_4$ | 1A | $ \left(\begin{array}{rr} 1 & 4 \\ 0 & 1 \end{array}\right) $ |
| $C_2^3:C_4$ | 2H | $2$ | $2$ | $C_2^4$ | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 6 & 3 \end{array}\right) $ |
| $C_2^3:C_4$ | 2I | $2$ | $2$ | $C_2^4$ | 1A | $ \left(\begin{array}{rr} 5 & 0 \\ 6 & 7 \end{array}\right) $ |
| $C_2^3:C_4$ | 2J | $2$ | $2$ | $C_2^4$ | 1A | $ \left(\begin{array}{rr} 3 & 4 \\ 6 & 1 \end{array}\right) $ |
| $C_2^3:C_4$ | 2K | $2$ | $2$ | $C_2^4$ | 1A | $ \left(\begin{array}{rr} 7 & 4 \\ 6 & 5 \end{array}\right) $ |
| $C_2^3:C_4$ | 4A1 | $4$ | $2$ | $C_2^2\times C_4$ | 2F | $ \left(\begin{array}{rr} 1 & 2 \\ 2 & 3 \end{array}\right) $ |
| $C_2^3:C_4$ | 4A-1 | $4$ | $2$ | $C_2^2\times C_4$ | 2F | $ \left(\begin{array}{rr} 5 & 2 \\ 2 & 7 \end{array}\right) $ |
| $C_2^3:C_4$ | 4B1 | $4$ | $2$ | $C_2^2\times C_4$ | 2G | $ \left(\begin{array}{rr} 1 & 2 \\ 4 & 5 \end{array}\right) $ |
| $C_2^3:C_4$ | 4B-1 | $4$ | $2$ | $C_2^2\times C_4$ | 2G | $ \left(\begin{array}{rr} 5 & 2 \\ 4 & 1 \end{array}\right) $ |
| $C_2^3:C_4$ | 4C1 | $4$ | $2$ | $C_2^2\times C_4$ | 2F | $ \left(\begin{array}{rr} 3 & 2 \\ 2 & 1 \end{array}\right) $ |
| $C_2^3:C_4$ | 4C-1 | $4$ | $2$ | $C_2^2\times C_4$ | 2F | $ \left(\begin{array}{rr} 7 & 2 \\ 2 & 5 \end{array}\right) $ |
| $C_2^3:C_4$ | 4D1 | $4$ | $2$ | $C_2^2\times C_4$ | 2G | $ \left(\begin{array}{rr} 3 & 2 \\ 0 & 7 \end{array}\right) $ |
| $C_2^3:C_4$ | 4D-1 | $4$ | $2$ | $C_2^2\times C_4$ | 2G | $ \left(\begin{array}{rr} 7 & 2 \\ 0 & 3 \end{array}\right) $ |