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Elements of the group are displayed as permutations of degree 15.
| Group | Label | Order | Size | Centralizer | Powers | Representative | ||
|---|---|---|---|---|---|---|---|---|
| 2P | 3P | 5P | ||||||
| $F_9:S_6$ | 1A | $1$ | $1$ | $F_9:S_6$ | 1A | 1A | 1A | $()$ |
| $F_9:S_6$ | 2A | $2$ | $9$ | $C_8:S_6$ | 1A | 2A | 2A | $(7,12)(8,11)(9,10)(13,15)$ |
| $F_9:S_6$ | 2B | $2$ | $45$ | $D_4\times F_9:C_2$ | 1A | 2B | 2B | $(1,5)(2,3)$ |
| $F_9:S_6$ | 2C | $2$ | $180$ | $D_6\times S_4$ | 1A | 2C | 2C | $(1,5)(2,3)(4,6)(7,11)(8,12)(9,10)$ |
| $F_9:S_6$ | 2D | $2$ | $180$ | $D_6\times S_4$ | 1A | 2D | 2D | $(3,4)(7,10)(8,14)(12,15)$ |
| $F_9:S_6$ | 2E | $2$ | $405$ | $D_4\times \SD_{16}$ | 1A | 2E | 2E | $(2,3)(4,5)(7,8)(10,14)(11,13)(12,15)$ |
| $F_9:S_6$ | 3A | $3$ | $8$ | $C_3^2:S_6$ | 3A | 1A | 3A | $(7,13,10)(8,14,11)(9,15,12)$ |
| $F_9:S_6$ | 3B | $3$ | $40$ | $C_3^4:\SD_{16}$ | 3B | 1A | 3B | $(1,6,3)(2,5,4)$ |
| $F_9:S_6$ | 3C | $3$ | $40$ | $C_3^4:\SD_{16}$ | 3C | 1A | 3C | $(1,4,5)$ |
| $F_9:S_6$ | 3D | $3$ | $320$ | $C_3^2\wr C_2$ | 3D | 1A | 3D | $(1,3,4)(2,6,5)(7,14,12)(8,15,10)(9,13,11)$ |
| $F_9:S_6$ | 3E | $3$ | $320$ | $C_3^2\wr C_2$ | 3E | 1A | 3E | $(1,6,5)(7,14,12)(8,15,10)(9,13,11)$ |
| $F_9:S_6$ | 4A | $4$ | $18$ | $C_8\times A_6$ | 2A | 4A | 4A | $(7,11,12,8)(9,15,10,13)$ |
| $F_9:S_6$ | 4B | $4$ | $90$ | $C_4\times F_9:C_2$ | 2B | 4B | 4B | $(1,6)(2,3,4,5)$ |
| $F_9:S_6$ | 4C | $4$ | $540$ | $C_4\times S_4$ | 2A | 4C | 4C | $(1,4)(2,6)(3,5)(7,13,12,15)(8,9,11,10)$ |
| $F_9:S_6$ | 4D | $4$ | $540$ | $C_4\times S_4$ | 2A | 4D | 4D | $(3,6)(7,14,13,9)(8,12,15,11)$ |
| $F_9:S_6$ | 4E | $4$ | $810$ | $C_8\times D_4$ | 2A | 4E | 4E | $(2,3)(4,5)(7,14,11,13)(8,9,10,12)$ |
| $F_9:S_6$ | 4F | $4$ | $810$ | $C_4\times \SD_{16}$ | 2B | 4F | 4F | $(1,6)(2,5,3,4)(8,9)(10,13)(11,15)(12,14)$ |
| $F_9:S_6$ | 4G | $4$ | $1080$ | $C_4\times D_6$ | 2B | 4G | 4G | $(1,3,5,2)(7,12)(9,13)(10,15)$ |
| $F_9:S_6$ | 4H | $4$ | $1620$ | $C_4\times C_8$ | 2E | 4H | 4H | $(1,3,5,4)(2,6)(7,9,10,11)(8,14,12,15)$ |
| $F_9:S_6$ | 4I | $4$ | $3240$ | $C_4^2$ | 2E | 4I | 4I | $(2,4,3,5)(7,12,8,15)(10,11,14,13)$ |
| $F_9:S_6$ | 5A | $5$ | $144$ | $C_5\times F_9$ | 5A | 5A | 1A | $(1,4,2,5,3)$ |
| $F_9:S_6$ | 6A | $6$ | $360$ | $C_{24}:C_6$ | 3B | 2A | 6A | $(1,3,6)(2,4,5)(7,12)(8,11)(9,10)(13,15)$ |
| $F_9:S_6$ | 6B | $6$ | $360$ | $C_{24}:C_6$ | 3C | 2A | 6B | $(1,5,4)(7,13)(8,15)(9,14)(11,12)$ |
| $F_9:S_6$ | 6C | $6$ | $360$ | $C_{12}:D_6$ | 3A | 2B | 6C | $(1,5)(2,3)(7,13,10)(8,14,11)(9,15,12)$ |
| $F_9:S_6$ | 6D | $6$ | $360$ | $C_6\times S_4$ | 3A | 2C | 6D | $(1,2)(3,4)(5,6)(7,8,12,10,14,15)(9,13,11)$ |
| $F_9:S_6$ | 6E | $6$ | $360$ | $C_6\times S_4$ | 3A | 2D | 6E | $(1,5)(7,10,8,11,9,12)(13,15,14)$ |
| $F_9:S_6$ | 6F | $6$ | $1440$ | $C_6\times S_3$ | 3B | 2C | 6F | $(1,3,6,5,2,4)(7,11)(8,12)(9,10)$ |
| $F_9:S_6$ | 6G | $6$ | $1440$ | $C_6\times S_3$ | 3C | 2D | 6G | $(1,4,3)(2,5)(10,14)(11,15)(12,13)$ |
| $F_9:S_6$ | 6H | $6$ | $2880$ | $C_3\times C_6$ | 3D | 2C | 6H | $(1,2,3,6,4,5)(7,12,14)(8,13,15,11,10,9)$ |
| $F_9:S_6$ | 6I | $6$ | $2880$ | $C_3\times C_6$ | 3E | 2D | 6I | $(1,5,6)(3,4)(7,15,14,10,12,8)(9,11,13)$ |
| $F_9:S_6$ | 8A1 | $8$ | $18$ | $C_8\times A_6$ | 4A | 8A1 | 8A-1 | $(7,9,11,15,12,10,8,13)$ |
| $F_9:S_6$ | 8A-1 | $8$ | $18$ | $C_8\times A_6$ | 4A | 8A-1 | 8A1 | $(7,13,8,10,12,15,11,9)$ |
| $F_9:S_6$ | 8B1 | $8$ | $810$ | $C_8\times D_4$ | 4A | 8B1 | 8B-1 | $(1,6)(3,4)(8,12,15,13,9,14,11,10)$ |
| $F_9:S_6$ | 8B-1 | $8$ | $810$ | $C_8\times D_4$ | 4A | 8B-1 | 8B1 | $(1,6)(3,4)(8,10,11,14,9,13,15,12)$ |
| $F_9:S_6$ | 8C1 | $8$ | $1620$ | $C_4\times C_8$ | 4E | 8C1 | 8C-1 | $(1,6)(2,5,3,4)(7,8,14,9,11,10,13,12)$ |
| $F_9:S_6$ | 8C-1 | $8$ | $1620$ | $C_4\times C_8$ | 4E | 8C-1 | 8C1 | $(1,6)(2,4,3,5)(7,12,13,10,11,9,14,8)$ |
| $F_9:S_6$ | 10A | $10$ | $1296$ | $C_{40}$ | 5A | 10A | 2A | $(1,5,4,3,2)(7,12)(8,11)(9,10)(13,15)$ |
| $F_9:S_6$ | 12A | $12$ | $720$ | $C_3\times C_{24}$ | 6A | 4A | 12A | $(1,6,2)(3,5,4)(7,14,8,10)(11,15,13,12)$ |
| $F_9:S_6$ | 12B | $12$ | $720$ | $C_3\times C_{24}$ | 6B | 4A | 12B | $(4,5,6)(7,14,8,10)(11,15,13,12)$ |
| $F_9:S_6$ | 12C | $12$ | $720$ | $S_3\times C_{12}$ | 6C | 4B | 12C | $(1,6)(2,5,4,3)(7,11,15)(8,12,13)(9,10,14)$ |
| $F_9:S_6$ | 12D | $12$ | $2160$ | $C_2\times C_{12}$ | 6C | 4G | 12D | $(1,2,5,3)(7,15,13,12,10,9)(8,11,14)$ |
| $F_9:S_6$ | 12E | $12$ | $4320$ | $C_{12}$ | 6A | 4C | 12E | $(1,2,3,4,6,5)(7,15,12,13)(8,10,11,9)$ |
| $F_9:S_6$ | 12F | $12$ | $4320$ | $C_{12}$ | 6B | 4D | 12F | $(1,4,5)(3,6)(7,9,13,14)(8,11,15,12)$ |
| $F_9:S_6$ | 15A | $15$ | $1152$ | $C_3\times C_{15}$ | 15A | 5A | 3A | $(1,4,2,5,3)(7,10,13)(8,11,14)(9,12,15)$ |
| $F_9:S_6$ | 20A1 | $20$ | $1296$ | $C_{40}$ | 10A | 20A1 | 4A | $(1,3,5,2,4)(7,11,12,8)(9,15,10,13)$ |
| $F_9:S_6$ | 20A-1 | $20$ | $1296$ | $C_{40}$ | 10A | 20A-1 | 4A | $(1,4,2,5,3)(7,8,12,11)(9,13,10,15)$ |
| $F_9:S_6$ | 24A1 | $24$ | $720$ | $C_3\times C_{24}$ | 12A | 8A-1 | 24A-1 | $(1,2,6)(3,4,5)(7,11,14,15,8,13,10,12)$ |
| $F_9:S_6$ | 24A-1 | $24$ | $720$ | $C_3\times C_{24}$ | 12A | 8A1 | 24A1 | $(1,6,2)(3,5,4)(7,12,10,13,8,15,14,11)$ |
| $F_9:S_6$ | 24B1 | $24$ | $720$ | $C_3\times C_{24}$ | 12B | 8A-1 | 24B-1 | $(4,6,5)(7,11,14,15,8,13,10,12)$ |
| $F_9:S_6$ | 24B-1 | $24$ | $720$ | $C_3\times C_{24}$ | 12B | 8A1 | 24B1 | $(4,5,6)(7,12,10,13,8,15,14,11)$ |