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Elements of the group are displayed as matrices in $\GL_{2}(\F_{199})$.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 11P | ||||||
| $C_{99}:D_4$ | 1A | $1$ | $1$ | $C_{99}:D_4$ | 1A | 1A | 1A | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right) $ |
| $C_{99}:D_4$ | 2A | $2$ | $1$ | $C_{99}:D_4$ | 1A | 2A | 2A | $ \left(\begin{array}{rr} 198 & 0 \\ 0 & 198 \end{array}\right) $ |
| $C_{99}:D_4$ | 2B | $2$ | $2$ | $C_2\times C_{198}$ | 1A | 2B | 2B | $ \left(\begin{array}{rr} 1 & 0 \\ 0 & 198 \end{array}\right) $ |
| $C_{99}:D_4$ | 2C | $2$ | $22$ | $C_2\times C_{18}$ | 1A | 2C | 2C | $ \left(\begin{array}{rr} 0 & 125 \\ 121 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 3A1 | $3$ | $1$ | $C_{99}:D_4$ | 3A-1 | 1A | 3A-1 | $ \left(\begin{array}{rr} 92 & 0 \\ 0 & 92 \end{array}\right) $ |
| $C_{99}:D_4$ | 3A-1 | $3$ | $1$ | $C_{99}:D_4$ | 3A1 | 1A | 3A1 | $ \left(\begin{array}{rr} 106 & 0 \\ 0 & 106 \end{array}\right) $ |
| $C_{99}:D_4$ | 4A | $4$ | $22$ | $C_{36}$ | 2A | 4A | 4A | $ \left(\begin{array}{rr} 0 & 125 \\ 78 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 6A1 | $6$ | $1$ | $C_{99}:D_4$ | 3A-1 | 2A | 6A-1 | $ \left(\begin{array}{rr} 107 & 0 \\ 0 & 107 \end{array}\right) $ |
| $C_{99}:D_4$ | 6A-1 | $6$ | $1$ | $C_{99}:D_4$ | 3A1 | 2A | 6A1 | $ \left(\begin{array}{rr} 93 & 0 \\ 0 & 93 \end{array}\right) $ |
| $C_{99}:D_4$ | 6B1 | $6$ | $2$ | $C_2\times C_{198}$ | 3A-1 | 2B | 6B-1 | $ \left(\begin{array}{rr} 92 & 0 \\ 0 & 107 \end{array}\right) $ |
| $C_{99}:D_4$ | 6B-1 | $6$ | $2$ | $C_2\times C_{198}$ | 3A1 | 2B | 6B1 | $ \left(\begin{array}{rr} 106 & 0 \\ 0 & 93 \end{array}\right) $ |
| $C_{99}:D_4$ | 6C1 | $6$ | $22$ | $C_2\times C_{18}$ | 3A1 | 2C | 6C-1 | $ \left(\begin{array}{rr} 0 & 116 \\ 90 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 6C-1 | $6$ | $22$ | $C_2\times C_{18}$ | 3A-1 | 2C | 6C1 | $ \left(\begin{array}{rr} 0 & 157 \\ 187 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 9A1 | $9$ | $1$ | $C_{99}:D_4$ | 9A2 | 3A1 | 9A-4 | $ \left(\begin{array}{rr} 58 & 0 \\ 0 & 58 \end{array}\right) $ |
| $C_{99}:D_4$ | 9A-1 | $9$ | $1$ | $C_{99}:D_4$ | 9A-2 | 3A-1 | 9A4 | $ \left(\begin{array}{rr} 175 & 0 \\ 0 & 175 \end{array}\right) $ |
| $C_{99}:D_4$ | 9A2 | $9$ | $1$ | $C_{99}:D_4$ | 9A4 | 3A-1 | 9A1 | $ \left(\begin{array}{rr} 180 & 0 \\ 0 & 180 \end{array}\right) $ |
| $C_{99}:D_4$ | 9A-2 | $9$ | $1$ | $C_{99}:D_4$ | 9A-4 | 3A1 | 9A-1 | $ \left(\begin{array}{rr} 178 & 0 \\ 0 & 178 \end{array}\right) $ |
| $C_{99}:D_4$ | 9A4 | $9$ | $1$ | $C_{99}:D_4$ | 9A-1 | 3A1 | 9A2 | $ \left(\begin{array}{rr} 162 & 0 \\ 0 & 162 \end{array}\right) $ |
| $C_{99}:D_4$ | 9A-4 | $9$ | $1$ | $C_{99}:D_4$ | 9A1 | 3A-1 | 9A-2 | $ \left(\begin{array}{rr} 43 & 0 \\ 0 & 43 \end{array}\right) $ |
| $C_{99}:D_4$ | 11A1 | $11$ | $2$ | $C_2\times C_{198}$ | 11A2 | 11A3 | 11A5 | $ \left(\begin{array}{rr} 125 & 0 \\ 0 & 121 \end{array}\right) $ |
| $C_{99}:D_4$ | 11A2 | $11$ | $2$ | $C_2\times C_{198}$ | 11A4 | 11A5 | 11A1 | $ \left(\begin{array}{rr} 103 & 0 \\ 0 & 114 \end{array}\right) $ |
| $C_{99}:D_4$ | 11A3 | $11$ | $2$ | $C_2\times C_{198}$ | 11A5 | 11A2 | 11A4 | $ \left(\begin{array}{rr} 139 & 0 \\ 0 & 63 \end{array}\right) $ |
| $C_{99}:D_4$ | 11A4 | $11$ | $2$ | $C_2\times C_{198}$ | 11A3 | 11A1 | 11A2 | $ \left(\begin{array}{rr} 62 & 0 \\ 0 & 61 \end{array}\right) $ |
| $C_{99}:D_4$ | 11A5 | $11$ | $2$ | $C_2\times C_{198}$ | 11A1 | 11A4 | 11A3 | $ \left(\begin{array}{rr} 188 & 0 \\ 0 & 18 \end{array}\right) $ |
| $C_{99}:D_4$ | 12A1 | $12$ | $22$ | $C_{36}$ | 6A1 | 4A | 12A-1 | $ \left(\begin{array}{rr} 0 & 83 \\ 90 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 12A-1 | $12$ | $22$ | $C_{36}$ | 6A-1 | 4A | 12A1 | $ \left(\begin{array}{rr} 0 & 157 \\ 12 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 18A1 | $18$ | $1$ | $C_{99}:D_4$ | 9A2 | 6A1 | 18A5 | $ \left(\begin{array}{rr} 141 & 0 \\ 0 & 141 \end{array}\right) $ |
| $C_{99}:D_4$ | 18A-1 | $18$ | $1$ | $C_{99}:D_4$ | 9A-2 | 6A-1 | 18A-5 | $ \left(\begin{array}{rr} 24 & 0 \\ 0 & 24 \end{array}\right) $ |
| $C_{99}:D_4$ | 18A5 | $18$ | $1$ | $C_{99}:D_4$ | 9A1 | 6A-1 | 18A7 | $ \left(\begin{array}{rr} 156 & 0 \\ 0 & 156 \end{array}\right) $ |
| $C_{99}:D_4$ | 18A-5 | $18$ | $1$ | $C_{99}:D_4$ | 9A-1 | 6A1 | 18A-7 | $ \left(\begin{array}{rr} 37 & 0 \\ 0 & 37 \end{array}\right) $ |
| $C_{99}:D_4$ | 18A7 | $18$ | $1$ | $C_{99}:D_4$ | 9A-4 | 6A1 | 18A-1 | $ \left(\begin{array}{rr} 21 & 0 \\ 0 & 21 \end{array}\right) $ |
| $C_{99}:D_4$ | 18A-7 | $18$ | $1$ | $C_{99}:D_4$ | 9A4 | 6A-1 | 18A1 | $ \left(\begin{array}{rr} 19 & 0 \\ 0 & 19 \end{array}\right) $ |
| $C_{99}:D_4$ | 18B1 | $18$ | $2$ | $C_2\times C_{198}$ | 9A2 | 6B1 | 18B5 | $ \left(\begin{array}{rr} 58 & 0 \\ 0 & 141 \end{array}\right) $ |
| $C_{99}:D_4$ | 18B-1 | $18$ | $2$ | $C_2\times C_{198}$ | 9A-2 | 6B-1 | 18B-5 | $ \left(\begin{array}{rr} 175 & 0 \\ 0 & 24 \end{array}\right) $ |
| $C_{99}:D_4$ | 18B5 | $18$ | $2$ | $C_2\times C_{198}$ | 9A1 | 6B-1 | 18B7 | $ \left(\begin{array}{rr} 43 & 0 \\ 0 & 156 \end{array}\right) $ |
| $C_{99}:D_4$ | 18B-5 | $18$ | $2$ | $C_2\times C_{198}$ | 9A-1 | 6B1 | 18B-7 | $ \left(\begin{array}{rr} 162 & 0 \\ 0 & 37 \end{array}\right) $ |
| $C_{99}:D_4$ | 18B7 | $18$ | $2$ | $C_2\times C_{198}$ | 9A-4 | 6B1 | 18B-1 | $ \left(\begin{array}{rr} 178 & 0 \\ 0 & 21 \end{array}\right) $ |
| $C_{99}:D_4$ | 18B-7 | $18$ | $2$ | $C_2\times C_{198}$ | 9A4 | 6B-1 | 18B1 | $ \left(\begin{array}{rr} 180 & 0 \\ 0 & 19 \end{array}\right) $ |
| $C_{99}:D_4$ | 18C1 | $18$ | $22$ | $C_2\times C_{18}$ | 9A1 | 6C1 | 18C5 | $ \left(\begin{array}{rr} 0 & 2 \\ 29 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 18C-1 | $18$ | $22$ | $C_2\times C_{18}$ | 9A-1 | 6C-1 | 18C-5 | $ \left(\begin{array}{rr} 0 & 9 \\ 130 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 18C5 | $18$ | $22$ | $C_2\times C_{18}$ | 9A-4 | 6C-1 | 18C7 | $ \left(\begin{array}{rr} 0 & 6 \\ 173 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 18C-5 | $18$ | $22$ | $C_2\times C_{18}$ | 9A4 | 6C1 | 18C-7 | $ \left(\begin{array}{rr} 0 & 3 \\ 54 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 18C7 | $18$ | $22$ | $C_2\times C_{18}$ | 9A-2 | 6C1 | 18C-1 | $ \left(\begin{array}{rr} 0 & 15 \\ 118 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 18C-7 | $18$ | $22$ | $C_2\times C_{18}$ | 9A2 | 6C-1 | 18C1 | $ \left(\begin{array}{rr} 0 & 4 \\ 45 & 0 \end{array}\right) $ |
| $C_{99}:D_4$ | 22A1 | $22$ | $2$ | $C_2\times C_{198}$ | 11A1 | 22A3 | 22A5 | $ \left(\begin{array}{rr} 181 & 0 \\ 0 & 11 \end{array}\right) $ |
| $C_{99}:D_4$ | 22A3 | $22$ | $2$ | $C_2\times C_{198}$ | 11A3 | 22A9 | 22A7 | $ \left(\begin{array}{rr} 138 & 0 \\ 0 & 137 \end{array}\right) $ |
| $C_{99}:D_4$ | 22A5 | $22$ | $2$ | $C_2\times C_{198}$ | 11A5 | 22A7 | 22A3 | $ \left(\begin{array}{rr} 136 & 0 \\ 0 & 60 \end{array}\right) $ |
| $C_{99}:D_4$ | 22A7 | $22$ | $2$ | $C_2\times C_{198}$ | 11A4 | 22A1 | 22A9 | $ \left(\begin{array}{rr} 85 & 0 \\ 0 & 96 \end{array}\right) $ |
| $C_{99}:D_4$ | 22A9 | $22$ | $2$ | $C_2\times C_{198}$ | 11A2 | 22A5 | 22A1 | $ \left(\begin{array}{rr} 78 & 0 \\ 0 & 74 \end{array}\right) $ |
| $C_{99}:D_4$ | 22B1 | $22$ | $2$ | $C_2\times C_{198}$ | 11A4 | 22B3 | 22B5 | $ \left(\begin{array}{rr} 114 & 0 \\ 0 & 96 \end{array}\right) $ |