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Elements of the group are displayed as permutations of degree 18.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $(C_3^3\times \He_3):C_4$ | 1A | $1$ | $1$ | $(C_3^3\times \He_3):C_4$ | 1A | 1A | $()$ |
| $(C_3^3\times \He_3):C_4$ | 2A | $2$ | $9$ | $(C_3\times \He_3):C_4$ | 1A | 2A | $(3,6)(4,5)$ |
| $(C_3^3\times \He_3):C_4$ | 3A1 | $3$ | $1$ | $(C_3^3\times \He_3):C_4$ | 3A-1 | 1A | $(10,15,13)(11,16,12)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3A-1 | $3$ | $1$ | $(C_3^3\times \He_3):C_4$ | 3A1 | 1A | $(10,13,15)(11,12,16)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3B | $3$ | $2$ | $C_3^5:C_6$ | 3B | 1A | $(7,9,8)$ |
| $(C_3^3\times \He_3):C_4$ | 3C1 | $3$ | $2$ | $C_3^5:C_6$ | 3C-1 | 1A | $(7,9,8)(10,15,13)(11,16,12)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3C-1 | $3$ | $2$ | $C_3^5:C_6$ | 3C1 | 1A | $(7,8,9)(10,13,15)(11,12,16)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3D | $3$ | $4$ | $C_3^3\times \He_3$ | 3D | 1A | $(2,4,5)$ |
| $(C_3^3\times \He_3):C_4$ | 3E | $3$ | $4$ | $C_3^3\times \He_3$ | 3E | 1A | $(1,3,6)(2,4,5)$ |
| $(C_3^3\times \He_3):C_4$ | 3F1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3F-1 | 1A | $(2,4,5)(10,13,15)(11,12,16)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3F-1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3F1 | 1A | $(2,4,5)(10,15,13)(11,16,12)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3G1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3G-1 | 1A | $(2,4,5)(7,8,9)$ |
| $(C_3^3\times \He_3):C_4$ | 3G-1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3G1 | 1A | $(2,4,5)(7,9,8)$ |
| $(C_3^3\times \He_3):C_4$ | 3H1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3H-1 | 1A | $(2,4,5)(7,8,9)(10,13,15)(11,12,16)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3H-1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3H1 | 1A | $(2,4,5)(7,9,8)(10,15,13)(11,16,12)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3I1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3I-1 | 1A | $(2,4,5)(7,8,9)(10,15,13)(11,16,12)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3I-1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3I1 | 1A | $(2,4,5)(7,9,8)(10,13,15)(11,12,16)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3J1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3J-1 | 1A | $(1,3,6)(2,4,5)(10,13,15)(11,12,16)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3J-1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3J1 | 1A | $(1,3,6)(2,4,5)(10,15,13)(11,16,12)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3K1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3K-1 | 1A | $(1,3,6)(2,4,5)(7,8,9)$ |
| $(C_3^3\times \He_3):C_4$ | 3K-1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3K1 | 1A | $(1,3,6)(2,4,5)(7,9,8)$ |
| $(C_3^3\times \He_3):C_4$ | 3L1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3L-1 | 1A | $(1,3,6)(2,4,5)(7,8,9)(10,13,15)(11,12,16)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3L-1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3L1 | 1A | $(1,3,6)(2,4,5)(7,9,8)(10,15,13)(11,16,12)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3M1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3M-1 | 1A | $(1,3,6)(2,4,5)(7,8,9)(10,15,13)(11,16,12)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3M-1 | $3$ | $4$ | $C_3^3\times \He_3$ | 3M1 | 1A | $(1,3,6)(2,4,5)(7,9,8)(10,13,15)(11,12,16)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3N | $3$ | $6$ | $C_3^4:C_6$ | 3N | 1A | $(11,16,12)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3O | $3$ | $6$ | $C_3^4:C_6$ | 3O | 1A | $(10,14,11)(12,13,17)(15,18,16)$ |
| $(C_3^3\times \He_3):C_4$ | 3P | $3$ | $6$ | $C_3^4:C_6$ | 3P | 1A | $(10,17,11)(12,13,18)(14,16,15)$ |
| $(C_3^3\times \He_3):C_4$ | 3Q | $3$ | $6$ | $C_3^4:C_6$ | 3Q | 1A | $(10,18,11)(12,13,14)(15,17,16)$ |
| $(C_3^3\times \He_3):C_4$ | 3R | $3$ | $6$ | $C_3^4:C_6$ | 3R | 1A | $(7,9,8)(11,16,12)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3S | $3$ | $6$ | $C_3^4:C_6$ | 3S | 1A | $(7,9,8)(11,12,16)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3T | $3$ | $6$ | $C_3^4:C_6$ | 3T | 1A | $(7,9,8)(10,14,11)(12,13,17)(15,18,16)$ |
| $(C_3^3\times \He_3):C_4$ | 3U | $3$ | $6$ | $C_3^4:C_6$ | 3U | 1A | $(7,9,8)(10,17,11)(12,13,18)(14,16,15)$ |
| $(C_3^3\times \He_3):C_4$ | 3V | $3$ | $6$ | $C_3^4:C_6$ | 3V | 1A | $(7,9,8)(10,18,11)(12,13,14)(15,17,16)$ |
| $(C_3^3\times \He_3):C_4$ | 3W | $3$ | $6$ | $C_3^4:C_6$ | 3W | 1A | $(7,9,8)(10,11,14)(12,17,13)(15,16,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3X | $3$ | $6$ | $C_3^4:C_6$ | 3X | 1A | $(7,9,8)(10,16,14)(11,17,13)(12,18,15)$ |
| $(C_3^3\times \He_3):C_4$ | 3Y | $3$ | $6$ | $C_3^4:C_6$ | 3Y | 1A | $(7,9,8)(10,12,14)(11,18,15)(13,16,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3Z1 | $3$ | $12$ | $C_3^5$ | 3Z-1 | 1A | $(2,4,5)(11,12,16)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3Z-1 | $3$ | $12$ | $C_3^5$ | 3Z1 | 1A | $(2,4,5)(11,16,12)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3AA1 | $3$ | $12$ | $C_3^5$ | 3AA-1 | 1A | $(2,4,5)(10,11,14)(12,17,13)(15,16,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3AA-1 | $3$ | $12$ | $C_3^5$ | 3AA1 | 1A | $(2,4,5)(10,14,11)(12,13,17)(15,18,16)$ |
| $(C_3^3\times \He_3):C_4$ | 3AB1 | $3$ | $12$ | $C_3^5$ | 3AB-1 | 1A | $(2,4,5)(10,11,17)(12,18,13)(14,15,16)$ |
| $(C_3^3\times \He_3):C_4$ | 3AB-1 | $3$ | $12$ | $C_3^5$ | 3AB1 | 1A | $(2,4,5)(10,14,12)(11,15,18)(13,17,16)$ |
| $(C_3^3\times \He_3):C_4$ | 3AC1 | $3$ | $12$ | $C_3^5$ | 3AC-1 | 1A | $(2,4,5)(10,11,18)(12,14,13)(15,16,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3AC-1 | $3$ | $12$ | $C_3^5$ | 3AC1 | 1A | $(2,4,5)(10,14,16)(11,13,17)(12,15,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3AD1 | $3$ | $12$ | $C_3^5$ | 3AD-1 | 1A | $(2,4,5)(7,8,9)(11,12,16)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3AD-1 | $3$ | $12$ | $C_3^5$ | 3AD1 | 1A | $(2,4,5)(7,9,8)(11,16,12)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3AE1 | $3$ | $12$ | $C_3^5$ | 3AE-1 | 1A | $(2,4,5)(7,8,9)(11,16,12)(14,17,18)$ |
| $(C_3^3\times \He_3):C_4$ | 3AE-1 | $3$ | $12$ | $C_3^5$ | 3AE1 | 1A | $(2,4,5)(7,9,8)(11,12,16)(14,18,17)$ |
| $(C_3^3\times \He_3):C_4$ | 3AF1 | $3$ | $12$ | $C_3^5$ | 3AF-1 | 1A | $(2,4,5)(7,8,9)(10,11,14)(12,17,13)(15,16,18)$ |