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Results (11 matches)
Download displayed columns for resultsElements of the group are displayed as matrices in $\AGL(2,3)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_3^2:\GL(2,3)$ | 1A | $1$ | $1$ | $C_3^2:\GL(2,3)$ | 1A | 1A | $ \left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right) $ |
| $C_3^2:\GL(2,3)$ | 2A | $2$ | $9$ | $\GL(2,3)$ | 1A | 2A | $ \left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 1 \end{array}\right) $ |
| $C_3^2:\GL(2,3)$ | 2B | $2$ | $36$ | $D_6$ | 1A | 2B | $ \left(\begin{array}{rrr} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 2 & 1 & 1 \end{array}\right) $ |
| $C_3^2:\GL(2,3)$ | 3A | $3$ | $8$ | $C_3^2:S_3$ | 3A | 1A | $ \left(\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 1 & 1 \end{array}\right) $ |
| $C_3^2:\GL(2,3)$ | 3B | $3$ | $24$ | $C_3\times S_3$ | 3B | 1A | $ \left(\begin{array}{rrr} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 1 \end{array}\right) $ |
| $C_3^2:\GL(2,3)$ | 3C | $3$ | $48$ | $C_3^2$ | 3C | 1A | $ \left(\begin{array}{rrr} 2 & 2 & 0 \\ 1 & 0 & 0 \\ 2 & 2 & 1 \end{array}\right) $ |
| $C_3^2:\GL(2,3)$ | 4A | $4$ | $54$ | $C_8$ | 2A | 4A | $ \left(\begin{array}{rrr} 2 & 2 & 0 \\ 2 & 1 & 0 \\ 1 & 2 & 1 \end{array}\right) $ |
| $C_3^2:\GL(2,3)$ | 6A | $6$ | $72$ | $C_6$ | 3A | 2B | $ \left(\begin{array}{rrr} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 0 & 1 \end{array}\right) $ |
| $C_3^2:\GL(2,3)$ | 6B | $6$ | $72$ | $C_6$ | 3B | 2A | $ \left(\begin{array}{rrr} 2 & 1 & 0 \\ 0 & 2 & 0 \\ 1 & 2 & 1 \end{array}\right) $ |
| $C_3^2:\GL(2,3)$ | 8A1 | $8$ | $54$ | $C_8$ | 4A | 8A1 | $ \left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \end{array}\right) $ |
| $C_3^2:\GL(2,3)$ | 8A-1 | $8$ | $54$ | $C_8$ | 4A | 8A-1 | $ \left(\begin{array}{rrr} 0 & 1 & 0 \\ 1 & 1 & 0 \\ 2 & 1 & 1 \end{array}\right) $ |