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Elements of the group are displayed as words in the presentation $\langle a, b \mid a^{30}=b^{2265}=1, b^{a}=b^{1246} \rangle$ .
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||
|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 151P | ||||||
| $C_{2265}:C_{30}$ | 1A | $1$ | $1$ | $C_{2265}:C_{30}$ | 1A | 1A | 1A | 1A | $1$ |
| $C_{2265}:C_{30}$ | 2A | $2$ | $1$ | $C_{2265}:C_{30}$ | 1A | 2A | 2A | 2A | $a^{15}$ |
| $C_{2265}:C_{30}$ | 3A1 | $3$ | $1$ | $C_{2265}:C_{30}$ | 3A-1 | 1A | 3A-1 | 3A1 | $b^{1510}$ |
| $C_{2265}:C_{30}$ | 3A-1 | $3$ | $1$ | $C_{2265}:C_{30}$ | 3A1 | 1A | 3A1 | 3A-1 | $b^{755}$ |
| $C_{2265}:C_{30}$ | 3B1 | $3$ | $151$ | $C_{15}\times C_{30}$ | 3B-1 | 1A | 3B-1 | 3B1 | $a^{10}$ |
| $C_{2265}:C_{30}$ | 3B-1 | $3$ | $151$ | $C_{15}\times C_{30}$ | 3B1 | 1A | 3B1 | 3B-1 | $a^{20}$ |
| $C_{2265}:C_{30}$ | 3C1 | $3$ | $151$ | $C_{15}\times C_{30}$ | 3C-1 | 1A | 3C-1 | 3C1 | $a^{10}b^{2260}$ |
| $C_{2265}:C_{30}$ | 3C-1 | $3$ | $151$ | $C_{15}\times C_{30}$ | 3C1 | 1A | 3C1 | 3C-1 | $a^{20}b^{1670}$ |
| $C_{2265}:C_{30}$ | 3D1 | $3$ | $151$ | $C_{15}\times C_{30}$ | 3D-1 | 1A | 3D-1 | 3D1 | $a^{10}b^{2255}$ |
| $C_{2265}:C_{30}$ | 3D-1 | $3$ | $151$ | $C_{15}\times C_{30}$ | 3D1 | 1A | 3D1 | 3D-1 | $a^{20}b^{1075}$ |
| $C_{2265}:C_{30}$ | 5A1 | $5$ | $1$ | $C_{2265}:C_{30}$ | 5A2 | 5A-2 | 1A | 5A1 | $b^{453}$ |
| $C_{2265}:C_{30}$ | 5A-1 | $5$ | $1$ | $C_{2265}:C_{30}$ | 5A-2 | 5A2 | 1A | 5A-1 | $b^{1812}$ |
| $C_{2265}:C_{30}$ | 5A2 | $5$ | $1$ | $C_{2265}:C_{30}$ | 5A-1 | 5A1 | 1A | 5A2 | $b^{906}$ |
| $C_{2265}:C_{30}$ | 5A-2 | $5$ | $1$ | $C_{2265}:C_{30}$ | 5A1 | 5A-1 | 1A | 5A-2 | $b^{1359}$ |
| $C_{2265}:C_{30}$ | 5B1 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5B2 | 5B-2 | 1A | 5B1 | $a^{6}$ |
| $C_{2265}:C_{30}$ | 5B-1 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5B-2 | 5B2 | 1A | 5B-1 | $a^{24}$ |
| $C_{2265}:C_{30}$ | 5B2 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5B-1 | 5B1 | 1A | 5B2 | $a^{12}$ |
| $C_{2265}:C_{30}$ | 5B-2 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5B1 | 5B-1 | 1A | 5B-2 | $a^{18}$ |
| $C_{2265}:C_{30}$ | 5C1 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5C2 | 5C-2 | 1A | 5C1 | $a^{6}b^{123}$ |
| $C_{2265}:C_{30}$ | 5C-1 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5C-2 | 5C2 | 1A | 5C-1 | $a^{24}b^{1287}$ |
| $C_{2265}:C_{30}$ | 5C2 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5C-1 | 5C1 | 1A | 5C2 | $a^{12}b^{201}$ |
| $C_{2265}:C_{30}$ | 5C-2 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5C1 | 5C-1 | 1A | 5C-2 | $a^{18}b^{2184}$ |
| $C_{2265}:C_{30}$ | 5D1 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5D2 | 5D-2 | 1A | 5D1 | $a^{6}b^{1551}$ |
| $C_{2265}:C_{30}$ | 5D-1 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5D-2 | 5D2 | 1A | 5D-1 | $a^{24}b^{429}$ |
| $C_{2265}:C_{30}$ | 5D2 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5D-1 | 5D1 | 1A | 5D2 | $a^{12}b^{822}$ |
| $C_{2265}:C_{30}$ | 5D-2 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5D1 | 5D-1 | 1A | 5D-2 | $a^{18}b^{2238}$ |
| $C_{2265}:C_{30}$ | 5E1 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5E2 | 5E-2 | 1A | 5E1 | $a^{6}b^{837}$ |
| $C_{2265}:C_{30}$ | 5E-1 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5E-2 | 5E2 | 1A | 5E-1 | $a^{24}b^{858}$ |
| $C_{2265}:C_{30}$ | 5E2 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5E-1 | 5E1 | 1A | 5E2 | $a^{12}b^{1644}$ |
| $C_{2265}:C_{30}$ | 5E-2 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5E1 | 5E-1 | 1A | 5E-2 | $a^{18}b^{2211}$ |
| $C_{2265}:C_{30}$ | 5F1 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5F2 | 5F-2 | 1A | 5F1 | $a^{6}b^{369}$ |
| $C_{2265}:C_{30}$ | 5F-1 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5F-2 | 5F2 | 1A | 5F-1 | $a^{24}b^{1596}$ |
| $C_{2265}:C_{30}$ | 5F2 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5F-1 | 5F1 | 1A | 5F2 | $a^{12}b^{603}$ |
| $C_{2265}:C_{30}$ | 5F-2 | $5$ | $151$ | $C_{15}\times C_{30}$ | 5F1 | 5F-1 | 1A | 5F-2 | $a^{18}b^{2022}$ |
| $C_{2265}:C_{30}$ | 6A1 | $6$ | $1$ | $C_{2265}:C_{30}$ | 3A1 | 2A | 6A-1 | 6A1 | $a^{15}b^{755}$ |
| $C_{2265}:C_{30}$ | 6A-1 | $6$ | $1$ | $C_{2265}:C_{30}$ | 3A-1 | 2A | 6A1 | 6A-1 | $a^{15}b^{1510}$ |
| $C_{2265}:C_{30}$ | 6B1 | $6$ | $151$ | $C_{15}\times C_{30}$ | 3B1 | 2A | 6B-1 | 6B1 | $a^{5}$ |
| $C_{2265}:C_{30}$ | 6B-1 | $6$ | $151$ | $C_{15}\times C_{30}$ | 3B-1 | 2A | 6B1 | 6B-1 | $a^{25}$ |
| $C_{2265}:C_{30}$ | 6C1 | $6$ | $151$ | $C_{15}\times C_{30}$ | 3C1 | 2A | 6C-1 | 6C1 | $a^{5}b^{1670}$ |
| $C_{2265}:C_{30}$ | 6C-1 | $6$ | $151$ | $C_{15}\times C_{30}$ | 3C-1 | 2A | 6C1 | 6C-1 | $a^{25}b^{2260}$ |
| $C_{2265}:C_{30}$ | 6D1 | $6$ | $151$ | $C_{15}\times C_{30}$ | 3D1 | 2A | 6D-1 | 6D1 | $a^{5}b^{1075}$ |
| $C_{2265}:C_{30}$ | 6D-1 | $6$ | $151$ | $C_{15}\times C_{30}$ | 3D-1 | 2A | 6D1 | 6D-1 | $a^{25}b^{2255}$ |
| $C_{2265}:C_{30}$ | 10A1 | $10$ | $1$ | $C_{2265}:C_{30}$ | 5A1 | 10A3 | 2A | 10A1 | $a^{15}b^{1359}$ |
| $C_{2265}:C_{30}$ | 10A-1 | $10$ | $1$ | $C_{2265}:C_{30}$ | 5A-1 | 10A-3 | 2A | 10A-1 | $a^{15}b^{906}$ |
| $C_{2265}:C_{30}$ | 10A3 | $10$ | $1$ | $C_{2265}:C_{30}$ | 5A-2 | 10A-1 | 2A | 10A3 | $a^{15}b^{1812}$ |
| $C_{2265}:C_{30}$ | 10A-3 | $10$ | $1$ | $C_{2265}:C_{30}$ | 5A2 | 10A1 | 2A | 10A-3 | $a^{15}b^{453}$ |
| $C_{2265}:C_{30}$ | 10B1 | $10$ | $151$ | $C_{15}\times C_{30}$ | 5B1 | 10B3 | 2A | 10B1 | $a^{3}$ |
| $C_{2265}:C_{30}$ | 10B-1 | $10$ | $151$ | $C_{15}\times C_{30}$ | 5B-1 | 10B-3 | 2A | 10B-1 | $a^{27}$ |
| $C_{2265}:C_{30}$ | 10B3 | $10$ | $151$ | $C_{15}\times C_{30}$ | 5B-2 | 10B-1 | 2A | 10B3 | $a^{9}$ |
| $C_{2265}:C_{30}$ | 10B-3 | $10$ | $151$ | $C_{15}\times C_{30}$ | 5B2 | 10B1 | 2A | 10B-3 | $a^{21}$ |