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Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b, c \mid b^{2}=c^{8}=[a,b]=[b,c]=1, a^{2}=c^{4}, c^{a}=bc^{3} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $Q_8:C_4$ | 1A | $1$ | $1$ | $Q_8:C_4$ | 1A | $1$ |
| $Q_8:C_4$ | 2A | $2$ | $1$ | $Q_8:C_4$ | 1A | $bc^{4}$ |
| $Q_8:C_4$ | 2B | $2$ | $1$ | $Q_8:C_4$ | 1A | $c^{4}$ |
| $Q_8:C_4$ | 2C | $2$ | $1$ | $Q_8:C_4$ | 1A | $b$ |
| $Q_8:C_4$ | 4A | $4$ | $2$ | $C_2\times C_8$ | 2B | $bc^{2}$ |
| $Q_8:C_4$ | 4B | $4$ | $2$ | $C_2\times C_8$ | 2B | $c^{2}$ |
| $Q_8:C_4$ | 4C | $4$ | $4$ | $C_2\times C_4$ | 2B | $a$ |
| $Q_8:C_4$ | 4D | $4$ | $4$ | $C_2\times C_4$ | 2B | $ac^{2}$ |
| $Q_8:C_4$ | 4E1 | $4$ | $4$ | $C_2\times C_4$ | 2C | $ac$ |
| $Q_8:C_4$ | 4E-1 | $4$ | $4$ | $C_2\times C_4$ | 2C | $ac^{3}$ |
| $Q_8:C_4$ | 8A1 | $8$ | $2$ | $C_2\times C_8$ | 4B | $c$ |
| $Q_8:C_4$ | 8A-1 | $8$ | $2$ | $C_2\times C_8$ | 4B | $c^{7}$ |
| $Q_8:C_4$ | 8A3 | $8$ | $2$ | $C_2\times C_8$ | 4B | $c^{3}$ |
| $Q_8:C_4$ | 8A-3 | $8$ | $2$ | $C_2\times C_8$ | 4B | $c^{5}$ |