Refine search
Elements of the group are displayed as matrices in $\GL_{4}(\F_{3})$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_6.C_3^4$ | 1A | $1$ | $1$ | $C_6.C_3^4$ | 1A | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right) $ |
| $C_6.C_3^4$ | 2A | $2$ | $1$ | $C_6.C_3^4$ | 1A | 2A | $ \left(\begin{array}{rrrr} 2 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3A1 | $3$ | $1$ | $C_6.C_3^4$ | 3A-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 1 & 2 & 2 \\ 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 2 \\ 0 & 2 & 1 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3A-1 | $3$ | $1$ | $C_6.C_3^4$ | 3A1 | 1A | $ \left(\begin{array}{rrrr} 1 & 2 & 1 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 2 & 2 & 1 \\ 0 & 1 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3B1 | $3$ | $3$ | $C_6\times \He_3$ | 3B-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 1 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 2 & 1 \\ 0 & 0 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3B-1 | $3$ | $3$ | $C_6\times \He_3$ | 3B1 | 1A | $ \left(\begin{array}{rrrr} 1 & 2 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 2 \\ 0 & 0 & 1 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3C1 | $3$ | $3$ | $C_6\times \He_3$ | 3C-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 \\ 2 & 0 & 0 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3C-1 | $3$ | $3$ | $C_6\times \He_3$ | 3C1 | 1A | $ \left(\begin{array}{rrrr} 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 \\ 2 & 0 & 1 & 2 \\ 1 & 0 & 0 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3D1 | $3$ | $3$ | $C_6\times \He_3$ | 3D-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 0 & 1 & 2 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 2 & 2 \\ 2 & 0 & 2 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3D-1 | $3$ | $3$ | $C_6\times \He_3$ | 3D1 | 1A | $ \left(\begin{array}{rrrr} 0 & 0 & 2 & 1 \\ 0 & 1 & 0 & 0 \\ 2 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3E1 | $3$ | $3$ | $C_6\times \He_3$ | 3E-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 0 & 2 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 2 & 0 & 1 & 1 \end{array}\right) $ |
| $C_6.C_3^4$ | 3E-1 | $3$ | $3$ | $C_6\times \He_3$ | 3E1 | 1A | $ \left(\begin{array}{rrrr} 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 2 & 0 & 2 & 0 \\ 1 & 0 & 2 & 1 \end{array}\right) $ |
| $C_6.C_3^4$ | 3F1 | $3$ | $3$ | $C_6\times \He_3$ | 3F-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 2 & 2 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 \\ 2 & 2 & 0 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3F-1 | $3$ | $3$ | $C_6\times \He_3$ | 3F1 | 1A | $ \left(\begin{array}{rrrr} 0 & 2 & 0 & 2 \\ 0 & 1 & 0 & 0 \\ 2 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3G1 | $3$ | $3$ | $C_6\times \He_3$ | 3G-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 1 & 2 & 0 & 0 \\ 2 & 1 & 1 & 1 \end{array}\right) $ |
| $C_6.C_3^4$ | 3G-1 | $3$ | $3$ | $C_6\times \He_3$ | 3G1 | 1A | $ \left(\begin{array}{rrrr} 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 2 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3H1 | $3$ | $3$ | $C_6\times \He_3$ | 3H-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3H-1 | $3$ | $3$ | $C_6\times \He_3$ | 3H1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 2 & 1 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3I1 | $3$ | $3$ | $C_6\times \He_3$ | 3I-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 2 & 2 & 2 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 0 & 1 \end{array}\right) $ |
| $C_6.C_3^4$ | 3I-1 | $3$ | $3$ | $C_6\times \He_3$ | 3I1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 2 & 2 & 1 \\ 0 & 0 & 0 & 1 \end{array}\right) $ |
| $C_6.C_3^4$ | 3J1 | $3$ | $3$ | $C_6\times \He_3$ | 3J-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 2 & 2 & 2 \\ 0 & 2 & 2 & 1 \\ 0 & 2 & 1 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3J-1 | $3$ | $3$ | $C_6\times \He_3$ | 3J1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 1 & 0 & 2 \\ 0 & 1 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3K1 | $3$ | $3$ | $C_6\times \He_3$ | 3K-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 1 & 0 & 2 \\ 0 & 2 & 1 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3K-1 | $3$ | $3$ | $C_6\times \He_3$ | 3K1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 2 & 2 & 1 \\ 0 & 1 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3L1 | $3$ | $3$ | $C_6\times \He_3$ | 3L-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 1 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 2 & 1 \\ 0 & 0 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3L-1 | $3$ | $3$ | $C_6\times \He_3$ | 3L1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 2 & 2 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 2 \\ 0 & 0 & 1 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3M1 | $3$ | $3$ | $C_6\times \He_3$ | 3M-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 0 & 2 & 2 & 2 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3M-1 | $3$ | $3$ | $C_6\times \He_3$ | 3M1 | 1A | $ \left(\begin{array}{rrrr} 1 & 2 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \\ 0 & 2 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3N1 | $3$ | $3$ | $C_6\times \He_3$ | 3N-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 1 & 1 & 1 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 1 \end{array}\right) $ |
| $C_6.C_3^4$ | 3N-1 | $3$ | $3$ | $C_6\times \He_3$ | 3N1 | 1A | $ \left(\begin{array}{rrrr} 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 2 & 0 & 2 \\ 0 & 0 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3O1 | $3$ | $3$ | $C_6\times \He_3$ | 3O-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 0 & 0 & 1 \\ 0 & 2 & 2 & 2 \\ 1 & 1 & 0 & 0 \\ 2 & 0 & 0 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3O-1 | $3$ | $3$ | $C_6\times \He_3$ | 3O1 | 1A | $ \left(\begin{array}{rrrr} 0 & 0 & 0 & 2 \\ 0 & 0 & 1 & 1 \\ 2 & 2 & 2 & 0 \\ 1 & 0 & 0 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3P1 | $3$ | $3$ | $C_6\times \He_3$ | 3P-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 1 & 2 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 \\ 2 & 0 & 0 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3P-1 | $3$ | $3$ | $C_6\times \He_3$ | 3P1 | 1A | $ \left(\begin{array}{rrrr} 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 \\ 2 & 1 & 0 & 1 \\ 1 & 2 & 1 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3Q1 | $3$ | $3$ | $C_6\times \He_3$ | 3Q-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 0 & 2 & 0 \\ 0 & 2 & 2 & 2 \\ 1 & 0 & 0 & 0 \\ 2 & 1 & 0 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3Q-1 | $3$ | $3$ | $C_6\times \He_3$ | 3Q1 | 1A | $ \left(\begin{array}{rrrr} 0 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 \\ 2 & 0 & 2 & 0 \\ 1 & 2 & 0 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3R1 | $3$ | $3$ | $C_6\times \He_3$ | 3R-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 2 & 0 & 1 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 2 & 0 & 1 & 1 \end{array}\right) $ |
| $C_6.C_3^4$ | 3R-1 | $3$ | $3$ | $C_6\times \He_3$ | 3R1 | 1A | $ \left(\begin{array}{rrrr} 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 2 & 2 & 0 & 1 \\ 1 & 1 & 1 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3S1 | $3$ | $3$ | $C_6\times \He_3$ | 3S-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 1 & 0 & 0 \\ 0 & 2 & 2 & 2 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3S-1 | $3$ | $3$ | $C_6\times \He_3$ | 3S1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 2 & 2 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \\ 0 & 2 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3T1 | $3$ | $3$ | $C_6\times \He_3$ | 3T-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 1 & 1 \\ 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 2 & 0 & 1 \end{array}\right) $ |
| $C_6.C_3^4$ | 3T-1 | $3$ | $3$ | $C_6\times \He_3$ | 3T1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 2 & 2 \\ 0 & 1 & 0 & 0 \\ 0 & 2 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{array}\right) $ |
| $C_6.C_3^4$ | 3U1 | $3$ | $3$ | $C_6\times \He_3$ | 3U-1 | 1A | $ \left(\begin{array}{rrrr} 1 & 2 & 0 & 0 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 1 \end{array}\right) $ |
| $C_6.C_3^4$ | 3U-1 | $3$ | $3$ | $C_6\times \He_3$ | 3U1 | 1A | $ \left(\begin{array}{rrrr} 1 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 2 & 0 & 2 \\ 0 & 0 & 2 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3V1 | $3$ | $3$ | $C_6\times \He_3$ | 3V-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 1 & 2 & 0 \\ 0 & 2 & 2 & 2 \\ 1 & 1 & 0 & 0 \\ 2 & 0 & 0 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3V-1 | $3$ | $3$ | $C_6\times \He_3$ | 3V1 | 1A | $ \left(\begin{array}{rrrr} 0 & 0 & 0 & 2 \\ 0 & 0 & 1 & 1 \\ 2 & 0 & 1 & 2 \\ 1 & 2 & 1 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3W1 | $3$ | $3$ | $C_6\times \He_3$ | 3W-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 0 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 1 & 2 & 2 & 2 \\ 2 & 0 & 0 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3W-1 | $3$ | $3$ | $C_6\times \He_3$ | 3W1 | 1A | $ \left(\begin{array}{rrrr} 0 & 0 & 0 & 2 \\ 0 & 2 & 2 & 2 \\ 2 & 1 & 0 & 1 \\ 1 & 0 & 0 & 2 \end{array}\right) $ |
| $C_6.C_3^4$ | 3X1 | $3$ | $3$ | $C_6\times \He_3$ | 3X-1 | 1A | $ \left(\begin{array}{rrrr} 2 & 2 & 1 & 2 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 \\ 2 & 0 & 0 & 0 \end{array}\right) $ |
| $C_6.C_3^4$ | 3X-1 | $3$ | $3$ | $C_6\times \He_3$ | 3X1 | 1A | $ \left(\begin{array}{rrrr} 0 & 0 & 0 & 2 \\ 0 & 1 & 0 & 0 \\ 2 & 2 & 2 & 0 \\ 1 & 1 & 2 & 1 \end{array}\right) $ |