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Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{2}=b^{2}=c^{6}=[a,b]=[a,c]=1, c^{b}=c^{5} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_2\times D_6$ | 1A | $1$ | $1$ | $C_2\times D_6$ | 1A | 1A | $1$ |
| $C_2\times D_6$ | 2A | $2$ | $1$ | $C_2\times D_6$ | 1A | 2A | $c^{3}$ |
| $C_2\times D_6$ | 2B | $2$ | $1$ | $C_2\times D_6$ | 1A | 2B | $a$ |
| $C_2\times D_6$ | 2C | $2$ | $1$ | $C_2\times D_6$ | 1A | 2C | $ac^{3}$ |
| $C_2\times D_6$ | 2D | $2$ | $3$ | $C_2^3$ | 1A | 2D | $b$ |
| $C_2\times D_6$ | 2E | $2$ | $3$ | $C_2^3$ | 1A | 2E | $bc$ |
| $C_2\times D_6$ | 2F | $2$ | $3$ | $C_2^3$ | 1A | 2F | $ab$ |
| $C_2\times D_6$ | 2G | $2$ | $3$ | $C_2^3$ | 1A | 2G | $abc$ |
| $C_2\times D_6$ | 3A | $3$ | $2$ | $C_2\times C_6$ | 3A | 1A | $c^{2}$ |
| $C_2\times D_6$ | 6A | $6$ | $2$ | $C_2\times C_6$ | 3A | 2A | $c$ |
| $C_2\times D_6$ | 6B | $6$ | $2$ | $C_2\times C_6$ | 3A | 2B | $ac^{2}$ |
| $C_2\times D_6$ | 6C | $6$ | $2$ | $C_2\times C_6$ | 3A | 2C | $ac$ |