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Elements of the group are displayed as permutations of degree 18.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_3^3:F_9$ | 1A | $1$ | $1$ | $C_3^3:F_9$ | 1A | 1A | $()$ |
| $C_3^3:F_9$ | 2A | $2$ | $9$ | $C_3^3:C_8$ | 1A | 2A | $(11,14)(12,17)(13,18)(15,16)$ |
| $C_3^3:F_9$ | 3A | $3$ | $2$ | $C_3^4:C_{12}$ | 3A | 1A | $(7,8,9)$ |
| $C_3^3:F_9$ | 3B | $3$ | $4$ | $C_3^4:C_6$ | 3B | 1A | $(2,6,4)$ |
| $C_3^3:F_9$ | 3C | $3$ | $4$ | $C_3^4:C_6$ | 3C | 1A | $(1,5,3)(2,6,4)$ |
| $C_3^3:F_9$ | 3D1 | $3$ | $4$ | $C_3^4:C_6$ | 3D-1 | 1A | $(2,6,4)(7,9,8)$ |
| $C_3^3:F_9$ | 3D-1 | $3$ | $4$ | $C_3^4:C_6$ | 3D1 | 1A | $(2,4,6)(7,8,9)$ |
| $C_3^3:F_9$ | 3E1 | $3$ | $4$ | $C_3^4:C_6$ | 3E-1 | 1A | $(1,5,3)(2,6,4)(7,9,8)$ |
| $C_3^3:F_9$ | 3E-1 | $3$ | $4$ | $C_3^4:C_6$ | 3E1 | 1A | $(1,3,5)(2,4,6)(7,8,9)$ |
| $C_3^3:F_9$ | 3F | $3$ | $8$ | $C_3^5$ | 3F | 1A | $(10,11,14)(12,15,18)(13,16,17)$ |
| $C_3^3:F_9$ | 3G1 | $3$ | $8$ | $C_3^5$ | 3G-1 | 1A | $(7,8,9)(10,11,14)(12,15,18)(13,16,17)$ |
| $C_3^3:F_9$ | 3G-1 | $3$ | $8$ | $C_3^5$ | 3G1 | 1A | $(7,8,9)(10,12,17)(11,15,13)(14,18,16)$ |
| $C_3^3:F_9$ | 3H1 | $3$ | $8$ | $C_3^5$ | 3H-1 | 1A | $(2,4,6)(10,11,14)(12,15,18)(13,16,17)$ |
| $C_3^3:F_9$ | 3H-1 | $3$ | $8$ | $C_3^5$ | 3H1 | 1A | $(2,4,6)(10,13,18)(11,16,12)(14,17,15)$ |
| $C_3^3:F_9$ | 3I1 | $3$ | $8$ | $C_3^5$ | 3I-1 | 1A | $(2,4,6)(10,12,17)(11,15,13)(14,18,16)$ |
| $C_3^3:F_9$ | 3I-1 | $3$ | $8$ | $C_3^5$ | 3I1 | 1A | $(2,4,6)(10,15,16)(11,18,17)(12,13,14)$ |
| $C_3^3:F_9$ | 3J1 | $3$ | $8$ | $C_3^5$ | 3J-1 | 1A | $(2,4,6)(7,8,9)(10,11,14)(12,15,18)(13,16,17)$ |
| $C_3^3:F_9$ | 3J-1 | $3$ | $8$ | $C_3^5$ | 3J1 | 1A | $(2,4,6)(7,9,8)(10,13,18)(11,16,12)(14,17,15)$ |
| $C_3^3:F_9$ | 3K1 | $3$ | $8$ | $C_3^5$ | 3K-1 | 1A | $(2,4,6)(7,8,9)(10,12,17)(11,15,13)(14,18,16)$ |
| $C_3^3:F_9$ | 3K-1 | $3$ | $8$ | $C_3^5$ | 3K1 | 1A | $(2,4,6)(7,9,8)(10,15,16)(11,18,17)(12,13,14)$ |
| $C_3^3:F_9$ | 3L1 | $3$ | $8$ | $C_3^5$ | 3L-1 | 1A | $(2,4,6)(7,8,9)(10,13,18)(11,16,12)(14,17,15)$ |
| $C_3^3:F_9$ | 3L-1 | $3$ | $8$ | $C_3^5$ | 3L1 | 1A | $(2,4,6)(7,9,8)(10,11,14)(12,15,18)(13,16,17)$ |
| $C_3^3:F_9$ | 3M1 | $3$ | $8$ | $C_3^5$ | 3M-1 | 1A | $(2,4,6)(7,8,9)(10,15,16)(11,18,17)(12,13,14)$ |
| $C_3^3:F_9$ | 3M-1 | $3$ | $8$ | $C_3^5$ | 3M1 | 1A | $(2,4,6)(7,9,8)(10,12,17)(11,15,13)(14,18,16)$ |
| $C_3^3:F_9$ | 3N1 | $3$ | $8$ | $C_3^5$ | 3N-1 | 1A | $(1,3,5)(2,4,6)(10,11,14)(12,15,18)(13,16,17)$ |
| $C_3^3:F_9$ | 3N-1 | $3$ | $8$ | $C_3^5$ | 3N1 | 1A | $(1,3,5)(2,4,6)(10,13,18)(11,16,12)(14,17,15)$ |
| $C_3^3:F_9$ | 3O1 | $3$ | $8$ | $C_3^5$ | 3O-1 | 1A | $(1,3,5)(2,4,6)(10,12,17)(11,15,13)(14,18,16)$ |
| $C_3^3:F_9$ | 3O-1 | $3$ | $8$ | $C_3^5$ | 3O1 | 1A | $(1,3,5)(2,4,6)(10,15,16)(11,18,17)(12,13,14)$ |
| $C_3^3:F_9$ | 3P1 | $3$ | $8$ | $C_3^5$ | 3P-1 | 1A | $(1,3,5)(2,4,6)(7,8,9)(10,11,14)(12,15,18)(13,16,17)$ |
| $C_3^3:F_9$ | 3P-1 | $3$ | $8$ | $C_3^5$ | 3P1 | 1A | $(1,3,5)(2,4,6)(7,9,8)(10,13,18)(11,16,12)(14,17,15)$ |
| $C_3^3:F_9$ | 3Q1 | $3$ | $8$ | $C_3^5$ | 3Q-1 | 1A | $(1,3,5)(2,4,6)(7,8,9)(10,12,17)(11,15,13)(14,18,16)$ |
| $C_3^3:F_9$ | 3Q-1 | $3$ | $8$ | $C_3^5$ | 3Q1 | 1A | $(1,3,5)(2,4,6)(7,9,8)(10,15,16)(11,18,17)(12,13,14)$ |
| $C_3^3:F_9$ | 3R1 | $3$ | $8$ | $C_3^5$ | 3R-1 | 1A | $(1,3,5)(2,4,6)(7,8,9)(10,13,18)(11,16,12)(14,17,15)$ |
| $C_3^3:F_9$ | 3R-1 | $3$ | $8$ | $C_3^5$ | 3R1 | 1A | $(1,3,5)(2,4,6)(7,9,8)(10,11,14)(12,15,18)(13,16,17)$ |
| $C_3^3:F_9$ | 3S1 | $3$ | $8$ | $C_3^5$ | 3S-1 | 1A | $(1,3,5)(2,4,6)(7,8,9)(10,15,16)(11,18,17)(12,13,14)$ |
| $C_3^3:F_9$ | 3S-1 | $3$ | $8$ | $C_3^5$ | 3S1 | 1A | $(1,3,5)(2,4,6)(7,9,8)(10,12,17)(11,15,13)(14,18,16)$ |
| $C_3^3:F_9$ | 4A1 | $4$ | $81$ | $C_3:C_8$ | 2A | 4A-1 | $(3,5)(4,6)(10,15,13,12)(11,14,17,16)$ |
| $C_3^3:F_9$ | 4A-1 | $4$ | $81$ | $C_3:C_8$ | 2A | 4A1 | $(3,5)(4,6)(10,12,13,15)(11,16,17,14)$ |
| $C_3^3:F_9$ | 6A | $6$ | $18$ | $C_3^2:C_{12}$ | 3A | 2A | $(7,9,8)(10,17)(11,16)(13,14)(15,18)$ |
| $C_3^3:F_9$ | 6B | $6$ | $36$ | $C_3^2\times C_6$ | 3B | 2A | $(2,4,6)(11,14)(12,17)(13,18)(15,16)$ |
| $C_3^3:F_9$ | 6C | $6$ | $36$ | $C_3^2\times C_6$ | 3C | 2A | $(1,3,5)(2,4,6)(11,14)(12,17)(13,18)(15,16)$ |
| $C_3^3:F_9$ | 6D1 | $6$ | $36$ | $C_3^2\times C_6$ | 3D1 | 2A | $(2,4,6)(7,8,9)(11,14)(12,17)(13,18)(15,16)$ |
| $C_3^3:F_9$ | 6D-1 | $6$ | $36$ | $C_3^2\times C_6$ | 3D-1 | 2A | $(2,4,6)(7,9,8)(11,14)(12,17)(13,18)(15,16)$ |
| $C_3^3:F_9$ | 6E1 | $6$ | $36$ | $C_3^2\times C_6$ | 3E1 | 2A | $(1,3,5)(2,4,6)(7,8,9)(11,14)(12,17)(13,18)(15,16)$ |
| $C_3^3:F_9$ | 6E-1 | $6$ | $36$ | $C_3^2\times C_6$ | 3E-1 | 2A | $(1,3,5)(2,4,6)(7,9,8)(11,14)(12,17)(13,18)(15,16)$ |
| $C_3^3:F_9$ | 8A1 | $8$ | $243$ | $C_8$ | 4A1 | 8A3 | $(1,2)(3,4,5,6)(8,9)(10,11,15,14,13,17,12,16)$ |
| $C_3^3:F_9$ | 8A-1 | $8$ | $243$ | $C_8$ | 4A-1 | 8A-3 | $(1,2)(3,6,5,4)(8,9)(10,16,12,17,13,14,15,11)$ |
| $C_3^3:F_9$ | 8A3 | $8$ | $243$ | $C_8$ | 4A-1 | 8A1 | $(1,2)(3,6,5,4)(8,9)(10,14,12,11,13,16,15,17)$ |
| $C_3^3:F_9$ | 8A-3 | $8$ | $243$ | $C_8$ | 4A1 | 8A-1 | $(1,2)(3,4,5,6)(8,9)(10,17,15,16,13,11,12,14)$ |
| $C_3^3:F_9$ | 12A1 | $12$ | $162$ | $C_{12}$ | 6A | 4A-1 | $(1,5)(2,4)(7,8,9)(10,13,17,14)(11,18,16,15)$ |