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Elements of the group are displayed as permutations of degree 17.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 7P | 11P | 13P | 17P | ||||||
| $S_{17}$ | 1A | $1$ | $1$ | not computed | 1A | 1A | 1A | 1A | 1A | 1A | 1A | $()$ |
| $S_{17}$ | 2A | $2$ | $136$ | not computed | 1A | 2A | 2A | 2A | 2A | 2A | 2A | $(6,15)$ |
| $S_{17}$ | 2B | $2$ | $7140$ | not computed | 1A | 2B | 2B | 2B | 2B | 2B | 2B | $(11,12)(14,17)$ |
| $S_{17}$ | 2C | $2$ | $185640$ | not computed | 1A | 2C | 2C | 2C | 2C | 2C | 2C | $(1,9)(3,12)(6,15)$ |
| $S_{17}$ | 2D | $2$ | $2552550$ | not computed | 1A | 2D | 2D | 2D | 2D | 2D | 2D | $(1,13)(4,12)(5,15)(9,16)$ |
| $S_{17}$ | 2E | $2$ | $18378360$ | not computed | 1A | 2E | 2E | 2E | 2E | 2E | 2E | $(2,10)(4,12)(5,14)(7,15)(9,17)$ |
| $S_{17}$ | 2F | $2$ | $34459425$ | not computed | 1A | 2F | 2F | 2F | 2F | 2F | 2F | $(1,7)(2,9)(3,17)(4,10)(5,11)(6,13)(8,14)(12,16)$ |
| $S_{17}$ | 2G | $2$ | $64324260$ | not computed | 1A | 2G | 2G | 2G | 2G | 2G | 2G | $(2,3)(4,13)(6,7)(9,10)(12,14)(15,17)$ |
| $S_{17}$ | 2H | $2$ | $91891800$ | not computed | 1A | 2H | 2H | 2H | 2H | 2H | 2H | $(1,2)(3,6)(7,12)(8,13)(9,10)(11,15)(14,17)$ |
| $S_{17}$ | 3A | $3$ | $1360$ | not computed | 3A | 1A | 3A | 3A | 3A | 3A | 3A | $(3,7,9)$ |
| $S_{17}$ | 3B | $3$ | $495040$ | not computed | 3B | 1A | 3B | 3B | 3B | 3B | 3B | $(7,14,10)(9,12,17)$ |
| $S_{17}$ | 3C | $3$ | $54454400$ | not computed | 3C | 1A | 3C | 3C | 3C | 3C | 3C | $(2,14,8)(3,11,7)(6,17,10)$ |
| $S_{17}$ | 3D | $3$ | $1524723200$ | not computed | 3D | 1A | 3D | 3D | 3D | 3D | 3D | $(1,2,12)(6,9,8)(7,16,15)(13,14,17)$ |
| $S_{17}$ | 3E | $3$ | $6098892800$ | not computed | 3E | 1A | 3E | 3E | 3E | 3E | 3E | $(1,11,15)(2,7,5)(4,13,6)(8,12,17)(9,16,14)$ |
| $S_{17}$ | 4A | $4$ | $14280$ | not computed | 2B | 4A | 4A | 4A | 4A | 4A | 4A | $(2,6,9,15)$ |
| $S_{17}$ | 4B | $4$ | $1113840$ | not computed | 2B | 4B | 4B | 4B | 4B | 4B | 4B | $(3,14,13,12)(4,15)$ |
| $S_{17}$ | 4C | $4$ | $30630600$ | not computed | 2D | 4C | 4C | 4C | 4C | 4C | 4C | $(1,15,13,5)(4,16,12,9)$ |
| $S_{17}$ | 4D | $4$ | $30630600$ | not computed | 2B | 4D | 4D | 4D | 4D | 4D | 4D | $(1,6)(3,15,17,8)(13,16)$ |
| $S_{17}$ | 4E | $4$ | $367567200$ | not computed | 2B | 4E | 4E | 4E | 4E | 4E | 4E | $(2,15)(5,6)(8,13)(11,17,12,14)$ |
| $S_{17}$ | 4F | $4$ | $1102701600$ | not computed | 2D | 4F | 4F | 4F | 4F | 4F | 4F | $(1,17)(2,6,9,11)(4,8,14,16)$ |
| $S_{17}$ | 4G | $4$ | $1929727800$ | not computed | 2B | 4G | 4G | 4G | 4G | 4G | 4G | $(1,7)(2,16)(3,11,5,10)(6,14)(8,13)(9,17)(12,15)$ |
| $S_{17}$ | 4H | $4$ | $1929727800$ | not computed | 2B | 4H | 4H | 4H | 4H | 4H | 4H | $(4,6,17,10)(5,8)(7,15)(9,13)(11,16)$ |
| $S_{17}$ | 4I | $4$ | $3859455600$ | not computed | 2B | 4I | 4I | 4I | 4I | 4I | 4I | $(1,3)(2,7,12,6)(5,11)(8,9)(10,13)(15,16)$ |
| $S_{17}$ | 4J | $4$ | $7718911200$ | not computed | 2G | 4J | 4J | 4J | 4J | 4J | 4J | $(2,8,13,5)(3,6,11,4)(7,17,9,10)$ |
| $S_{17}$ | 4K | $4$ | $11578366800$ | not computed | 2D | 4K | 4K | 4K | 4K | 4K | 4K | $(1,10,2,8)(4,13,7,14)(6,12)(9,15)$ |
| $S_{17}$ | 4L | $4$ | $28945917000$ | not computed | 2D | 4L | 4L | 4L | 4L | 4L | 4L | $(1,4,5,11)(2,10)(3,9)(6,7,12,8)(13,15)(16,17)$ |
| $S_{17}$ | 4M | $4$ | $38594556000$ | not computed | 2D | 4M | 4M | 4M | 4M | 4M | 4M | $(1,17,3,6)(2,11,9,14)(4,10)(7,12)(13,16)$ |
| $S_{17}$ | 4N | $4$ | $57891834000$ | not computed | 2F | 4N | 4N | 4N | 4N | 4N | 4N | $(1,16,7,12)(2,5,9,11)(3,8,17,14)(4,6,10,13)$ |
| $S_{17}$ | 4O | $4$ | $77189112000$ | not computed | 2G | 4O | 4O | 4O | 4O | 4O | 4O | $(1,6,9,7)(2,15,13,14)(3,10)(4,16,5,11)$ |
| $S_{17}$ | 4P | $4$ | $115783668000$ | not computed | 2G | 4P | 4P | 4P | 4P | 4P | 4P | $(1,9,13,4)(2,15,10,12)(3,14)(5,17,7,8)(11,16)$ |
| $S_{17}$ | 5A | $5$ | $148512$ | not computed | 5A | 5A | 1A | 5A | 5A | 5A | 5A | $(3,11,17,5,16)$ |
| $S_{17}$ | 5B | $5$ | $1411458048$ | not computed | 5B | 5B | 1A | 5B | 5B | 5B | 5B | $(2,5,9,12,15)(4,7,10,14,17)$ |
| $S_{17}$ | 5C | $5$ | $237124952064$ | not computed | 5C | 5C | 1A | 5C | 5C | 5C | 5C | $(1,16,11,8,5)(2,17,14,10,6)(3,15,12,9,7)$ |
| $S_{17}$ | 6A | $6$ | $123760$ | not computed | 3A | 2A | 6A | 6A | 6A | 6A | 6A | $(6,15)(7,12,10)$ |
| $S_{17}$ | 6B | $6$ | $1485120$ | not computed | 3B | 2C | 6B | 6B | 6B | 6B | 6B | $(1,15,12,9,6,3)$ |
| $S_{17}$ | 6C | $6$ | $4084080$ | not computed | 3A | 2B | 6C | 6C | 6C | 6C | 6C | $(3,9,7)(11,12)(14,17)$ |
| $S_{17}$ | 6D | $6$ | $27227200$ | not computed | 3B | 2A | 6D | 6D | 6D | 6D | 6D | $(1,13,9)(4,14,12)(5,17)$ |
| $S_{17}$ | 6E | $6$ | $61261200$ | not computed | 3A | 2C | 6E | 6E | 6E | 6E | 6E | $(1,6)(4,9)(8,11,16)(10,14)$ |
| $S_{17}$ | 6F | $6$ | $81681600$ | not computed | 3B | 2D | 6F | 6F | 6F | 6F | 6F | $(1,15,17,8,6,10)(3,9)$ |
| $S_{17}$ | 6G | $6$ | $183783600$ | not computed | 3A | 2H | 6G | 6G | 6G | 6G | 6G | $(1,7)(2,11)(3,14)(4,12)(5,15)(6,16,10)(8,13)(9,17)$ |
| $S_{17}$ | 6H | $6$ | $428828400$ | not computed | 3A | 2D | 6H | 6H | 6H | 6H | 6H | $(2,12)(3,9,14)(4,6)(5,16)(7,13)$ |
| $S_{17}$ | 6I | $6$ | $490089600$ | not computed | 3B | 2B | 6I | 6I | 6I | 6I | 6I | $(2,7,5)(4,10,11)(13,16)(14,17)$ |
| $S_{17}$ | 6J | $6$ | $490089600$ | not computed | 3C | 2C | 6J | 6J | 6J | 6J | 6J | $(1,12,3)(2,17,5,7,15,6)$ |
| $S_{17}$ | 6K | $6$ | $1286485200$ | not computed | 3A | 2G | 6K | 6K | 6K | 6K | 6K | $(1,13)(2,4)(3,17)(5,9)(7,16)(8,14,15)(10,11)$ |
| $S_{17}$ | 6L | $6$ | $1286485200$ | not computed | 3A | 2E | 6L | 6L | 6L | 6L | 6L | $(2,11)(3,6)(4,7)(5,17)(8,13)(12,16,14)$ |
| $S_{17}$ | 6M | $6$ | $1470268800$ | not computed | 3B | 2E | 6M | 6M | 6M | 6M | 6M | $(1,15)(3,17,10,14,9,5)(4,11)$ |
| $S_{17}$ | 6N | $6$ | $1524723200$ | not computed | 3C | 2A | 6N | 6N | 6N | 6N | 6N | $(1,4,13)(2,3,8)(5,15)(11,12,17)$ |
| $S_{17}$ | 6O | $6$ | $3430627200$ | not computed | 3B | 2C | 6O | 6O | 6O | 6O | 6O | $(1,4,12)(3,6)(7,17)(8,9)(10,15,13)$ |
| $S_{17}$ | 6P | $6$ | $5145940800$ | not computed | 3B | 2E | 6P | 6P | 6P | 6P | 6P | $(1,8)(2,12,5)(3,17)(4,15)(6,11)(7,16)(9,10,14)$ |
| $S_{17}$ | 6Q | $6$ | $5717712000$ | not computed | 3C | 2D | 6Q | 6Q | 6Q | 6Q | 6Q | $(1,13)(2,8,14)(3,7,11)(4,12)(5,15)(6,10,17)(9,16)$ |