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Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b \mid a^{4}=b^{5}=1, b^{a}=b^{4} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 5P | ||||||
| $C_5:C_4$ | 1A | $1$ | $1$ | $C_5:C_4$ | 1A | 1A | $1$ |
| $C_5:C_4$ | 2A | $2$ | $1$ | $C_5:C_4$ | 1A | 2A | $a^{2}$ |
| $C_5:C_4$ | 4A1 | $4$ | $5$ | $C_4$ | 2A | 4A1 | $a^{3}$ |
| $C_5:C_4$ | 4A-1 | $4$ | $5$ | $C_4$ | 2A | 4A-1 | $a$ |
| $C_5:C_4$ | 5A1 | $5$ | $2$ | $C_{10}$ | 5A2 | 1A | $b^{2}$ |
| $C_5:C_4$ | 5A2 | $5$ | $2$ | $C_{10}$ | 5A1 | 1A | $b^{4}$ |
| $C_5:C_4$ | 10A1 | $10$ | $2$ | $C_{10}$ | 5A1 | 2A | $a^{2}b$ |
| $C_5:C_4$ | 10A3 | $10$ | $2$ | $C_{10}$ | 5A2 | 2A | $a^{2}b^{2}$ |