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