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Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{2}=c^{8}=[a,b]=1, c^{a}=bc, c^{b}=c^{5} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $\OD_{16}:C_2$ | 1A | $1$ | $1$ | $\OD_{16}:C_2$ | 1A | $1$ |
| $\OD_{16}:C_2$ | 2A | $2$ | $1$ | $\OD_{16}:C_2$ | 1A | $c^{4}$ |
| $\OD_{16}:C_2$ | 2B | $2$ | $2$ | $C_2\times D_4$ | 1A | $b$ |
| $\OD_{16}:C_2$ | 2C | $2$ | $4$ | $C_2^3$ | 1A | $a$ |
| $\OD_{16}:C_2$ | 2D | $2$ | $4$ | $C_2^3$ | 1A | $ac^{2}$ |
| $\OD_{16}:C_2$ | 4A | $4$ | $2$ | $\OD_{16}$ | 2A | $c^{2}$ |
| $\OD_{16}:C_2$ | 4B | $4$ | $2$ | $\OD_{16}$ | 2A | $bc^{2}$ |
| $\OD_{16}:C_2$ | 8A1 | $8$ | $4$ | $C_8$ | 4A | $c$ |
| $\OD_{16}:C_2$ | 8A-1 | $8$ | $4$ | $C_8$ | 4A | $c^{3}$ |
| $\OD_{16}:C_2$ | 8B1 | $8$ | $4$ | $C_8$ | 4B | $ac$ |
| $\OD_{16}:C_2$ | 8B-1 | $8$ | $4$ | $C_8$ | 4B | $ac^{3}$ |