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Results (12 matches)
Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{18}=1, b^{a}=b^{17} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $D_{18}$ | 1A | $1$ | $1$ | $D_{18}$ | 1A | 1A | $1$ |
| $D_{18}$ | 2A | $2$ | $1$ | $D_{18}$ | 1A | 2A | $b^{9}$ |
| $D_{18}$ | 2B | $2$ | $9$ | $C_2^2$ | 1A | 2B | $ab^{16}$ |
| $D_{18}$ | 2C | $2$ | $9$ | $C_2^2$ | 1A | 2C | $ab^{7}$ |
| $D_{18}$ | 3A | $3$ | $2$ | $C_{18}$ | 3A | 1A | $b^{6}$ |
| $D_{18}$ | 6A | $6$ | $2$ | $C_{18}$ | 3A | 2A | $b^{3}$ |
| $D_{18}$ | 9A1 | $9$ | $2$ | $C_{18}$ | 9A2 | 3A | $b^{2}$ |
| $D_{18}$ | 9A2 | $9$ | $2$ | $C_{18}$ | 9A4 | 3A | $b^{4}$ |
| $D_{18}$ | 9A4 | $9$ | $2$ | $C_{18}$ | 9A1 | 3A | $b^{8}$ |
| $D_{18}$ | 18A1 | $18$ | $2$ | $C_{18}$ | 9A1 | 6A | $b$ |
| $D_{18}$ | 18A5 | $18$ | $2$ | $C_{18}$ | 9A4 | 6A | $b^{13}$ |
| $D_{18}$ | 18A7 | $18$ | $2$ | $C_{18}$ | 9A2 | 6A | $b^{7}$ |