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Elements of the group are displayed as permutations of degree 16.
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $C_2\wr \OD_{16}$ | 1A | $1$ | $1$ | not computed | 1A | $()$ |
| $C_2\wr \OD_{16}$ | 2A | $2$ | $1$ | not computed | 1A | $(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)$ |
| $C_2\wr \OD_{16}$ | 2B | $2$ | $2$ | not computed | 1A | $(9,10)(11,12)(13,14)(15,16)$ |
| $C_2\wr \OD_{16}$ | 2C | $2$ | $4$ | not computed | 1A | $(11,12)(15,16)$ |
| $C_2\wr \OD_{16}$ | 2D | $2$ | $4$ | not computed | 1A | $(3,4)(7,8)(11,12)(15,16)$ |
| $C_2\wr \OD_{16}$ | 2E | $2$ | $4$ | not computed | 1A | $(3,4)(7,8)(9,10)(11,12)(13,14)(15,16)$ |
| $C_2\wr \OD_{16}$ | 2F | $2$ | $8$ | not computed | 1A | $(13,14)(15,16)$ |
| $C_2\wr \OD_{16}$ | 2G | $2$ | $8$ | not computed | 1A | $(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 2H | $2$ | $8$ | not computed | 1A | $(9,10)(11,15)(12,16)(13,14)$ |
| $C_2\wr \OD_{16}$ | 2I | $2$ | $8$ | not computed | 1A | $(9,13)(10,14)(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 2J | $2$ | $8$ | not computed | 1A | $(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)$ |
| $C_2\wr \OD_{16}$ | 2K | $2$ | $8$ | not computed | 1A | $(3,4)(7,8)(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 2L | $2$ | $8$ | not computed | 1A | $(3,4)(7,8)(9,10)(11,15)(12,16)(13,14)$ |
| $C_2\wr \OD_{16}$ | 2M | $2$ | $8$ | not computed | 1A | $(3,4)(7,8)(9,13)(10,14)$ |
| $C_2\wr \OD_{16}$ | 2N | $2$ | $8$ | not computed | 1A | $(3,4)(7,8)(9,13)(10,14)(11,12)(15,16)$ |
| $C_2\wr \OD_{16}$ | 2O | $2$ | $8$ | not computed | 1A | $(3,4)(7,8)(9,13)(10,14)(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 2P | $2$ | $8$ | not computed | 1A | $(3,4)(7,8)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2\wr \OD_{16}$ | 2Q | $2$ | $8$ | not computed | 1A | $(3,7)(4,8)(9,10)(11,12)(13,14)(15,16)$ |
| $C_2\wr \OD_{16}$ | 2R | $2$ | $8$ | not computed | 1A | $(1,2)(3,4)(5,6)(7,8)(9,10)(11,15)(12,16)(13,14)$ |
| $C_2\wr \OD_{16}$ | 2S | $2$ | $8$ | not computed | 1A | $(1,2)(3,4)(5,6)(7,8)(9,13)(10,14)(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 2T | $2$ | $16$ | not computed | 1A | $(5,6)(7,8)(11,12)(15,16)$ |
| $C_2\wr \OD_{16}$ | 2U | $2$ | $16$ | not computed | 1A | $(3,7)(4,8)(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 2V | $2$ | $16$ | not computed | 1A | $(3,7)(4,8)(9,10)(11,15)(12,16)(13,14)$ |
| $C_2\wr \OD_{16}$ | 2W | $2$ | $16$ | not computed | 1A | $(3,7)(4,8)(9,13)(10,14)(11,12)(15,16)$ |
| $C_2\wr \OD_{16}$ | 2X | $2$ | $16$ | not computed | 1A | $(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 2Y | $2$ | $16$ | not computed | 1A | $(3,7)(4,8)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2\wr \OD_{16}$ | 2Z | $2$ | $16$ | not computed | 1A | $(1,2)(3,7)(4,8)(5,6)(9,10)(11,15)(12,16)(13,14)$ |
| $C_2\wr \OD_{16}$ | 2AA | $2$ | $16$ | not computed | 1A | $(1,2)(3,7)(4,8)(5,6)(9,13)(10,14)(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 2AB | $2$ | $16$ | not computed | 1A | $(1,2)(3,7)(4,8)(5,6)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2\wr \OD_{16}$ | 2AC | $2$ | $16$ | not computed | 1A | $(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 2AD | $2$ | $16$ | not computed | 1A | $(1,2)(3,4)(11,12)(13,14)$ |
| $C_2\wr \OD_{16}$ | 2AE | $2$ | $32$ | not computed | 1A | $(5,6)(7,8)(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 2AF | $2$ | $32$ | not computed | 1A | $(5,6)(7,8)(9,10)(11,15)(12,16)(13,14)$ |
| $C_2\wr \OD_{16}$ | 2AG | $2$ | $32$ | not computed | 1A | $(5,6)(7,8)(9,13)(10,14)(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 4A | $4$ | $8$ | not computed | 2B | $(9,13,10,14)(11,15,12,16)$ |
| $C_2\wr \OD_{16}$ | 4B | $4$ | $8$ | not computed | 2B | $(1,2)(3,4)(5,6)(7,8)(9,13,10,14)(11,15,12,16)$ |
| $C_2\wr \OD_{16}$ | 4C | $4$ | $16$ | not computed | 2C | $(11,15,12,16)(13,14)$ |
| $C_2\wr \OD_{16}$ | 4D | $4$ | $16$ | not computed | 2C | $(3,4)(7,8)(11,15,12,16)(13,14)$ |
| $C_2\wr \OD_{16}$ | 4E | $4$ | $16$ | not computed | 2C | $(3,4)(7,8)(9,13,10,14)(15,16)$ |
| $C_2\wr \OD_{16}$ | 4F | $4$ | $16$ | not computed | 2B | $(3,4)(7,8)(9,13,10,14)(11,15,12,16)$ |
| $C_2\wr \OD_{16}$ | 4G | $4$ | $16$ | not computed | 2C | $(3,7,4,8)(5,6)(9,10)(11,12)(13,14)(15,16)$ |
| $C_2\wr \OD_{16}$ | 4H | $4$ | $16$ | not computed | 2A | $(1,6,2,5)(3,7,4,8)(9,14,10,13)(11,16,12,15)$ |
| $C_2\wr \OD_{16}$ | 4I | $4$ | $32$ | not computed | 2C | $(3,7)(4,8)(11,15,12,16)(13,14)$ |
| $C_2\wr \OD_{16}$ | 4J | $4$ | $32$ | not computed | 2C | $(3,7)(4,8)(9,13,10,14)(15,16)$ |
| $C_2\wr \OD_{16}$ | 4K | $4$ | $32$ | not computed | 2B | $(3,7)(4,8)(9,13,10,14)(11,15,12,16)$ |
| $C_2\wr \OD_{16}$ | 4L | $4$ | $32$ | not computed | 2C | $(3,7,4,8)(5,6)(9,10)(11,15)(12,16)(13,14)$ |
| $C_2\wr \OD_{16}$ | 4M | $4$ | $32$ | not computed | 2C | $(3,7,4,8)(5,6)(9,13)(10,14)(11,12)(15,16)$ |
| $C_2\wr \OD_{16}$ | 4N | $4$ | $32$ | not computed | 2C | $(3,7,4,8)(5,6)(9,13)(10,14)(11,15)(12,16)$ |
| $C_2\wr \OD_{16}$ | 4O | $4$ | $32$ | not computed | 2C | $(3,7,4,8)(5,6)(9,13)(10,14)(11,16)(12,15)$ |
| $C_2\wr \OD_{16}$ | 4P | $4$ | $32$ | not computed | 2B | $(1,2)(3,7)(4,8)(5,6)(9,13,10,14)(11,15,12,16)$ |