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Elements of the group are displayed as matrices in $\GL_{2}(\Z/{121}\Z)$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||
|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 11P | ||||||
| $C_5\times C_{11}\wr S_3$ | 1A | $1$ | $1$ | $C_5\times C_{11}\wr S_3$ | 1A | 1A | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 2A | $2$ | $33$ | $C_{11}\times C_{110}$ | 1A | 2A | 2A | 2A | $ \left(\begin{array}{rr} 120 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 3A | $3$ | $242$ | $C_{165}$ | 3A | 1A | 3A | 3A | $ \left(\begin{array}{rr} 49 & 89 \\ 35 & 71 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 5A1 | $5$ | $1$ | $C_5\times C_{11}\wr S_3$ | 5A2 | 5A-2 | 1A | 5A1 | $ \left(\begin{array}{rr} 81 & 0 \\ 0 & 81 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 5A-1 | $5$ | $1$ | $C_5\times C_{11}\wr S_3$ | 5A-2 | 5A2 | 1A | 5A-1 | $ \left(\begin{array}{rr} 3 & 0 \\ 0 & 3 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 5A2 | $5$ | $1$ | $C_5\times C_{11}\wr S_3$ | 5A-1 | 5A1 | 1A | 5A2 | $ \left(\begin{array}{rr} 27 & 0 \\ 0 & 27 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 5A-2 | $5$ | $1$ | $C_5\times C_{11}\wr S_3$ | 5A1 | 5A-1 | 1A | 5A-2 | $ \left(\begin{array}{rr} 9 & 0 \\ 0 & 9 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 10A1 | $10$ | $33$ | $C_{11}\times C_{110}$ | 5A2 | 10A3 | 2A | 10A1 | $ \left(\begin{array}{rr} 40 & 0 \\ 0 & 81 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 10A-1 | $10$ | $33$ | $C_{11}\times C_{110}$ | 5A-2 | 10A-3 | 2A | 10A-1 | $ \left(\begin{array}{rr} 118 & 0 \\ 0 & 3 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 10A3 | $10$ | $33$ | $C_{11}\times C_{110}$ | 5A1 | 10A-1 | 2A | 10A3 | $ \left(\begin{array}{rr} 112 & 0 \\ 0 & 9 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 10A-3 | $10$ | $33$ | $C_{11}\times C_{110}$ | 5A-1 | 10A1 | 2A | 10A-3 | $ \left(\begin{array}{rr} 94 & 0 \\ 0 & 27 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11A1 | $11$ | $1$ | $C_5\times C_{11}\wr S_3$ | 11A2 | 11A3 | 11A5 | 1A | $ \left(\begin{array}{rr} 78 & 0 \\ 0 & 78 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11A-1 | $11$ | $1$ | $C_5\times C_{11}\wr S_3$ | 11A-2 | 11A-3 | 11A-5 | 1A | $ \left(\begin{array}{rr} 45 & 0 \\ 0 & 45 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11A2 | $11$ | $1$ | $C_5\times C_{11}\wr S_3$ | 11A4 | 11A-5 | 11A-1 | 1A | $ \left(\begin{array}{rr} 34 & 0 \\ 0 & 34 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11A-2 | $11$ | $1$ | $C_5\times C_{11}\wr S_3$ | 11A-4 | 11A5 | 11A1 | 1A | $ \left(\begin{array}{rr} 89 & 0 \\ 0 & 89 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11A3 | $11$ | $1$ | $C_5\times C_{11}\wr S_3$ | 11A-5 | 11A-2 | 11A4 | 1A | $ \left(\begin{array}{rr} 111 & 0 \\ 0 & 111 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11A-3 | $11$ | $1$ | $C_5\times C_{11}\wr S_3$ | 11A5 | 11A2 | 11A-4 | 1A | $ \left(\begin{array}{rr} 12 & 0 \\ 0 & 12 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11A4 | $11$ | $1$ | $C_5\times C_{11}\wr S_3$ | 11A-3 | 11A1 | 11A-2 | 1A | $ \left(\begin{array}{rr} 67 & 0 \\ 0 & 67 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11A-4 | $11$ | $1$ | $C_5\times C_{11}\wr S_3$ | 11A3 | 11A-1 | 11A2 | 1A | $ \left(\begin{array}{rr} 56 & 0 \\ 0 & 56 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11A5 | $11$ | $1$ | $C_5\times C_{11}\wr S_3$ | 11A-1 | 11A4 | 11A3 | 1A | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11A-5 | $11$ | $1$ | $C_5\times C_{11}\wr S_3$ | 11A1 | 11A-4 | 11A-3 | 1A | $ \left(\begin{array}{rr} 100 & 0 \\ 0 & 100 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11B1 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11B2 | 11B3 | 11B5 | 1A | $ \left(\begin{array}{rr} 34 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11B-1 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11B-2 | 11B-3 | 11B-5 | 1A | $ \left(\begin{array}{rr} 89 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11B2 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11B4 | 11B-5 | 11B-1 | 1A | $ \left(\begin{array}{rr} 67 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11B-2 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11B-4 | 11B5 | 11B1 | 1A | $ \left(\begin{array}{rr} 56 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11B3 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11B-5 | 11B-2 | 11B4 | 1A | $ \left(\begin{array}{rr} 100 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11B-3 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11B5 | 11B2 | 11B-4 | 1A | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11B4 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11B-3 | 11B1 | 11B-2 | 1A | $ \left(\begin{array}{rr} 12 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11B-4 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11B3 | 11B-1 | 11B2 | 1A | $ \left(\begin{array}{rr} 111 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11B5 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11B-1 | 11B4 | 11B3 | 1A | $ \left(\begin{array}{rr} 45 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11B-5 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11B1 | 11B-4 | 11B-3 | 1A | $ \left(\begin{array}{rr} 78 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11C1 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11C2 | 11C3 | 11C5 | 1A | $ \left(\begin{array}{rr} 67 & 0 \\ 0 & 89 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11C-1 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11C-2 | 11C-3 | 11C-5 | 1A | $ \left(\begin{array}{rr} 56 & 0 \\ 0 & 34 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11C2 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11C4 | 11C-5 | 11C-1 | 1A | $ \left(\begin{array}{rr} 12 & 0 \\ 0 & 56 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11C-2 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11C-4 | 11C5 | 11C1 | 1A | $ \left(\begin{array}{rr} 111 & 0 \\ 0 & 67 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11C3 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11C-5 | 11C-2 | 11C4 | 1A | $ \left(\begin{array}{rr} 78 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11C-3 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11C5 | 11C2 | 11C-4 | 1A | $ \left(\begin{array}{rr} 45 & 0 \\ 0 & 100 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11C4 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11C-3 | 11C1 | 11C-2 | 1A | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 111 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11C-4 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11C3 | 11C-1 | 11C2 | 1A | $ \left(\begin{array}{rr} 100 & 0 \\ 0 & 12 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11C5 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11C-1 | 11C4 | 11C3 | 1A | $ \left(\begin{array}{rr} 89 & 0 \\ 0 & 78 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11C-5 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11C1 | 11C-4 | 11C-3 | 1A | $ \left(\begin{array}{rr} 34 & 0 \\ 0 & 45 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11D1 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11D2 | 11D3 | 11D5 | 1A | $ \left(\begin{array}{rr} 100 & 0 \\ 0 & 56 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11D-1 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11D-2 | 11D-3 | 11D-5 | 1A | $ \left(\begin{array}{rr} 23 & 0 \\ 0 & 67 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11D2 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11D4 | 11D-5 | 11D-1 | 1A | $ \left(\begin{array}{rr} 78 & 0 \\ 0 & 111 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11D-2 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11D-4 | 11D5 | 11D1 | 1A | $ \left(\begin{array}{rr} 45 & 0 \\ 0 & 12 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11D3 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11D-5 | 11D-2 | 11D4 | 1A | $ \left(\begin{array}{rr} 56 & 0 \\ 0 & 45 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11D-3 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11D5 | 11D2 | 11D-4 | 1A | $ \left(\begin{array}{rr} 67 & 0 \\ 0 & 78 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11D4 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11D-3 | 11D1 | 11D-2 | 1A | $ \left(\begin{array}{rr} 34 & 0 \\ 0 & 100 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11D-4 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11D3 | 11D-1 | 11D2 | 1A | $ \left(\begin{array}{rr} 89 & 0 \\ 0 & 23 \end{array}\right) $ |
| $C_5\times C_{11}\wr S_3$ | 11D5 | $11$ | $3$ | $C_{11}^2:C_{110}$ | 11D-1 | 11D4 | 11D3 | 1A | $ \left(\begin{array}{rr} 12 & 0 \\ 0 & 34 \end{array}\right) $ |