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Results (10 matches)
Download displayed columns for resultsElements of the group are displayed as matrices in $\GL_{2}(\F_{5})$.
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $D_4:C_2$ | 1A | $1$ | $1$ | $D_4:C_2$ | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $D_4:C_2$ | 2A | $2$ | $1$ | $D_4:C_2$ | 1A | $ \left(\begin{array}{rr} 4 & 0 \\ 0 & 4 \end{array}\right) $ |
| $D_4:C_2$ | 2B | $2$ | $2$ | $C_2\times C_4$ | 1A | $ \left(\begin{array}{rr} 0 & 1 \\ 1 & 0 \end{array}\right) $ |
| $D_4:C_2$ | 2C | $2$ | $2$ | $C_2\times C_4$ | 1A | $ \left(\begin{array}{rr} 0 & 2 \\ 3 & 0 \end{array}\right) $ |
| $D_4:C_2$ | 2D | $2$ | $2$ | $C_2\times C_4$ | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 4 \end{array}\right) $ |
| $D_4:C_2$ | 4A1 | $4$ | $1$ | $D_4:C_2$ | 2A | $ \left(\begin{array}{rr} 2 & 0 \\ 0 & 2 \end{array}\right) $ |
| $D_4:C_2$ | 4A-1 | $4$ | $1$ | $D_4:C_2$ | 2A | $ \left(\begin{array}{rr} 3 & 0 \\ 0 & 3 \end{array}\right) $ |
| $D_4:C_2$ | 4B | $4$ | $2$ | $C_2\times C_4$ | 2A | $ \left(\begin{array}{rr} 0 & 1 \\ 4 & 0 \end{array}\right) $ |
| $D_4:C_2$ | 4C | $4$ | $2$ | $C_2\times C_4$ | 2A | $ \left(\begin{array}{rr} 0 & 2 \\ 2 & 0 \end{array}\right) $ |
| $D_4:C_2$ | 4D | $4$ | $2$ | $C_2\times C_4$ | 2A | $ \left(\begin{array}{rr} 2 & 0 \\ 0 & 3 \end{array}\right) $ |