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Download displayed columns for resultsElements of the group are displayed as words in the presentation of the abelian group $\langle a, b \mid a^{2}=b^{8}=1 \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_2\times C_8$ | 1A | $1$ | $1$ | $C_2\times C_8$ | 1A | $1$ |
| $C_2\times C_8$ | 2A | $2$ | $1$ | $C_2\times C_8$ | 1A | $a$ |
| $C_2\times C_8$ | 2B | $2$ | $1$ | $C_2\times C_8$ | 1A | $ab^{4}$ |
| $C_2\times C_8$ | 2C | $2$ | $1$ | $C_2\times C_8$ | 1A | $b^{4}$ |
| $C_2\times C_8$ | 4A1 | $4$ | $1$ | $C_2\times C_8$ | 2C | $ab^{2}$ |
| $C_2\times C_8$ | 4A-1 | $4$ | $1$ | $C_2\times C_8$ | 2C | $ab^{6}$ |
| $C_2\times C_8$ | 4B1 | $4$ | $1$ | $C_2\times C_8$ | 2C | $b^{2}$ |
| $C_2\times C_8$ | 4B-1 | $4$ | $1$ | $C_2\times C_8$ | 2C | $b^{6}$ |
| $C_2\times C_8$ | 8A1 | $8$ | $1$ | $C_2\times C_8$ | 4B1 | $b$ |
| $C_2\times C_8$ | 8A-1 | $8$ | $1$ | $C_2\times C_8$ | 4B-1 | $b^{7}$ |
| $C_2\times C_8$ | 8A3 | $8$ | $1$ | $C_2\times C_8$ | 4B-1 | $b^{3}$ |
| $C_2\times C_8$ | 8A-3 | $8$ | $1$ | $C_2\times C_8$ | 4B1 | $b^{5}$ |
| $C_2\times C_8$ | 8B1 | $8$ | $1$ | $C_2\times C_8$ | 4B1 | $ab$ |
| $C_2\times C_8$ | 8B-1 | $8$ | $1$ | $C_2\times C_8$ | 4B-1 | $ab^{7}$ |
| $C_2\times C_8$ | 8B3 | $8$ | $1$ | $C_2\times C_8$ | 4B-1 | $ab^{3}$ |
| $C_2\times C_8$ | 8B-3 | $8$ | $1$ | $C_2\times C_8$ | 4B1 | $ab^{5}$ |