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Results (14 matches)
Download displayed columns for resultsElements of the group are displayed as matrices in $\GL_{2}(\Z/{16}\Z)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $A_4:Q_8$ | 1A | $1$ | $1$ | $A_4:Q_8$ | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $A_4:Q_8$ | 2A | $2$ | $1$ | $A_4:Q_8$ | 1A | 2A | $ \left(\begin{array}{rr} 9 & 0 \\ 0 & 9 \end{array}\right) $ |
| $A_4:Q_8$ | 2B | $2$ | $3$ | $C_2^2:Q_8$ | 1A | 2B | $ \left(\begin{array}{rr} 9 & 0 \\ 8 & 9 \end{array}\right) $ |
| $A_4:Q_8$ | 2C | $2$ | $3$ | $C_2^2:Q_8$ | 1A | 2C | $ \left(\begin{array}{rr} 1 & 8 \\ 0 & 1 \end{array}\right) $ |
| $A_4:Q_8$ | 3A | $3$ | $8$ | $C_{12}$ | 3A | 1A | $ \left(\begin{array}{rr} 12 & 11 \\ 9 & 3 \end{array}\right) $ |
| $A_4:Q_8$ | 4A | $4$ | $2$ | $C_4\times A_4$ | 2A | 4A | $ \left(\begin{array}{rr} 5 & 8 \\ 8 & 13 \end{array}\right) $ |
| $A_4:Q_8$ | 4B | $4$ | $6$ | $C_2^2\times C_4$ | 2A | 4B | $ \left(\begin{array}{rr} 13 & 8 \\ 0 & 5 \end{array}\right) $ |
| $A_4:Q_8$ | 4C | $4$ | $12$ | $C_2\times C_4$ | 2C | 4C | $ \left(\begin{array}{rr} 5 & 3 \\ 8 & 3 \end{array}\right) $ |
| $A_4:Q_8$ | 4D | $4$ | $12$ | $C_2\times C_4$ | 2C | 4D | $ \left(\begin{array}{rr} 1 & 15 \\ 0 & 7 \end{array}\right) $ |
| $A_4:Q_8$ | 4E | $4$ | $12$ | $C_2\times C_4$ | 2A | 4E | $ \left(\begin{array}{rr} 13 & 11 \\ 0 & 3 \end{array}\right) $ |
| $A_4:Q_8$ | 4F | $4$ | $12$ | $C_2\times C_4$ | 2A | 4F | $ \left(\begin{array}{rr} 4 & 1 \\ 9 & 12 \end{array}\right) $ |
| $A_4:Q_8$ | 6A | $6$ | $8$ | $C_{12}$ | 3A | 2A | $ \left(\begin{array}{rr} 11 & 13 \\ 15 & 12 \end{array}\right) $ |
| $A_4:Q_8$ | 12A1 | $12$ | $8$ | $C_{12}$ | 6A | 4A | $ \left(\begin{array}{rr} 4 & 7 \\ 13 & 7 \end{array}\right) $ |
| $A_4:Q_8$ | 12A5 | $12$ | $8$ | $C_{12}$ | 6A | 4A | $ \left(\begin{array}{rr} 15 & 1 \\ 11 & 4 \end{array}\right) $ |