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Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{15}=1, b^{a}=b^{14} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | ||||||
| $D_{15}$ | 1A | $1$ | $1$ | $D_{15}$ | 1A | 1A | 1A | $1$ |
| $D_{15}$ | 2A | $2$ | $15$ | $C_2$ | 1A | 2A | 2A | $a$ |
| $D_{15}$ | 3A | $3$ | $2$ | $C_{15}$ | 3A | 1A | 3A | $b^{5}$ |
| $D_{15}$ | 5A1 | $5$ | $2$ | $C_{15}$ | 5A2 | 5A2 | 1A | $b^{3}$ |
| $D_{15}$ | 5A2 | $5$ | $2$ | $C_{15}$ | 5A1 | 5A1 | 1A | $b^{6}$ |
| $D_{15}$ | 15A1 | $15$ | $2$ | $C_{15}$ | 15A2 | 5A1 | 3A | $b$ |
| $D_{15}$ | 15A2 | $15$ | $2$ | $C_{15}$ | 15A4 | 5A2 | 3A | $b^{2}$ |
| $D_{15}$ | 15A4 | $15$ | $2$ | $C_{15}$ | 15A7 | 5A1 | 3A | $b^{4}$ |
| $D_{15}$ | 15A7 | $15$ | $2$ | $C_{15}$ | 15A1 | 5A2 | 3A | $b^{7}$ |