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Elements of the group are displayed as words in the presentation of the abelian group $\langle a, b \mid a^{173}=b^{173}=1 \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 173P | ||||||
| $C_{173}^2$ | 1A | $1$ | $1$ | $C_{173}^2$ | 1A | $1$ |
| $C_{173}^2$ | 173A1 | $173$ | $1$ | $C_{173}^2$ | 173A2 | $b$ |
| $C_{173}^2$ | 173A-1 | $173$ | $1$ | $C_{173}^2$ | 173A-2 | $b^{172}$ |
| $C_{173}^2$ | 173A2 | $173$ | $1$ | $C_{173}^2$ | 173A4 | $b^{2}$ |
| $C_{173}^2$ | 173A-2 | $173$ | $1$ | $C_{173}^2$ | 173A-4 | $b^{171}$ |
| $C_{173}^2$ | 173A3 | $173$ | $1$ | $C_{173}^2$ | 173A6 | $b^{3}$ |
| $C_{173}^2$ | 173A-3 | $173$ | $1$ | $C_{173}^2$ | 173A-6 | $b^{170}$ |
| $C_{173}^2$ | 173A4 | $173$ | $1$ | $C_{173}^2$ | 173A8 | $b^{4}$ |
| $C_{173}^2$ | 173A-4 | $173$ | $1$ | $C_{173}^2$ | 173A-8 | $b^{169}$ |
| $C_{173}^2$ | 173A5 | $173$ | $1$ | $C_{173}^2$ | 173A10 | $b^{5}$ |
| $C_{173}^2$ | 173A-5 | $173$ | $1$ | $C_{173}^2$ | 173A-10 | $b^{168}$ |
| $C_{173}^2$ | 173A6 | $173$ | $1$ | $C_{173}^2$ | 173A12 | $b^{6}$ |
| $C_{173}^2$ | 173A-6 | $173$ | $1$ | $C_{173}^2$ | 173A-12 | $b^{167}$ |
| $C_{173}^2$ | 173A7 | $173$ | $1$ | $C_{173}^2$ | 173A14 | $b^{7}$ |
| $C_{173}^2$ | 173A-7 | $173$ | $1$ | $C_{173}^2$ | 173A-14 | $b^{166}$ |
| $C_{173}^2$ | 173A8 | $173$ | $1$ | $C_{173}^2$ | 173A16 | $b^{8}$ |
| $C_{173}^2$ | 173A-8 | $173$ | $1$ | $C_{173}^2$ | 173A-16 | $b^{165}$ |
| $C_{173}^2$ | 173A9 | $173$ | $1$ | $C_{173}^2$ | 173A18 | $b^{9}$ |
| $C_{173}^2$ | 173A-9 | $173$ | $1$ | $C_{173}^2$ | 173A-18 | $b^{164}$ |
| $C_{173}^2$ | 173A10 | $173$ | $1$ | $C_{173}^2$ | 173A20 | $b^{10}$ |
| $C_{173}^2$ | 173A-10 | $173$ | $1$ | $C_{173}^2$ | 173A-20 | $b^{163}$ |
| $C_{173}^2$ | 173A11 | $173$ | $1$ | $C_{173}^2$ | 173A22 | $b^{11}$ |
| $C_{173}^2$ | 173A-11 | $173$ | $1$ | $C_{173}^2$ | 173A-22 | $b^{162}$ |
| $C_{173}^2$ | 173A12 | $173$ | $1$ | $C_{173}^2$ | 173A24 | $b^{12}$ |
| $C_{173}^2$ | 173A-12 | $173$ | $1$ | $C_{173}^2$ | 173A-24 | $b^{161}$ |
| $C_{173}^2$ | 173A13 | $173$ | $1$ | $C_{173}^2$ | 173A26 | $b^{13}$ |
| $C_{173}^2$ | 173A-13 | $173$ | $1$ | $C_{173}^2$ | 173A-26 | $b^{160}$ |
| $C_{173}^2$ | 173A14 | $173$ | $1$ | $C_{173}^2$ | 173A28 | $b^{14}$ |
| $C_{173}^2$ | 173A-14 | $173$ | $1$ | $C_{173}^2$ | 173A-28 | $b^{159}$ |
| $C_{173}^2$ | 173A15 | $173$ | $1$ | $C_{173}^2$ | 173A30 | $b^{15}$ |
| $C_{173}^2$ | 173A-15 | $173$ | $1$ | $C_{173}^2$ | 173A-30 | $b^{158}$ |
| $C_{173}^2$ | 173A16 | $173$ | $1$ | $C_{173}^2$ | 173A32 | $b^{16}$ |
| $C_{173}^2$ | 173A-16 | $173$ | $1$ | $C_{173}^2$ | 173A-32 | $b^{157}$ |
| $C_{173}^2$ | 173A17 | $173$ | $1$ | $C_{173}^2$ | 173A34 | $b^{17}$ |
| $C_{173}^2$ | 173A-17 | $173$ | $1$ | $C_{173}^2$ | 173A-34 | $b^{156}$ |
| $C_{173}^2$ | 173A18 | $173$ | $1$ | $C_{173}^2$ | 173A36 | $b^{18}$ |
| $C_{173}^2$ | 173A-18 | $173$ | $1$ | $C_{173}^2$ | 173A-36 | $b^{155}$ |
| $C_{173}^2$ | 173A19 | $173$ | $1$ | $C_{173}^2$ | 173A38 | $b^{19}$ |
| $C_{173}^2$ | 173A-19 | $173$ | $1$ | $C_{173}^2$ | 173A-38 | $b^{154}$ |
| $C_{173}^2$ | 173A20 | $173$ | $1$ | $C_{173}^2$ | 173A40 | $b^{20}$ |
| $C_{173}^2$ | 173A-20 | $173$ | $1$ | $C_{173}^2$ | 173A-40 | $b^{153}$ |
| $C_{173}^2$ | 173A21 | $173$ | $1$ | $C_{173}^2$ | 173A42 | $b^{21}$ |
| $C_{173}^2$ | 173A-21 | $173$ | $1$ | $C_{173}^2$ | 173A-42 | $b^{152}$ |
| $C_{173}^2$ | 173A22 | $173$ | $1$ | $C_{173}^2$ | 173A44 | $b^{22}$ |
| $C_{173}^2$ | 173A-22 | $173$ | $1$ | $C_{173}^2$ | 173A-44 | $b^{151}$ |
| $C_{173}^2$ | 173A23 | $173$ | $1$ | $C_{173}^2$ | 173A46 | $b^{23}$ |
| $C_{173}^2$ | 173A-23 | $173$ | $1$ | $C_{173}^2$ | 173A-46 | $b^{150}$ |
| $C_{173}^2$ | 173A24 | $173$ | $1$ | $C_{173}^2$ | 173A48 | $b^{24}$ |
| $C_{173}^2$ | 173A-24 | $173$ | $1$ | $C_{173}^2$ | 173A-48 | $b^{149}$ |
| $C_{173}^2$ | 173A25 | $173$ | $1$ | $C_{173}^2$ | 173A50 | $b^{25}$ |