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Elements of the group are displayed as permutations of degree 17.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_6:D_6^2:S_4$ | 1A | $1$ | $1$ | $C_6:D_6^2:S_4$ | 1A | 1A | $()$ |
| $C_6:D_6^2:S_4$ | 2A | $2$ | $3$ | $C_3^3.C_2^6.C_2^2$ | 1A | 2A | $(10,12)(11,17)(13,16)(14,15)$ |
| $C_6:D_6^2:S_4$ | 2B | $2$ | $4$ | $C_6^3:S_4$ | 1A | 2B | $(10,11)(12,17)(13,14)(15,16)$ |
| $C_6:D_6^2:S_4$ | 2C | $2$ | $6$ | $C_3^3.C_2^6.C_2$ | 1A | 2C | $(11,17)(14,15)$ |
| $C_6:D_6^2:S_4$ | 2D | $2$ | $6$ | $C_3^3.C_2^6.C_2$ | 1A | 2D | $(10,13)(11,15)(12,16)(14,17)$ |
| $C_6:D_6^2:S_4$ | 2E | $2$ | $27$ | $C_2^4:(C_2\times D_{12})$ | 1A | 2E | $(4,9)(5,6)(10,16)(11,15)(12,13)(14,17)$ |
| $C_6:D_6^2:S_4$ | 2F | $2$ | $27$ | $C_2^4:(C_2\times D_{12})$ | 1A | 2F | $(1,5)(3,4)$ |
| $C_6:D_6^2:S_4$ | 2G | $2$ | $54$ | $C_2^5:D_6$ | 1A | 2G | $(5,6)(7,8)(10,13)(11,14)(12,16)(15,17)$ |
| $C_6:D_6^2:S_4$ | 2H | $2$ | $54$ | $C_2^4:D_{12}$ | 1A | 2H | $(5,6)(7,8)(10,16)(11,14)(12,13)(15,17)$ |
| $C_6:D_6^2:S_4$ | 2I | $2$ | $54$ | $C_2^4:D_{12}$ | 1A | 2I | $(2,7)(5,6)(11,17)(14,15)$ |
| $C_6:D_6^2:S_4$ | 2J | $2$ | $108$ | $D_6\times C_2^4$ | 1A | 2J | $(1,5)(2,8)(10,16)(12,13)$ |
| $C_6:D_6^2:S_4$ | 2K | $2$ | $108$ | $C_2^3:D_{12}$ | 1A | 2K | $(2,7)(5,6)(10,14)(11,13)(12,15)(16,17)$ |
| $C_6:D_6^2:S_4$ | 2L | $2$ | $108$ | $D_6\times C_2^4$ | 1A | 2L | $(5,6)(7,8)(10,12)(11,15)(13,16)(14,17)$ |
| $C_6:D_6^2:S_4$ | 2M | $2$ | $216$ | $D_4\times D_6$ | 1A | 2M | $(1,9)(2,7)(3,5)(4,6)(10,16)(11,15)$ |
| $C_6:D_6^2:S_4$ | 2N | $2$ | $216$ | $D_4\times D_6$ | 1A | 2N | $(1,8)(2,5)(3,9)(6,7)(10,14)(11,16)(12,15)(13,17)$ |
| $C_6:D_6^2:S_4$ | 3A | $3$ | $6$ | $C_6^3.C_2^3.C_2$ | 3A | 1A | $(3,9,4)$ |
| $C_6:D_6^2:S_4$ | 3B | $3$ | $8$ | $C_6^3:A_4$ | 3B | 1A | $(1,6,5)(2,8,7)(3,9,4)$ |
| $C_6:D_6^2:S_4$ | 3C | $3$ | $12$ | $C_6^3:D_4$ | 3C | 1A | $(2,8,7)(3,9,4)$ |
| $C_6:D_6^2:S_4$ | 3D | $3$ | $1152$ | $C_3\times C_6$ | 3D | 1A | $(1,8,3)(2,9,5)(4,6,7)(11,15,14)(12,13,16)$ |
| $C_6:D_6^2:S_4$ | 4A | $4$ | $12$ | $(C_6\times C_{12}):D_{12}$ | 2A | 4A | $(10,17,12,11)(13,15,16,14)$ |
| $C_6:D_6^2:S_4$ | 4B | $4$ | $108$ | $C_4^2:D_6$ | 2A | 4B | $(1,6)(3,4)(10,15,16,11)(12,14,13,17)$ |
| $C_6:D_6^2:S_4$ | 4C | $4$ | $216$ | $D_4:D_6$ | 2A | 4C | $(1,5)(2,9)(3,8)(4,7)(10,12,13,16)(11,17,14,15)$ |
| $C_6:D_6^2:S_4$ | 4D | $4$ | $216$ | $D_4\times C_{12}$ | 2E | 4D | $(1,3)(4,6,9,5)(10,11,16,15)(12,14,13,17)$ |
| $C_6:D_6^2:S_4$ | 4E | $4$ | $216$ | $D_4:D_6$ | 2A | 4E | $(1,4)(2,8)(3,5)(6,9)(10,17,16,14)(11,12,15,13)$ |
| $C_6:D_6^2:S_4$ | 4F | $4$ | $216$ | $D_4\times C_{12}$ | 2E | 4F | $(1,7,6,2)(5,8)(10,16,12,13)(11,15,17,14)$ |
| $C_6:D_6^2:S_4$ | 4G | $4$ | $216$ | $C_{12}:C_2^3$ | 2A | 4G | $(2,7)(4,9)(10,17,16,14)(11,13,15,12)$ |
| $C_6:D_6^2:S_4$ | 4H | $4$ | $216$ | $D_4\times C_{12}$ | 2F | 4H | $(1,4,5,3)(6,9)(10,11)(12,14)(13,17)(15,16)$ |
| $C_6:D_6^2:S_4$ | 4I | $4$ | $216$ | $D_4\times C_{12}$ | 2F | 4I | $(2,3,8,9)(4,7)(10,13)(15,17)$ |
| $C_6:D_6^2:S_4$ | 4J | $4$ | $432$ | $C_4\times D_6$ | 2D | 4J | $(1,5)(2,9)(3,7)(4,8)(10,15,16,14)(11,13,17,12)$ |
| $C_6:D_6^2:S_4$ | 4K | $4$ | $432$ | $C_2^2\times C_{12}$ | 2H | 4K | $(1,2)(5,8,6,7)(10,11,16,14)(12,17,13,15)$ |
| $C_6:D_6^2:S_4$ | 4L | $4$ | $432$ | $C_2^2\times C_{12}$ | 2I | 4L | $(1,8)(2,5,7,6)(10,12)(11,15,17,14)$ |
| $C_6:D_6^2:S_4$ | 4M | $4$ | $432$ | $C_4\times D_6$ | 2C | 4M | $(1,2)(3,9)(5,7)(6,8)(10,12)(11,15,17,14)$ |
| $C_6:D_6^2:S_4$ | 6A | $6$ | $6$ | $C_6^3.C_2^3.C_2$ | 3A | 2A | $(3,9,4)(10,12)(11,17)(13,16)(14,15)$ |
| $C_6:D_6^2:S_4$ | 6B | $6$ | $12$ | $(C_2\times C_6^3):C_4$ | 3A | 2C | $(3,4,9)(11,17)(14,15)$ |
| $C_6:D_6^2:S_4$ | 6C | $6$ | $12$ | $(C_2\times C_6^3):C_4$ | 3A | 2D | $(3,4,9)(10,13)(11,15)(12,16)(14,17)$ |
| $C_6:D_6^2:S_4$ | 6D | $6$ | $12$ | $C_6^3:C_2^3$ | 3A | 2A | $(3,9,4)(10,13)(11,14)(12,16)(15,17)$ |
| $C_6:D_6^2:S_4$ | 6E | $6$ | $12$ | $C_6^3:D_4$ | 3C | 2A | $(2,8,7)(3,9,4)(10,13)(11,14)(12,16)(15,17)$ |
| $C_6:D_6^2:S_4$ | 6F | $6$ | $24$ | $C_6^3:C_2^2$ | 3A | 2C | $(3,4,9)(11,14)(15,17)$ |
| $C_6:D_6^2:S_4$ | 6G | $6$ | $24$ | $C_6^3:C_4$ | 3A | 2B | $(3,4,9)(10,11)(12,17)(13,14)(15,16)$ |
| $C_6:D_6^2:S_4$ | 6H | $6$ | $24$ | $C_6^3:C_2^2$ | 3A | 2D | $(3,4,9)(10,12)(11,14)(13,16)(15,17)$ |
| $C_6:D_6^2:S_4$ | 6I | $6$ | $24$ | $C_6^3:C_2^2$ | 3C | 2A | $(2,8,7)(3,9,4)(10,12)(11,17)(13,16)(14,15)$ |
| $C_6:D_6^2:S_4$ | 6J | $6$ | $24$ | $C_6^3:C_2^2$ | 3B | 2A | $(1,6,5)(2,8,7)(3,9,4)(10,12)(11,17)(13,16)(14,15)$ |
| $C_6:D_6^2:S_4$ | 6K | $6$ | $24$ | $C_6^3.C_2^2$ | 3C | 2D | $(2,8,7)(3,9,4)(10,16)(11,17)(12,13)(14,15)$ |
| $C_6:D_6^2:S_4$ | 6L | $6$ | $24$ | $C_6^3.C_2^2$ | 3C | 2C | $(1,5,6)(2,7,8)(11,17)(14,15)$ |
| $C_6:D_6^2:S_4$ | 6M | $6$ | $32$ | $C_6\wr C_3$ | 3B | 2B | $(1,5,6)(2,8,7)(3,4,9)(10,11)(12,17)(13,14)(15,16)$ |
| $C_6:D_6^2:S_4$ | 6N | $6$ | $48$ | $C_2\times C_6^3$ | 3C | 2C | $(2,7,8)(3,4,9)(11,15)(14,17)$ |
| $C_6:D_6^2:S_4$ | 6O | $6$ | $48$ | $C_6^3:C_2$ | 3C | 2B | $(2,7,8)(3,4,9)(10,11)(12,17)(13,14)(15,16)$ |
| $C_6:D_6^2:S_4$ | 6P | $6$ | $48$ | $C_2\times C_6^3$ | 3C | 2D | $(2,7,8)(3,4,9)(10,12)(11,14)(13,16)(15,17)$ |
| $C_6:D_6^2:S_4$ | 6Q | $6$ | $48$ | $C_2\times C_6^3$ | 3B | 2C | $(1,5,6)(2,7,8)(3,4,9)(11,14)(15,17)$ |
| $C_6:D_6^2:S_4$ | 6R | $6$ | $48$ | $C_2\times C_6^3$ | 3B | 2D | $(1,5,6)(2,7,8)(3,4,9)(10,12)(11,14)(13,16)(15,17)$ |