Refine search
Results (16 matches)
Download displayed columns for resultsElements of the group are displayed as matrices in $\GL_{3}(\F_{5})$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 5P | ||||||
| $C_2\times C_5^2:Q_8$ | 1A | $1$ | $1$ | $C_2\times C_5^2:Q_8$ | 1A | 1A | $ \left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 2A | $2$ | $1$ | $C_2\times C_5^2:Q_8$ | 1A | 2A | $ \left(\begin{array}{rrr} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 2B | $2$ | $25$ | $C_2\times Q_8$ | 1A | 2B | $ \left(\begin{array}{rrr} 4 & 4 & 0 \\ 0 & 1 & 0 \\ 0 & 3 & 4 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 2C | $2$ | $25$ | $C_2\times Q_8$ | 1A | 2C | $ \left(\begin{array}{rrr} 1 & 3 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 4A | $4$ | $50$ | $C_2\times C_4$ | 2B | 4A | $ \left(\begin{array}{rrr} 4 & 3 & 3 \\ 0 & 4 & 0 \\ 1 & 0 & 1 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 4B | $4$ | $50$ | $C_2\times C_4$ | 2B | 4B | $ \left(\begin{array}{rrr} 3 & 3 & 1 \\ 0 & 4 & 0 \\ 0 & 2 & 2 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 4C | $4$ | $50$ | $C_2\times C_4$ | 2B | 4C | $ \left(\begin{array}{rrr} 3 & 0 & 0 \\ 0 & 4 & 0 \\ 2 & 0 & 2 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 4D | $4$ | $50$ | $C_2\times C_4$ | 2B | 4D | $ \left(\begin{array}{rrr} 2 & 2 & 0 \\ 0 & 1 & 0 \\ 3 & 1 & 3 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 4E | $4$ | $50$ | $C_2\times C_4$ | 2B | 4E | $ \left(\begin{array}{rrr} 4 & 4 & 3 \\ 0 & 1 & 0 \\ 1 & 1 & 1 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 4F | $4$ | $50$ | $C_2\times C_4$ | 2B | 4F | $ \left(\begin{array}{rrr} 3 & 4 & 1 \\ 0 & 1 & 0 \\ 0 & 1 & 2 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 5A | $5$ | $8$ | $C_5\times C_{10}$ | 5A | 1A | $ \left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 3 & 1 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 5B | $5$ | $8$ | $C_5\times C_{10}$ | 5B | 1A | $ \left(\begin{array}{rrr} 1 & 3 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 5C | $5$ | $8$ | $C_5\times C_{10}$ | 5C | 1A | $ \left(\begin{array}{rrr} 1 & 3 & 0 \\ 0 & 1 & 0 \\ 0 & 3 & 1 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 10A | $10$ | $8$ | $C_5\times C_{10}$ | 5A | 2A | $ \left(\begin{array}{rrr} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 1 & 4 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 10B | $10$ | $8$ | $C_5\times C_{10}$ | 5B | 2A | $ \left(\begin{array}{rrr} 4 & 1 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{array}\right) $ |
| $C_2\times C_5^2:Q_8$ | 10C | $10$ | $8$ | $C_5\times C_{10}$ | 5C | 2A | $ \left(\begin{array}{rrr} 4 & 1 & 0 \\ 0 & 4 & 0 \\ 0 & 1 & 4 \end{array}\right) $ |