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Results (13 matches)
Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b \mid b^{20}=1, a^{2}=b^{10}, b^{a}=b^{19} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 5P | ||||||
| $C_5:Q_8$ | 1A | $1$ | $1$ | $C_5:Q_8$ | 1A | 1A | $1$ |
| $C_5:Q_8$ | 2A | $2$ | $1$ | $C_5:Q_8$ | 1A | 2A | $b^{10}$ |
| $C_5:Q_8$ | 4A | $4$ | $2$ | $C_{20}$ | 2A | 4A | $b^{5}$ |
| $C_5:Q_8$ | 4B | $4$ | $10$ | $C_4$ | 2A | 4B | $ab^{16}$ |
| $C_5:Q_8$ | 4C | $4$ | $10$ | $C_4$ | 2A | 4C | $ab^{13}$ |
| $C_5:Q_8$ | 5A1 | $5$ | $2$ | $C_{20}$ | 5A2 | 1A | $b^{4}$ |
| $C_5:Q_8$ | 5A2 | $5$ | $2$ | $C_{20}$ | 5A1 | 1A | $b^{8}$ |
| $C_5:Q_8$ | 10A1 | $10$ | $2$ | $C_{20}$ | 5A1 | 2A | $b^{2}$ |
| $C_5:Q_8$ | 10A3 | $10$ | $2$ | $C_{20}$ | 5A2 | 2A | $b^{6}$ |
| $C_5:Q_8$ | 20A1 | $20$ | $2$ | $C_{20}$ | 10A1 | 4A | $b$ |
| $C_5:Q_8$ | 20A3 | $20$ | $2$ | $C_{20}$ | 10A3 | 4A | $b^{3}$ |
| $C_5:Q_8$ | 20A7 | $20$ | $2$ | $C_{20}$ | 10A3 | 4A | $b^{13}$ |
| $C_5:Q_8$ | 20A9 | $20$ | $2$ | $C_{20}$ | 10A1 | 4A | $b^{9}$ |