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Elements of the group are displayed as permutations of degree 15.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $(C_2^4\times C_6):S_4$ | 1A | $1$ | $1$ | $(C_2^4\times C_6):S_4$ | 1A | 1A | $()$ |
| $(C_2^4\times C_6):S_4$ | 2A | $2$ | $3$ | $C_2^6:D_6$ | 1A | 2A | $(4,5)(6,7)$ |
| $(C_2^4\times C_6):S_4$ | 2B | $2$ | $3$ | $C_2^6:D_6$ | 1A | 2B | $(4,5)(6,7)(8,10)(9,13)(11,15)(12,14)$ |
| $(C_2^4\times C_6):S_4$ | 2C | $2$ | $3$ | $C_2^6:D_6$ | 1A | 2C | $(8,10)(9,13)(11,15)(12,14)$ |
| $(C_2^4\times C_6):S_4$ | 2D | $2$ | $4$ | $(C_2^2\times C_6):S_4$ | 1A | 2D | $(8,9)(10,13)(11,14)(12,15)$ |
| $(C_2^4\times C_6):S_4$ | 2E | $2$ | $6$ | $C_2^6:C_6$ | 1A | 2E | $(4,5)(6,7)(8,11)(9,14)(10,15)(12,13)$ |
| $(C_2^4\times C_6):S_4$ | 2F | $2$ | $6$ | $C_2^6:S_3$ | 1A | 2F | $(9,12)(13,14)$ |
| $(C_2^4\times C_6):S_4$ | 2G | $2$ | $6$ | $C_2^6:S_3$ | 1A | 2G | $(8,10)(9,12)(11,15)(13,14)$ |
| $(C_2^4\times C_6):S_4$ | 2H | $2$ | $6$ | $C_2^6:S_3$ | 1A | 2H | $(4,5)(6,7)(9,13)(12,14)$ |
| $(C_2^4\times C_6):S_4$ | 2I | $2$ | $6$ | $C_2^6:S_3$ | 1A | 2I | $(4,5)(6,7)(8,11)(9,12)(10,15)(13,14)$ |
| $(C_2^4\times C_6):S_4$ | 2J | $2$ | $12$ | $C_2^5\times C_6$ | 1A | 2J | $(4,5)(6,7)(9,12)(13,14)$ |
| $(C_2^4\times C_6):S_4$ | 2K | $2$ | $12$ | $C_2^5\times C_6$ | 1A | 2K | $(4,5)(6,7)(8,10)(9,12)(11,15)(13,14)$ |
| $(C_2^4\times C_6):S_4$ | 2L | $2$ | $12$ | $C_2^4:D_6$ | 1A | 2L | $(4,5)(6,7)(8,9)(10,13)(11,14)(12,15)$ |
| $(C_2^4\times C_6):S_4$ | 2M | $2$ | $72$ | $C_2^2\times D_4$ | 1A | 2M | $(1,2)(6,7)(9,13)(11,15)$ |
| $(C_2^4\times C_6):S_4$ | 2N | $2$ | $72$ | $C_2^2\times D_4$ | 1A | 2N | $(1,2)(4,5)(8,9)(10,13)(11,12)(14,15)$ |
| $(C_2^4\times C_6):S_4$ | 3A | $3$ | $2$ | $C_3\times C_2^5:A_4$ | 3A | 1A | $(1,3,2)$ |
| $(C_2^4\times C_6):S_4$ | 3B | $3$ | $128$ | $C_3\times C_6$ | 3B | 1A | $(4,6,5)(9,13,14)(10,15,11)$ |
| $(C_2^4\times C_6):S_4$ | 3C | $3$ | $128$ | $C_3\times C_6$ | 3C | 1A | $(1,3,2)(4,7,6)(8,11,15)(9,14,12)$ |
| $(C_2^4\times C_6):S_4$ | 3D | $3$ | $128$ | $C_3\times C_6$ | 3D | 1A | $(1,2,3)(4,5,7)(9,12,13)(10,15,11)$ |
| $(C_2^4\times C_6):S_4$ | 4A | $4$ | $12$ | $C_2^4.D_6$ | 2C | 4A | $(8,13,10,9)(11,12,15,14)$ |
| $(C_2^4\times C_6):S_4$ | 4B | $4$ | $12$ | $C_2^4.D_6$ | 2C | 4B | $(4,5)(6,7)(8,13,10,9)(11,12,15,14)$ |
| $(C_2^4\times C_6):S_4$ | 4C | $4$ | $24$ | $C_2^3\times C_{12}$ | 2C | 4C | $(4,5)(6,7)(8,14,11,9)(10,12,15,13)$ |
| $(C_2^4\times C_6):S_4$ | 4D | $4$ | $72$ | $C_4\times D_4$ | 2B | 4D | $(2,3)(4,5,7,6)(8,13,11,12)(9,10,14,15)$ |
| $(C_2^4\times C_6):S_4$ | 4E | $4$ | $72$ | $D_4:C_2^2$ | 2C | 4E | $(2,3)(5,6)(8,9,11,14)(10,12,15,13)$ |
| $(C_2^4\times C_6):S_4$ | 4F | $4$ | $72$ | $C_4\times D_4$ | 2A | 4F | $(1,3)(4,6,7,5)(8,14)(9,11)(10,13)(12,15)$ |
| $(C_2^4\times C_6):S_4$ | 4G | $4$ | $72$ | $C_4\times D_4$ | 2A | 4G | $(1,2)(4,6,7,5)(9,14)(10,15)$ |
| $(C_2^4\times C_6):S_4$ | 4H | $4$ | $72$ | $C_4\times D_4$ | 2B | 4H | $(1,3)(4,6,5,7)(8,15,10,11)(9,12,13,14)$ |
| $(C_2^4\times C_6):S_4$ | 4I | $4$ | $72$ | $D_4:C_2^2$ | 2C | 4I | $(1,2)(5,6)(8,15,11,10)(9,13,14,12)$ |
| $(C_2^4\times C_6):S_4$ | 4J | $4$ | $144$ | $C_2^2\times C_4$ | 2H | 4J | $(2,3)(4,6,7,5)(8,11)(9,13,14,12)$ |
| $(C_2^4\times C_6):S_4$ | 4K | $4$ | $144$ | $C_2^2\times C_4$ | 2I | 4K | $(1,3)(4,5,6,7)(8,12,11,14)(9,10,13,15)$ |
| $(C_2^4\times C_6):S_4$ | 4L | $4$ | $144$ | $C_2^2\times C_4$ | 2F | 4L | $(2,3)(4,7)(8,11)(9,13,14,12)$ |
| $(C_2^4\times C_6):S_4$ | 4M | $4$ | $144$ | $C_2^2\times C_4$ | 2G | 4M | $(1,3)(5,6)(8,13,10,14)(9,11,12,15)$ |
| $(C_2^4\times C_6):S_4$ | 6A | $6$ | $6$ | $C_2^6:C_6$ | 3A | 2A | $(1,2,3)(4,5)(6,7)$ |
| $(C_2^4\times C_6):S_4$ | 6B | $6$ | $6$ | $C_2^6:C_6$ | 3A | 2B | $(1,2,3)(4,5)(6,7)(8,10)(9,13)(11,15)(12,14)$ |
| $(C_2^4\times C_6):S_4$ | 6C | $6$ | $6$ | $C_2^6:C_6$ | 3A | 2C | $(1,3,2)(8,10)(9,13)(11,15)(12,14)$ |
| $(C_2^4\times C_6):S_4$ | 6D1 | $6$ | $6$ | $C_2^6:C_6$ | 3A | 2E | $(1,2,3)(4,5)(6,7)(8,11)(9,14)(10,15)(12,13)$ |
| $(C_2^4\times C_6):S_4$ | 6D-1 | $6$ | $6$ | $C_2^6:C_6$ | 3A | 2E | $(1,2,3)(4,5)(6,7)(8,15)(9,12)(10,11)(13,14)$ |
| $(C_2^4\times C_6):S_4$ | 6E | $6$ | $8$ | $C_2^5:C_3^2$ | 3A | 2D | $(1,2,3)(8,9)(10,13)(11,14)(12,15)$ |
| $(C_2^4\times C_6):S_4$ | 6F | $6$ | $12$ | $C_2^5\times C_6$ | 3A | 2F | $(1,2,3)(9,12)(13,14)$ |
| $(C_2^4\times C_6):S_4$ | 6G | $6$ | $12$ | $C_2^5\times C_6$ | 3A | 2G | $(1,2,3)(8,10)(9,12)(11,15)(13,14)$ |
| $(C_2^4\times C_6):S_4$ | 6H | $6$ | $12$ | $C_2^5\times C_6$ | 3A | 2H | $(1,2,3)(4,5)(6,7)(9,13)(12,14)$ |
| $(C_2^4\times C_6):S_4$ | 6I | $6$ | $12$ | $C_2^5\times C_6$ | 3A | 2I | $(1,2,3)(4,5)(6,7)(8,11)(9,12)(10,15)(13,14)$ |
| $(C_2^4\times C_6):S_4$ | 6J1 | $6$ | $12$ | $C_2^5\times C_6$ | 3A | 2J | $(1,2,3)(4,5)(6,7)(9,12)(13,14)$ |
| $(C_2^4\times C_6):S_4$ | 6J-1 | $6$ | $12$ | $C_2^5\times C_6$ | 3A | 2J | $(1,2,3)(4,5)(6,7)(9,14)(12,13)$ |
| $(C_2^4\times C_6):S_4$ | 6K1 | $6$ | $12$ | $C_2^5\times C_6$ | 3A | 2K | $(1,2,3)(4,5)(6,7)(8,10)(9,12)(11,15)(13,14)$ |
| $(C_2^4\times C_6):S_4$ | 6K-1 | $6$ | $12$ | $C_2^5\times C_6$ | 3A | 2K | $(1,2,3)(4,5)(6,7)(8,10)(9,14)(11,15)(12,13)$ |
| $(C_2^4\times C_6):S_4$ | 6L | $6$ | $24$ | $C_2^4\times C_6$ | 3A | 2L | $(1,2,3)(4,5)(6,7)(8,9)(10,13)(11,14)(12,15)$ |
| $(C_2^4\times C_6):S_4$ | 6M | $6$ | $128$ | $C_3\times C_6$ | 3B | 2D | $(4,5,6)(8,12)(9,10,13,15,14,11)$ |
| $(C_2^4\times C_6):S_4$ | 6N | $6$ | $128$ | $C_3\times C_6$ | 3C | 2D | $(1,2,3)(4,6,7)(8,12,11,9,15,14)(10,13)$ |
| $(C_2^4\times C_6):S_4$ | 6O | $6$ | $128$ | $C_3\times C_6$ | 3D | 2D | $(1,3,2)(4,7,5)(8,14)(9,15,12,11,13,10)$ |