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Elements of the group are displayed as permutations of degree 14.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_2^3:S_4\times S_3^2$ | 1A | $1$ | $1$ | $C_2^3:S_4\times S_3^2$ | 1A | 1A | $()$ |
| $C_2^3:S_4\times S_3^2$ | 2A | $2$ | $1$ | $C_2^3:S_4\times S_3^2$ | 1A | 2A | $(7,14)(8,13)(9,12)(10,11)$ |
| $C_2^3:S_4\times S_3^2$ | 2B | $2$ | $3$ | $S_3\times C_2^4:S_4$ | 1A | 2B | $(1,4)(2,5)(3,6)$ |
| $C_2^3:S_4\times S_3^2$ | 2C | $2$ | $3$ | $S_3\times C_2^4:S_4$ | 1A | 2C | $(1,4)(2,5)(3,6)(7,14)(8,13)(9,12)(10,11)$ |
| $C_2^3:S_4\times S_3^2$ | 2D | $2$ | $3$ | $S_3\times C_2^4:S_4$ | 1A | 2D | $(1,6)(2,5)(3,4)$ |
| $C_2^3:S_4\times S_3^2$ | 2E | $2$ | $3$ | $S_3\times C_2^4:S_4$ | 1A | 2E | $(1,6)(2,5)(3,4)(7,14)(8,13)(9,12)(10,11)$ |
| $C_2^3:S_4\times S_3^2$ | 2F | $2$ | $6$ | $D_6^2:D_4$ | 1A | 2F | $(8,13)(9,12)$ |
| $C_2^3:S_4\times S_3^2$ | 2G | $2$ | $6$ | $D_6^2:D_4$ | 1A | 2G | $(7,9)(8,10)(11,13)(12,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2H | $2$ | $6$ | $D_6^2:D_4$ | 1A | 2H | $(7,9)(8,11)(10,13)(12,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2I | $2$ | $9$ | $C_2^5:S_4$ | 1A | 2I | $(1,5)(2,4)(7,14)(8,13)(9,12)(10,11)$ |
| $C_2^3:S_4\times S_3^2$ | 2J | $2$ | $9$ | $C_2^5:S_4$ | 1A | 2J | $(1,3)(2,4)$ |
| $C_2^3:S_4\times S_3^2$ | 2K | $2$ | $12$ | $C_2^2\times D_6^2$ | 1A | 2K | $(9,10)(11,12)$ |
| $C_2^3:S_4\times S_3^2$ | 2L | $2$ | $12$ | $C_2^2\times D_6^2$ | 1A | 2L | $(7,8)(9,12)(10,11)(13,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2M | $2$ | $18$ | $C_2^5:D_6$ | 1A | 2M | $(1,4)(2,5)(3,6)(9,12)(10,11)$ |
| $C_2^3:S_4\times S_3^2$ | 2N | $2$ | $18$ | $C_2^5:D_6$ | 1A | 2N | $(1,4)(2,5)(3,6)(7,8)(9,10)(11,12)(13,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2O | $2$ | $18$ | $C_2^5:D_6$ | 1A | 2O | $(1,4)(2,5)(3,6)(7,8)(9,11)(10,12)(13,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2P | $2$ | $18$ | $C_2^5:D_6$ | 1A | 2P | $(1,6)(2,5)(3,4)(9,12)(10,11)$ |
| $C_2^3:S_4\times S_3^2$ | 2Q | $2$ | $18$ | $C_2^5:D_6$ | 1A | 2Q | $(1,6)(2,5)(3,4)(7,8)(9,10)(11,12)(13,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2R | $2$ | $18$ | $C_2^5:D_6$ | 1A | 2R | $(1,6)(2,5)(3,4)(7,8)(9,11)(10,12)(13,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2S | $2$ | $36$ | $D_6\times C_2^4$ | 1A | 2S | $(1,4)(2,5)(3,6)(9,10)(11,12)$ |
| $C_2^3:S_4\times S_3^2$ | 2T | $2$ | $36$ | $D_6\times C_2^4$ | 1A | 2T | $(1,4)(2,5)(3,6)(7,8)(9,12)(10,11)(13,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2U | $2$ | $36$ | $D_6\times C_2^4$ | 1A | 2U | $(1,6)(2,5)(3,4)(9,10)(11,12)$ |
| $C_2^3:S_4\times S_3^2$ | 2V | $2$ | $36$ | $D_6\times C_2^4$ | 1A | 2V | $(1,6)(2,5)(3,4)(7,8)(9,12)(10,11)(13,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2W | $2$ | $54$ | $C_2^4:D_4$ | 1A | 2W | $(3,5)(4,6)(9,12)(10,11)$ |
| $C_2^3:S_4\times S_3^2$ | 2X | $2$ | $54$ | $C_2^4:D_4$ | 1A | 2X | $(3,5)(4,6)(7,8)(9,10)(11,12)(13,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2Y | $2$ | $54$ | $C_2^4:D_4$ | 1A | 2Y | $(3,5)(4,6)(7,8)(9,11)(10,12)(13,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2Z | $2$ | $108$ | $C_2^6$ | 1A | 2Z | $(2,6)(3,5)(7,11)(8,13)(9,12)(10,14)$ |
| $C_2^3:S_4\times S_3^2$ | 2AA | $2$ | $108$ | $C_2^6$ | 1A | 2AA | $(2,4)(3,5)(7,13)(8,14)$ |
| $C_2^3:S_4\times S_3^2$ | 3A | $3$ | $2$ | $C_6^2:C_2^2:S_4$ | 3A | 1A | $(1,3,5)(2,4,6)$ |
| $C_2^3:S_4\times S_3^2$ | 3B | $3$ | $2$ | $C_6^2:C_2^2:S_4$ | 3B | 1A | $(1,3,5)(2,6,4)$ |
| $C_2^3:S_4\times S_3^2$ | 3C | $3$ | $4$ | $C_3^2\times C_2^3:S_4$ | 3C | 1A | $(2,6,4)$ |
| $C_2^3:S_4\times S_3^2$ | 3D | $3$ | $32$ | $C_6\times S_3^2$ | 3D | 1A | $(7,9,13)(8,14,12)$ |
| $C_2^3:S_4\times S_3^2$ | 3E | $3$ | $64$ | $C_3^2\times D_6$ | 3E | 1A | $(1,5,3)(2,6,4)(7,9,13)(8,14,12)$ |
| $C_2^3:S_4\times S_3^2$ | 3F | $3$ | $64$ | $C_3^2\times D_6$ | 3F | 1A | $(1,5,3)(2,4,6)(7,9,13)(8,14,12)$ |
| $C_2^3:S_4\times S_3^2$ | 3G | $3$ | $128$ | $C_3^2\times C_6$ | 3G | 1A | $(1,5,3)(7,8,10)(11,14,13)$ |
| $C_2^3:S_4\times S_3^2$ | 4A | $4$ | $12$ | $C_4.D_6^2$ | 2A | 4A | $(7,13,14,8)(9,11,12,10)$ |
| $C_2^3:S_4\times S_3^2$ | 4B | $4$ | $24$ | $C_2.D_6^2$ | 2F | 4B | $(8,12,13,9)(10,11)$ |
| $C_2^3:S_4\times S_3^2$ | 4C | $4$ | $24$ | $C_2.D_6^2$ | 2G | 4C | $(7,10,9,8)(11,12,13,14)$ |
| $C_2^3:S_4\times S_3^2$ | 4D | $4$ | $24$ | $C_2.D_6^2$ | 2H | 4D | $(7,11,9,8)(10,12,13,14)$ |
| $C_2^3:S_4\times S_3^2$ | 4E | $4$ | $36$ | $D_{12}:C_2^3$ | 2A | 4E | $(1,4)(2,5)(3,6)(7,13,14,8)(9,11,12,10)$ |
| $C_2^3:S_4\times S_3^2$ | 4F | $4$ | $36$ | $D_{12}:C_2^3$ | 2A | 4F | $(1,6)(2,5)(3,4)(7,13,14,8)(9,11,12,10)$ |
| $C_2^3:S_4\times S_3^2$ | 4G | $4$ | $72$ | $C_{12}:C_2^3$ | 2H | 4G | $(1,2)(3,4)(5,6)(7,10,8,12)(9,14,11,13)$ |
| $C_2^3:S_4\times S_3^2$ | 4H | $4$ | $72$ | $C_{12}:C_2^3$ | 2F | 4H | $(1,6)(2,3)(4,5)(7,14)(9,11,12,10)$ |
| $C_2^3:S_4\times S_3^2$ | 4I | $4$ | $72$ | $C_{12}:C_2^3$ | 2G | 4I | $(1,2)(3,4)(5,6)(7,11,9,13)(8,14,10,12)$ |
| $C_2^3:S_4\times S_3^2$ | 4J | $4$ | $72$ | $C_{12}:C_2^3$ | 2F | 4J | $(1,4)(2,3)(5,6)(7,14)(8,11,13,10)$ |
| $C_2^3:S_4\times S_3^2$ | 4K | $4$ | $72$ | $C_{12}:C_2^3$ | 2H | 4K | $(1,6)(2,5)(3,4)(7,13,12,11)(8,9,10,14)$ |
| $C_2^3:S_4\times S_3^2$ | 4L | $4$ | $72$ | $C_{12}:C_2^3$ | 2G | 4L | $(1,4)(2,3)(5,6)(7,12,13,10)(8,11,14,9)$ |
| $C_2^3:S_4\times S_3^2$ | 4M | $4$ | $108$ | $D_4:C_2^3$ | 2A | 4M | $(1,5)(4,6)(7,13,14,8)(9,10,12,11)$ |
| $C_2^3:S_4\times S_3^2$ | 4N | $4$ | $216$ | $C_2^3\times C_4$ | 2G | 4N | $(1,3)(4,6)(7,9,10,8)(11,13,14,12)$ |
| $C_2^3:S_4\times S_3^2$ | 4O | $4$ | $216$ | $C_2^3\times C_4$ | 2F | 4O | $(1,5)(4,6)(7,14)(8,9,13,12)$ |