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Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b \mid a^{4}=b^{3}=1, b^{a}=b^{2} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_3:C_4$ | 1A | $1$ | $1$ | $C_3:C_4$ | 1A | 1A | $1$ |
| $C_3:C_4$ | 2A | $2$ | $1$ | $C_3:C_4$ | 1A | 2A | $a^{2}$ |
| $C_3:C_4$ | 3A | $3$ | $2$ | $C_6$ | 3A | 1A | $b^{2}$ |
| $C_3:C_4$ | 4A1 | $4$ | $3$ | $C_4$ | 2A | 4A-1 | $a$ |
| $C_3:C_4$ | 4A-1 | $4$ | $3$ | $C_4$ | 2A | 4A1 | $a^{3}$ |
| $C_3:C_4$ | 6A | $6$ | $2$ | $C_6$ | 3A | 2A | $a^{2}b$ |