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Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{28}=1, b^{a}=b^{27} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 7P | ||||||
| $D_{28}$ | 1A | $1$ | $1$ | $D_{28}$ | 1A | 1A | $1$ |
| $D_{28}$ | 2A | $2$ | $1$ | $D_{28}$ | 1A | 2A | $b^{14}$ |
| $D_{28}$ | 2B | $2$ | $14$ | $C_2^2$ | 1A | 2B | $ab^{24}$ |
| $D_{28}$ | 2C | $2$ | $14$ | $C_2^2$ | 1A | 2C | $ab^{3}$ |
| $D_{28}$ | 4A | $4$ | $2$ | $C_{28}$ | 2A | 4A | $b^{7}$ |
| $D_{28}$ | 7A1 | $7$ | $2$ | $C_{28}$ | 7A2 | 7A3 | $b^{4}$ |
| $D_{28}$ | 7A2 | $7$ | $2$ | $C_{28}$ | 7A3 | 7A1 | $b^{8}$ |
| $D_{28}$ | 7A3 | $7$ | $2$ | $C_{28}$ | 7A1 | 7A2 | $b^{12}$ |
| $D_{28}$ | 14A1 | $14$ | $2$ | $C_{28}$ | 7A1 | 14A3 | $b^{2}$ |
| $D_{28}$ | 14A3 | $14$ | $2$ | $C_{28}$ | 7A3 | 14A5 | $b^{6}$ |
| $D_{28}$ | 14A5 | $14$ | $2$ | $C_{28}$ | 7A2 | 14A1 | $b^{10}$ |
| $D_{28}$ | 28A1 | $28$ | $2$ | $C_{28}$ | 14A1 | 28A3 | $b$ |
| $D_{28}$ | 28A3 | $28$ | $2$ | $C_{28}$ | 14A3 | 28A9 | $b^{3}$ |
| $D_{28}$ | 28A5 | $28$ | $2$ | $C_{28}$ | 14A5 | 28A13 | $b^{5}$ |
| $D_{28}$ | 28A9 | $28$ | $2$ | $C_{28}$ | 14A5 | 28A1 | $b^{9}$ |
| $D_{28}$ | 28A11 | $28$ | $2$ | $C_{28}$ | 14A3 | 28A5 | $b^{17}$ |
| $D_{28}$ | 28A13 | $28$ | $2$ | $C_{28}$ | 14A1 | 28A11 | $b^{13}$ |