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Elements of the group are displayed as words in the presentation $\langle a \mid a^{1737}=1 \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 3P | 193P | ||||||
| $C_{1737}$ | 1A | $1$ | $1$ | $C_{1737}$ | 1A | 1A | $1$ |
| $C_{1737}$ | 3A1 | $3$ | $1$ | $C_{1737}$ | 3A-1 | 1A | $a^{579}$ |
| $C_{1737}$ | 3A-1 | $3$ | $1$ | $C_{1737}$ | 3A1 | 1A | $a^{1158}$ |
| $C_{1737}$ | 9A1 | $9$ | $1$ | $C_{1737}$ | 9A2 | 3A1 | $a^{193}$ |
| $C_{1737}$ | 9A-1 | $9$ | $1$ | $C_{1737}$ | 9A-2 | 3A-1 | $a^{1544}$ |
| $C_{1737}$ | 9A2 | $9$ | $1$ | $C_{1737}$ | 9A4 | 3A-1 | $a^{386}$ |
| $C_{1737}$ | 9A-2 | $9$ | $1$ | $C_{1737}$ | 9A-4 | 3A1 | $a^{1351}$ |
| $C_{1737}$ | 9A4 | $9$ | $1$ | $C_{1737}$ | 9A-1 | 3A1 | $a^{772}$ |
| $C_{1737}$ | 9A-4 | $9$ | $1$ | $C_{1737}$ | 9A1 | 3A-1 | $a^{965}$ |
| $C_{1737}$ | 193A1 | $193$ | $1$ | $C_{1737}$ | 193A2 | 193A3 | $a^{9}$ |
| $C_{1737}$ | 193A-1 | $193$ | $1$ | $C_{1737}$ | 193A-2 | 193A-3 | $a^{1728}$ |
| $C_{1737}$ | 193A2 | $193$ | $1$ | $C_{1737}$ | 193A4 | 193A6 | $a^{18}$ |
| $C_{1737}$ | 193A-2 | $193$ | $1$ | $C_{1737}$ | 193A-4 | 193A-6 | $a^{1719}$ |
| $C_{1737}$ | 193A3 | $193$ | $1$ | $C_{1737}$ | 193A6 | 193A9 | $a^{27}$ |
| $C_{1737}$ | 193A-3 | $193$ | $1$ | $C_{1737}$ | 193A-6 | 193A-9 | $a^{1710}$ |
| $C_{1737}$ | 193A4 | $193$ | $1$ | $C_{1737}$ | 193A8 | 193A12 | $a^{36}$ |
| $C_{1737}$ | 193A-4 | $193$ | $1$ | $C_{1737}$ | 193A-8 | 193A-12 | $a^{1701}$ |
| $C_{1737}$ | 193A5 | $193$ | $1$ | $C_{1737}$ | 193A10 | 193A15 | $a^{45}$ |
| $C_{1737}$ | 193A-5 | $193$ | $1$ | $C_{1737}$ | 193A-10 | 193A-15 | $a^{1692}$ |
| $C_{1737}$ | 193A6 | $193$ | $1$ | $C_{1737}$ | 193A12 | 193A18 | $a^{54}$ |
| $C_{1737}$ | 193A-6 | $193$ | $1$ | $C_{1737}$ | 193A-12 | 193A-18 | $a^{1683}$ |
| $C_{1737}$ | 193A7 | $193$ | $1$ | $C_{1737}$ | 193A14 | 193A21 | $a^{63}$ |
| $C_{1737}$ | 193A-7 | $193$ | $1$ | $C_{1737}$ | 193A-14 | 193A-21 | $a^{1674}$ |
| $C_{1737}$ | 193A8 | $193$ | $1$ | $C_{1737}$ | 193A16 | 193A24 | $a^{72}$ |
| $C_{1737}$ | 193A-8 | $193$ | $1$ | $C_{1737}$ | 193A-16 | 193A-24 | $a^{1665}$ |
| $C_{1737}$ | 193A9 | $193$ | $1$ | $C_{1737}$ | 193A18 | 193A27 | $a^{81}$ |
| $C_{1737}$ | 193A-9 | $193$ | $1$ | $C_{1737}$ | 193A-18 | 193A-27 | $a^{1656}$ |
| $C_{1737}$ | 193A10 | $193$ | $1$ | $C_{1737}$ | 193A20 | 193A30 | $a^{90}$ |
| $C_{1737}$ | 193A-10 | $193$ | $1$ | $C_{1737}$ | 193A-20 | 193A-30 | $a^{1647}$ |
| $C_{1737}$ | 193A11 | $193$ | $1$ | $C_{1737}$ | 193A22 | 193A33 | $a^{99}$ |
| $C_{1737}$ | 193A-11 | $193$ | $1$ | $C_{1737}$ | 193A-22 | 193A-33 | $a^{1638}$ |
| $C_{1737}$ | 193A12 | $193$ | $1$ | $C_{1737}$ | 193A24 | 193A36 | $a^{108}$ |
| $C_{1737}$ | 193A-12 | $193$ | $1$ | $C_{1737}$ | 193A-24 | 193A-36 | $a^{1629}$ |
| $C_{1737}$ | 193A13 | $193$ | $1$ | $C_{1737}$ | 193A26 | 193A39 | $a^{117}$ |
| $C_{1737}$ | 193A-13 | $193$ | $1$ | $C_{1737}$ | 193A-26 | 193A-39 | $a^{1620}$ |
| $C_{1737}$ | 193A14 | $193$ | $1$ | $C_{1737}$ | 193A28 | 193A42 | $a^{126}$ |
| $C_{1737}$ | 193A-14 | $193$ | $1$ | $C_{1737}$ | 193A-28 | 193A-42 | $a^{1611}$ |
| $C_{1737}$ | 193A15 | $193$ | $1$ | $C_{1737}$ | 193A30 | 193A45 | $a^{135}$ |
| $C_{1737}$ | 193A-15 | $193$ | $1$ | $C_{1737}$ | 193A-30 | 193A-45 | $a^{1602}$ |
| $C_{1737}$ | 193A16 | $193$ | $1$ | $C_{1737}$ | 193A32 | 193A48 | $a^{144}$ |
| $C_{1737}$ | 193A-16 | $193$ | $1$ | $C_{1737}$ | 193A-32 | 193A-48 | $a^{1593}$ |
| $C_{1737}$ | 193A17 | $193$ | $1$ | $C_{1737}$ | 193A34 | 193A51 | $a^{153}$ |
| $C_{1737}$ | 193A-17 | $193$ | $1$ | $C_{1737}$ | 193A-34 | 193A-51 | $a^{1584}$ |
| $C_{1737}$ | 193A18 | $193$ | $1$ | $C_{1737}$ | 193A36 | 193A54 | $a^{162}$ |
| $C_{1737}$ | 193A-18 | $193$ | $1$ | $C_{1737}$ | 193A-36 | 193A-54 | $a^{1575}$ |
| $C_{1737}$ | 193A19 | $193$ | $1$ | $C_{1737}$ | 193A38 | 193A57 | $a^{171}$ |
| $C_{1737}$ | 193A-19 | $193$ | $1$ | $C_{1737}$ | 193A-38 | 193A-57 | $a^{1566}$ |
| $C_{1737}$ | 193A20 | $193$ | $1$ | $C_{1737}$ | 193A40 | 193A60 | $a^{180}$ |
| $C_{1737}$ | 193A-20 | $193$ | $1$ | $C_{1737}$ | 193A-40 | 193A-60 | $a^{1557}$ |
| $C_{1737}$ | 193A21 | $193$ | $1$ | $C_{1737}$ | 193A42 | 193A63 | $a^{189}$ |