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Results (48 matches)
Download displayed columns for resultsElements of the group are displayed as permutations of degree 18.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_2^6:S_4$ | 1A | $1$ | $1$ | $C_2^6:S_4$ | 1A | 1A | $()$ |
| $C_2^6:S_4$ | 2A | $2$ | $1$ | $C_2^6:S_4$ | 1A | 2A | $(17,18)$ |
| $C_2^6:S_4$ | 2B | $2$ | $3$ | $D_4^2:C_2^3$ | 1A | 2B | $(1,2)(3,6)(4,7)(5,8)(9,12)(10,13)(11,16)(14,15)(17,18)$ |
| $C_2^6:S_4$ | 2C | $2$ | $3$ | $D_4^2:C_2^3$ | 1A | 2C | $(1,6)(2,3)(4,12)(5,13)(7,9)(8,10)(11,14)(15,16)$ |
| $C_2^6:S_4$ | 2D | $2$ | $4$ | $C_2^2\wr S_3$ | 1A | 2D | $(4,12)(5,10)(7,9)(8,13)(11,16)(14,15)$ |
| $C_2^6:S_4$ | 2E | $2$ | $4$ | $C_2^2\wr S_3$ | 1A | 2E | $(4,12)(5,10)(7,9)(8,13)(11,16)(14,15)(17,18)$ |
| $C_2^6:S_4$ | 2F | $2$ | $6$ | $C_2^5:D_4$ | 1A | 2F | $(5,13)(8,10)(11,14)(15,16)$ |
| $C_2^6:S_4$ | 2G | $2$ | $6$ | $C_2^5:D_4$ | 1A | 2G | $(5,13)(8,10)(11,14)(15,16)(17,18)$ |
| $C_2^6:S_4$ | 2H | $2$ | $6$ | $C_2^6:C_4$ | 1A | 2H | $(1,2)(3,6)(4,7)(5,10)(8,13)(9,12)(11,15)(14,16)$ |
| $C_2^6:S_4$ | 2I | $2$ | $6$ | $C_2^6:C_4$ | 1A | 2I | $(1,2)(3,6)(4,7)(5,10)(8,13)(9,12)(11,15)(14,16)(17,18)$ |
| $C_2^6:S_4$ | 2J | $2$ | $12$ | $C_2^4:D_4$ | 1A | 2J | $(4,7)(5,10)(8,13)(9,12)(11,14)(15,16)(17,18)$ |
| $C_2^6:S_4$ | 2K | $2$ | $12$ | $C_2^4:D_4$ | 1A | 2K | $(1,4)(2,7)(3,9)(5,11)(6,12)(8,16)(10,15)(13,14)(17,18)$ |
| $C_2^6:S_4$ | 2L | $2$ | $12$ | $C_2^5:C_4$ | 1A | 2L | $(1,4)(2,7)(3,9)(5,14)(6,12)(8,15)(10,16)(11,13)$ |
| $C_2^6:S_4$ | 2M | $2$ | $12$ | $C_2^5:C_4$ | 1A | 2M | $(1,4)(2,7)(3,9)(5,14)(6,12)(8,15)(10,16)(11,13)(17,18)$ |
| $C_2^6:S_4$ | 2N | $2$ | $12$ | $C_2^4:D_4$ | 1A | 2N | $(1,8)(2,5)(3,13)(4,16)(6,10)(7,11)(9,14)(12,15)$ |
| $C_2^6:S_4$ | 2O | $2$ | $12$ | $C_2^4:D_4$ | 1A | 2O | $(1,2)(3,6)(5,13)(8,10)(11,15)(14,16)$ |
| $C_2^6:S_4$ | 2P | $2$ | $24$ | $D_4\times C_2^3$ | 1A | 2P | $(3,6)(4,5)(7,8)(9,13)(10,12)(14,15)$ |
| $C_2^6:S_4$ | 2Q | $2$ | $24$ | $D_4\times C_2^3$ | 1A | 2Q | $(3,6)(4,5)(7,8)(9,13)(10,12)(14,15)(17,18)$ |
| $C_2^6:S_4$ | 2R | $2$ | $24$ | $D_4\times C_2^3$ | 1A | 2R | $(3,6)(4,8)(5,7)(9,10)(12,13)(14,15)$ |
| $C_2^6:S_4$ | 2S | $2$ | $24$ | $D_4\times C_2^3$ | 1A | 2S | $(3,6)(4,8)(5,7)(9,10)(12,13)(14,15)(17,18)$ |
| $C_2^6:S_4$ | 3A | $3$ | $128$ | $C_2\times C_6$ | 3A | 1A | $(2,6,3)(4,13,14)(5,16,7)(8,15,12)(9,10,11)$ |
| $C_2^6:S_4$ | 4A | $4$ | $12$ | $D_8:C_2^3$ | 2C | 4A | $(1,4,6,12)(2,7,3,9)(5,15,13,16)(8,14,10,11)$ |
| $C_2^6:S_4$ | 4B | $4$ | $12$ | $D_8:C_2^3$ | 2C | 4B | $(1,4,6,12)(2,7,3,9)(5,15,13,16)(8,14,10,11)(17,18)$ |
| $C_2^6:S_4$ | 4C | $4$ | $12$ | $C_4^2:C_2^3$ | 2C | 4C | $(1,4,6,12)(2,7,3,9)(5,16,13,15)(8,11,10,14)(17,18)$ |
| $C_2^6:S_4$ | 4D | $4$ | $12$ | $C_4^2:C_2^3$ | 2C | 4D | $(1,5,3,10)(2,8,6,13)(4,16,9,14)(7,11,12,15)$ |
| $C_2^6:S_4$ | 4E | $4$ | $24$ | $D_4:C_2^3$ | 2C | 4E | $(1,2,3,6)(4,11,9,15)(5,13,10,8)(7,14,12,16)$ |
| $C_2^6:S_4$ | 4F | $4$ | $24$ | $D_4:C_2^3$ | 2C | 4F | $(1,2,3,6)(4,11,9,15)(5,13,10,8)(7,14,12,16)(17,18)$ |
| $C_2^6:S_4$ | 4G | $4$ | $24$ | $D_4:C_2^3$ | 2C | 4G | $(1,2,3,6)(4,15,9,11)(5,13,10,8)(7,16,12,14)$ |
| $C_2^6:S_4$ | 4H | $4$ | $24$ | $D_4:C_2^3$ | 2C | 4H | $(1,2,3,6)(4,15,9,11)(5,13,10,8)(7,16,12,14)(17,18)$ |
| $C_2^6:S_4$ | 4I | $4$ | $24$ | $C_4^2:C_2^2$ | 2C | 4I | $(1,4,2,7)(3,9,6,12)(5,15,8,14)(10,11,13,16)$ |
| $C_2^6:S_4$ | 4J | $4$ | $24$ | $C_4^2:C_2^2$ | 2C | 4J | $(1,4,2,7)(3,9,6,12)(5,15,8,14)(10,11,13,16)(17,18)$ |
| $C_2^6:S_4$ | 4K | $4$ | $24$ | $C_4^2:C_2^2$ | 2C | 4K | $(1,4,2,7)(3,9,6,12)(5,16,8,11)(10,14,13,15)$ |
| $C_2^6:S_4$ | 4L | $4$ | $24$ | $C_4^2:C_2^2$ | 2C | 4L | $(1,4,2,7)(3,9,6,12)(5,16,8,11)(10,14,13,15)(17,18)$ |
| $C_2^6:S_4$ | 4M | $4$ | $48$ | $C_2^3\times C_4$ | 2N | 4M | $(1,12,8,15)(2,4,5,16)(3,7,13,11)(6,9,10,14)$ |
| $C_2^6:S_4$ | 4N | $4$ | $48$ | $C_2^3\times C_4$ | 2O | 4N | $(1,10,2,8)(3,5,6,13)(4,9)(11,14,15,16)$ |
| $C_2^6:S_4$ | 4O | $4$ | $48$ | $C_2^3\times C_4$ | 2N | 4O | $(1,14,8,9)(2,11,5,7)(3,16,13,4)(6,15,10,12)(17,18)$ |
| $C_2^6:S_4$ | 4P | $4$ | $48$ | $C_2^3\times C_4$ | 2O | 4P | $(1,2)(4,5,9,13)(7,8,12,10)(11,14,16,15)(17,18)$ |
| $C_2^6:S_4$ | 4Q | $4$ | $48$ | $C_2^3\times C_4$ | 2O | 4Q | $(1,6)(4,9,12,7)(5,11,8,15)(10,16,13,14)$ |
| $C_2^6:S_4$ | 4R | $4$ | $48$ | $C_2^3\times C_4$ | 2N | 4R | $(1,15,13,7)(2,16,10,9)(3,11,8,12)(4,6,14,5)$ |
| $C_2^6:S_4$ | 4S | $4$ | $48$ | $C_2^3\times C_4$ | 2O | 4S | $(1,5,6,8)(2,13,3,10)(4,12,9,7)(14,16)(17,18)$ |
| $C_2^6:S_4$ | 4T | $4$ | $48$ | $C_2^3\times C_4$ | 2N | 4T | $(1,11,8,7)(2,14,5,9)(3,15,13,12)(4,6,16,10)(17,18)$ |
| $C_2^6:S_4$ | 6A | $6$ | $128$ | $C_2\times C_6$ | 3A | 2A | $(2,3,6)(4,14,13)(5,7,16)(8,12,15)(9,11,10)(17,18)$ |
| $C_2^6:S_4$ | 6B | $6$ | $128$ | $C_2\times C_6$ | 3A | 2D | $(1,3,2)(4,11,10,12,16,5)(7,15,8,9,14,13)$ |
| $C_2^6:S_4$ | 6C | $6$ | $128$ | $C_2\times C_6$ | 3A | 2E | $(1,6,2)(4,8,16,12,13,11)(5,15,7,10,14,9)(17,18)$ |
| $C_2^6:S_4$ | 8A | $8$ | $48$ | $C_2^2\times C_8$ | 4D | 8A | $(1,4,5,16,3,9,10,14)(2,12,8,15,6,7,13,11)(17,18)$ |
| $C_2^6:S_4$ | 8B | $8$ | $48$ | $C_2^2\times C_8$ | 4D | 8B | $(1,15,13,9,3,11,8,4)(2,16,10,7,6,14,5,12)(17,18)$ |
| $C_2^6:S_4$ | 8C | $8$ | $48$ | $C_2^2\times C_8$ | 4D | 8C | $(1,14,10,9,3,16,5,4)(2,11,13,7,6,15,8,12)$ |
| $C_2^6:S_4$ | 8D | $8$ | $48$ | $C_2^2\times C_8$ | 4D | 8D | $(1,11,13,4,3,15,8,9)(2,14,10,12,6,16,5,7)$ |