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Elements of the group are displayed as permutations of degree 16.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | 7P | 11P | 13P | ||||||
| $S_{16}$ | 1A | $1$ | $1$ | not computed | 1A | 1A | 1A | 1A | 1A | 1A | $()$ |
| $S_{16}$ | 2A | $2$ | $120$ | not computed | 1A | 2A | 2A | 2A | 2A | 2A | $(7,8)$ |
| $S_{16}$ | 2B | $2$ | $5460$ | not computed | 1A | 2B | 2B | 2B | 2B | 2B | $(2,5)(3,16)$ |
| $S_{16}$ | 2C | $2$ | $120120$ | not computed | 1A | 2C | 2C | 2C | 2C | 2C | $(3,12)(6,13)(7,16)$ |
| $S_{16}$ | 2D | $2$ | $1351350$ | not computed | 1A | 2D | 2D | 2D | 2D | 2D | $(2,6)(5,10)(7,9)(11,12)$ |
| $S_{16}$ | 2E | $2$ | $2027025$ | not computed | 1A | 2E | 2E | 2E | 2E | 2E | $(1,9)(2,11)(3,10)(4,12)(5,13)(6,14)(7,15)(8,16)$ |
| $S_{16}$ | 2F | $2$ | $7567560$ | not computed | 1A | 2F | 2F | 2F | 2F | 2F | $(1,14)(3,11)(5,10)(6,7)(9,15)$ |
| $S_{16}$ | 2G | $2$ | $16216200$ | not computed | 1A | 2G | 2G | 2G | 2G | 2G | $(1,16)(2,3)(5,6)(7,8)(9,11)(12,13)(14,15)$ |
| $S_{16}$ | 2H | $2$ | $18918900$ | not computed | 1A | 2H | 2H | 2H | 2H | 2H | $(2,3)(5,16)(6,13)(7,11)(8,10)(9,14)$ |
| $S_{16}$ | 3A | $3$ | $1120$ | not computed | 3A | 1A | 3A | 3A | 3A | 3A | $(3,6,13)$ |
| $S_{16}$ | 3B | $3$ | $320320$ | not computed | 3B | 1A | 3B | 3B | 3B | 3B | $(6,9,11)(7,13,14)$ |
| $S_{16}$ | 3C | $3$ | $25625600$ | not computed | 3C | 1A | 3C | 3C | 3C | 3C | $(1,4,5)(3,6,7)(10,15,14)$ |
| $S_{16}$ | 3D | $3$ | $448448000$ | not computed | 3D | 1A | 3D | 3D | 3D | 3D | $(1,9,6)(2,11,7)(4,16,10)(5,12,8)$ |
| $S_{16}$ | 3E | $3$ | $717516800$ | not computed | 3E | 1A | 3E | 3E | 3E | 3E | $(1,11,6)(2,14,4)(3,15,8)(7,13,9)(10,12,16)$ |
| $S_{16}$ | 4A | $4$ | $10920$ | not computed | 2B | 4A | 4A | 4A | 4A | 4A | $(3,15,5,8)$ |
| $S_{16}$ | 4B | $4$ | $720720$ | not computed | 2B | 4B | 4B | 4B | 4B | 4B | $(2,16,5,3)(7,8)$ |
| $S_{16}$ | 4C | $4$ | $16216200$ | not computed | 2D | 4C | 4C | 4C | 4C | 4C | $(2,13,6,7)(4,15,11,16)$ |
| $S_{16}$ | 4D | $4$ | $16216200$ | not computed | 2B | 4D | 4D | 4D | 4D | 4D | $(2,4)(3,13)(6,9,11,15)$ |
| $S_{16}$ | 4E | $4$ | $113513400$ | not computed | 2B | 4E | 4E | 4E | 4E | 4E | $(1,14)(2,4)(3,7)(5,6)(8,9,15,12)(10,11)(13,16)$ |
| $S_{16}$ | 4F | $4$ | $151351200$ | not computed | 2B | 4F | 4F | 4F | 4F | 4F | $(2,9,14,4)(7,8)(10,16)(11,12)$ |
| $S_{16}$ | 4G | $4$ | $454053600$ | not computed | 2D | 4G | 4G | 4G | 4G | 4G | $(3,16,8,6)(4,10)(7,13,9,12)$ |
| $S_{16}$ | 4H | $4$ | $567567000$ | not computed | 2B | 4H | 4H | 4H | 4H | 4H | $(1,13)(2,4)(3,7,5,9)(6,15)(10,16)$ |
| $S_{16}$ | 4I | $4$ | $681080400$ | not computed | 2B | 4I | 4I | 4I | 4I | 4I | $(1,14,10,11)(2,16)(3,15)(4,13)(5,12)(6,7)$ |
| $S_{16}$ | 4J | $4$ | $1702701000$ | not computed | 2D | 4J | 4J | 4J | 4J | 4J | $(1,9,5,12)(2,16)(3,13,7,6)(4,8)(10,11)(14,15)$ |
| $S_{16}$ | 4K | $4$ | $2270268000$ | not computed | 2H | 4K | 4K | 4K | 4K | 4K | $(1,11,8,4)(2,12,10,6)(5,16,9,7)$ |
| $S_{16}$ | 4L | $4$ | $3405402000$ | not computed | 2E | 4L | 4L | 4L | 4L | 4L | $(1,5,9,13)(2,6,11,14)(3,7,10,15)(4,8,12,16)$ |
| $S_{16}$ | 4M | $4$ | $3405402000$ | not computed | 2D | 4M | 4M | 4M | 4M | 4M | $(1,8)(2,12,6,11)(4,15)(5,9,10,7)$ |
| $S_{16}$ | 4N | $4$ | $6810804000$ | not computed | 2H | 4N | 4N | 4N | 4N | 4N | $(1,12)(2,10,7,6)(3,5,4,15)(8,9,14,16)(11,13)$ |
| $S_{16}$ | 4O | $4$ | $6810804000$ | not computed | 2D | 4O | 4O | 4O | 4O | 4O | $(2,10)(3,12)(5,13,6,8)(7,14,9,15)(11,16)$ |
| $S_{16}$ | 4P | $4$ | $13621608000$ | not computed | 2H | 4P | 4P | 4P | 4P | 4P | $(1,3,13,4)(2,7,11,12)(5,8,10,16)(9,15)$ |
| $S_{16}$ | 5A | $5$ | $104832$ | not computed | 5A | 5A | 1A | 5A | 5A | 5A | $(1,5,8,11,14)$ |
| $S_{16}$ | 5B | $5$ | $581188608$ | not computed | 5B | 5B | 1A | 5B | 5B | 5B | $(1,6,9,10,15)(3,5,7,12,14)$ |
| $S_{16}$ | 5C | $5$ | $27897053184$ | not computed | 5C | 5C | 1A | 5C | 5C | 5C | $(1,4,13,3,10)(2,9,15,12,11)(6,14,7,8,16)$ |
| $S_{16}$ | 6A | $6$ | $87360$ | not computed | 3A | 2A | 6A | 6A | 6A | 6A | $(7,8)(9,11,10)$ |
| $S_{16}$ | 6B | $6$ | $960960$ | not computed | 3B | 2C | 6B | 6B | 6B | 6B | $(1,14,16,9,3,15)$ |
| $S_{16}$ | 6C | $6$ | $2402400$ | not computed | 3A | 2B | 6C | 6C | 6C | 6C | $(2,14)(3,13,6)(4,9)$ |
| $S_{16}$ | 6D | $6$ | $14414400$ | not computed | 3B | 2A | 6D | 6D | 6D | 6D | $(2,6,4)(7,11)(8,9,13)$ |
| $S_{16}$ | 6E | $6$ | $28828800$ | not computed | 3A | 2C | 6E | 6E | 6E | 6E | $(3,12)(6,13)(7,16)(8,10,15)$ |
| $S_{16}$ | 6F | $6$ | $43243200$ | not computed | 3B | 2D | 6F | 6F | 6F | 6F | $(2,14,11,9,3,12)(4,13)$ |
| $S_{16}$ | 6G | $6$ | $151351200$ | not computed | 3A | 2D | 6G | 6G | 6G | 6G | $(1,3)(2,7)(4,12)(9,13,16)(10,14)$ |
| $S_{16}$ | 6H | $6$ | $151351200$ | not computed | 3A | 2H | 6H | 6H | 6H | 6H | $(1,3)(4,6)(5,8)(7,14)(9,10)(11,12,13)(15,16)$ |
| $S_{16}$ | 6I | $6$ | $201801600$ | not computed | 3B | 2B | 6I | 6I | 6I | 6I | $(2,5)(3,16)(6,11,10)(9,14,13)$ |
| $S_{16}$ | 6J | $6$ | $230630400$ | not computed | 3C | 2C | 6J | 6J | 6J | 6J | $(1,3,13,4,9,15)(7,14,10)$ |
| $S_{16}$ | 6K | $6$ | $302702400$ | not computed | 3A | 2F | 6K | 6K | 6K | 6K | $(1,6,3)(2,7)(4,15)(5,12)(8,9)(13,16)$ |
| $S_{16}$ | 6L | $6$ | $302702400$ | not computed | 3B | 2F | 6L | 6L | 6L | 6L | $(1,10,9)(2,3)(4,12,15)(5,11)(6,8)(7,14)(13,16)$ |
| $S_{16}$ | 6M | $6$ | $538137600$ | not computed | 3C | 2A | 6M | 6M | 6M | 6M | $(1,2,11)(3,10,13)(4,7,8)(9,14)$ |
| $S_{16}$ | 6N | $6$ | $605404800$ | not computed | 3B | 2F | 6N | 6N | 6N | 6N | $(1,6,10,14,7,5)(3,11)(9,15)$ |
| $S_{16}$ | 6O | $6$ | $908107200$ | not computed | 3B | 2E | 6O | 6O | 6O | 6O | $(1,3)(2,16,13,11,8,4)(5,6)(7,9)(10,12)(14,15)$ |
| $S_{16}$ | 6P | $6$ | $1009008000$ | not computed | 3B | 2C | 6P | 6P | 6P | 6P | $(1,2,14)(5,6,15)(7,13)(8,16)(10,11)$ |
| $S_{16}$ | 6Q | $6$ | $1345344000$ | not computed | 3D | 2B | 6Q | 6Q | 6Q | 6Q | $(1,9)(2,14,13)(3,15,16)(4,12,8)(5,6,11)(7,10)$ |