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Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b, c \mid a^{4}=b^{5}=c^{5}=[b,c]=1, b^{a}=b^{2}, c^{a}=c^{4} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 5P | ||||||
| $C_5:F_5$ | 10A1 | $10$ | $10$ | $C_{10}$ | 5A1 | 2A | $a^{2}c$ |
| $C_5:F_5$ | 10A3 | $10$ | $10$ | $C_{10}$ | 5A2 | 2A | $a^{2}c^{2}$ |