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Results (19 matches)
Download displayed columns for resultsElements of the group are displayed as words in the presentation $\langle a, b \mid a^{2}=b^{32}=1, b^{a}=b^{15} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $\SD_{64}$ | 1A | $1$ | $1$ | $\SD_{64}$ | 1A | $1$ |
| $\SD_{64}$ | 2A | $2$ | $1$ | $\SD_{64}$ | 1A | $b^{16}$ |
| $\SD_{64}$ | 2B | $2$ | $16$ | $C_2^2$ | 1A | $ab^{24}$ |
| $\SD_{64}$ | 4A | $4$ | $2$ | $C_{32}$ | 2A | $b^{8}$ |
| $\SD_{64}$ | 4B | $4$ | $16$ | $C_4$ | 2A | $ab^{3}$ |
| $\SD_{64}$ | 8A1 | $8$ | $2$ | $C_{32}$ | 4A | $b^{4}$ |
| $\SD_{64}$ | 8A3 | $8$ | $2$ | $C_{32}$ | 4A | $b^{12}$ |
| $\SD_{64}$ | 16A1 | $16$ | $2$ | $C_{32}$ | 8A1 | $b^{2}$ |
| $\SD_{64}$ | 16A3 | $16$ | $2$ | $C_{32}$ | 8A3 | $b^{6}$ |
| $\SD_{64}$ | 16A5 | $16$ | $2$ | $C_{32}$ | 8A3 | $b^{10}$ |
| $\SD_{64}$ | 16A7 | $16$ | $2$ | $C_{32}$ | 8A1 | $b^{14}$ |
| $\SD_{64}$ | 32A1 | $32$ | $2$ | $C_{32}$ | 16A1 | $b$ |
| $\SD_{64}$ | 32A-1 | $32$ | $2$ | $C_{32}$ | 16A1 | $b^{17}$ |
| $\SD_{64}$ | 32A3 | $32$ | $2$ | $C_{32}$ | 16A3 | $b^{3}$ |
| $\SD_{64}$ | 32A-3 | $32$ | $2$ | $C_{32}$ | 16A3 | $b^{19}$ |
| $\SD_{64}$ | 32A5 | $32$ | $2$ | $C_{32}$ | 16A5 | $b^{5}$ |
| $\SD_{64}$ | 32A-5 | $32$ | $2$ | $C_{32}$ | 16A5 | $b^{21}$ |
| $\SD_{64}$ | 32A7 | $32$ | $2$ | $C_{32}$ | 16A7 | $b^{9}$ |
| $\SD_{64}$ | 32A-7 | $32$ | $2$ | $C_{32}$ | 16A7 | $b^{25}$ |