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Elements of the group are displayed as permutations of degree 36.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 1A | $1$ | $1$ | $C_3^6.(C_3^2\times S_3^2):C_4$ | 1A | 1A | $()$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 2A | $2$ | $54$ | $C_3^4.C_3^3.C_2^3$ | 1A | 2A | $(4,10)(5,12)(6,11)(16,34)(17,36)(18,35)(22,28)(23,30)(24,29)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 2B | $2$ | $729$ | not computed | 1A | 2B | $(1,8)(2,9)(3,7)(4,23)(5,22)(6,24)(10,17)(11,16)(12,18)(13,33)(14,31)(15,32)(19,25)(20,26)(21,27)(28,34)(29,36)(30,35)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 2C | $2$ | $729$ | not computed | 1A | 2C | $(1,31)(2,33)(3,32)(4,23)(5,24)(6,22)(7,13)(8,15)(9,14)(10,29)(11,30)(12,28)(16,34)(17,35)(18,36)(19,25)(20,27)(21,26)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 2D | $2$ | $4374$ | not computed | 1A | 2D | $(1,9)(2,8)(3,7)(4,6)(10,36)(11,35)(12,34)(13,20)(14,19)(15,21)(16,28)(17,30)(18,29)(22,23)(25,33)(26,32)(27,31)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 2E | $2$ | $6561$ | not computed | 1A | 2E | $(1,25)(2,27)(3,26)(4,29)(5,28)(6,30)(7,20)(8,19)(9,21)(10,22)(11,24)(12,23)(13,14)(16,17)(31,33)(35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3A | $3$ | $4$ | $C_3^6.C_3^4.C_2^2$ | 3A | 1A | $(4,6,5)(10,12,11)(16,18,17)(22,24,23)(28,30,29)(34,36,35)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3B | $3$ | $4$ | $C_3^6.C_3\wr C_4$ | 3B | 1A | $(4,5,6)(10,12,11)(16,17,18)(22,24,23)(28,29,30)(34,36,35)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3C | $3$ | $4$ | $C_3^5.C_3^4.C_6.C_2$ | 3C | 1A | $(1,2,3)(4,6,5)(7,8,9)(10,11,12)(13,14,15)(16,18,17)(19,20,21)(22,23,24)(25,26,27)(28,30,29)(31,32,33)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3D | $3$ | $4$ | $C_3^6.C_3^4.C_2^2$ | 3D | 1A | $(1,2,3)(4,6,5)(7,9,8)(10,12,11)(13,14,15)(16,18,17)(19,21,20)(22,24,23)(25,26,27)(28,30,29)(31,33,32)(34,36,35)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3E | $3$ | $8$ | $C_3^3.C_3^5.C_3.C_6$ | 3E | 1A | $(7,9,8)(19,21,20)(31,33,32)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3F | $3$ | $8$ | $C_3^3.C_3^5.C_3.C_6$ | 3F | 1A | $(4,5,6)(7,9,8)(10,12,11)(16,17,18)(19,21,20)(22,24,23)(28,29,30)(31,33,32)(34,36,35)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3G | $3$ | $8$ | $C_3^3.C_3^5.C_3.C_6$ | 3G | 1A | $(4,6,5)(7,9,8)(10,11,12)(16,18,17)(19,21,20)(22,23,24)(28,30,29)(31,33,32)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3H | $3$ | $8$ | $C_3^3.C_3^5.C_3.C_6$ | 3H | 1A | $(1,3,2)(4,6,5)(7,8,9)(10,11,12)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(25,27,26)(28,30,29)(31,32,33)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3I | $3$ | $16$ | $C_3^6.C_3^4$ | 3I | 1A | $(7,8,9)(10,11,12)(19,20,21)(22,23,24)(31,32,33)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3J | $3$ | $16$ | $C_3^6.C_3^4$ | 3J | 1A | $(4,5,6)(7,8,9)(10,11,12)(16,17,18)(19,20,21)(22,23,24)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3K | $3$ | $36$ | $C_3^3.C_3^5.C_2^2$ | 3K | 1A | $(13,15,14)(19,21,20)(25,26,27)(31,32,33)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3L | $3$ | $72$ | $C_3^4.C_3^4.C_2$ | 3L | 1A | $(1,3,2)(4,5,6)(10,11,12)(13,14,15)(16,17,18)(19,21,20)(22,23,24)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3M | $3$ | $72$ | $C_3^3.C_3^5.C_2$ | 3M | 1A | $(1,3,2)(4,5,6)(7,21,33)(8,19,31)(9,20,32)(10,12,11)(16,17,18)(22,24,23)(28,29,30)(34,36,35)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3N | $3$ | $72$ | $C_3^3.C_3^5.C_2$ | 3N | 1A | $(1,25,13)(2,26,14)(3,27,15)(4,6,5)(10,11,12)(16,18,17)(19,21,20)(22,23,24)(28,30,29)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3O | $3$ | $72$ | $C_3^3.C_3^5.C_2$ | 3O | 1A | $(1,25,14)(2,26,15)(3,27,13)(4,6,5)(10,11,12)(16,18,17)(19,20,21)(22,23,24)(28,30,29)(31,32,33)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3P | $3$ | $72$ | $C_3^3.C_3^5.C_2$ | 3P | 1A | $(4,5,6)(10,22,34)(11,23,35)(12,24,36)(28,29,30)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3Q | $3$ | $72$ | $C_3^3.C_3^5.C_2$ | 3Q | 1A | $(1,2,3)(7,8,9)(10,12,11)(13,14,15)(16,18,17)(19,20,21)(25,26,27)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3R | $3$ | $72$ | $C_3^3.C_3^5.C_2$ | 3R | 1A | $(1,3,2)(7,20,33)(8,21,31)(9,19,32)(13,15,14)(25,26,27)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3S | $3$ | $72$ | $C_3^3.C_3^5.C_2$ | 3S | 1A | $(1,3,2)(4,6,5)(7,9,8)(10,22,34)(11,23,35)(12,24,36)(13,15,14)(16,17,18)(19,21,20)(25,27,26)(28,30,29)(31,33,32)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3T | $3$ | $72$ | $C_3^3.C_3^5.C_2$ | 3T | 1A | $(4,29,18)(5,30,16)(6,28,17)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3U | $3$ | $72$ | $C_3^3.C_3^5.C_2$ | 3U | 1A | $(1,3,2)(4,30,17)(5,28,18)(6,29,16)(7,9,8)(10,12,11)(13,15,14)(19,21,20)(22,24,23)(25,27,26)(31,33,32)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3V | $3$ | $72$ | $C_3^3.C_3^5.C_2$ | 3V | 1A | $(1,3,2)(4,6,5)(7,20,32)(8,21,33)(9,19,31)(10,11,12)(13,14,15)(16,18,17)(22,23,24)(25,27,26)(28,30,29)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3W | $3$ | $144$ | $C_3^3\times C_3.C_3\wr C_3$ | 3W | 1A | $(10,11,12)(13,14,15)(19,20,21)(22,23,24)(25,27,26)(31,33,32)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3X | $3$ | $144$ | $C_3^3\times C_3.C_3\wr C_3$ | 3X | 1A | $(7,8,9)(10,22,36)(11,23,34)(12,24,35)(19,20,21)(28,30,29)(31,32,33)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3Y | $3$ | $144$ | $C_3^3\times C_3.C_3\wr C_3$ | 3Y | 1A | $(7,8,9)(10,22,35)(11,23,36)(12,24,34)(16,17,18)(19,20,21)(28,29,30)(31,32,33)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3Z | $3$ | $144$ | $C_3^3\times C_3.C_3\wr C_3$ | 3Z | 1A | $(7,8,9)(10,34,24)(11,35,22)(12,36,23)(19,20,21)(28,29,30)(31,32,33)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AA | $3$ | $144$ | $C_3^3\times C_3.C_3\wr C_3$ | 3AA | 1A | $(7,8,9)(10,34,23)(11,35,24)(12,36,22)(16,18,17)(19,20,21)(28,30,29)(31,32,33)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AB | $3$ | $144$ | $C_3^3\times C_3.C_3\wr C_3$ | 3AB | 1A | $(4,5,6)(7,8,9)(10,22,35)(11,23,36)(12,24,34)(16,18,17)(19,20,21)(28,30,29)(31,32,33)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AC | $3$ | $144$ | $C_3^3\times C_3.C_3\wr C_3$ | 3AC | 1A | $(4,5,6)(7,8,9)(10,34,24)(11,35,22)(12,36,23)(16,17,18)(19,20,21)(28,30,29)(31,32,33)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AD | $3$ | $144$ | $C_3^3\times C_3.C_3\wr C_3$ | 3AD | 1A | $(4,5,6)(7,19,31)(8,20,32)(9,21,33)(10,11,12)(16,17,18)(22,23,24)(25,27,26)(28,29,30)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AE | $3$ | $144$ | $C_3^3\times C_3.C_3\wr C_3$ | 3AE | 1A | $(4,5,6)(7,19,32)(8,20,33)(9,21,31)(10,11,12)(13,14,15)(16,17,18)(22,23,24)(25,26,27)(28,29,30)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AF | $3$ | $144$ | $C_3^3\times C_3.C_3\wr C_3$ | 3AF | 1A | $(1,2,3)(4,5,6)(7,9,8)(10,22,35)(11,23,36)(12,24,34)(13,14,15)(16,18,17)(19,21,20)(25,26,27)(28,30,29)(31,33,32)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AG | $3$ | $324$ | not computed | 3AG | 1A | $(1,2,3)(4,5,6)(7,9,8)(10,11,12)(19,20,21)(22,24,23)(25,27,26)(28,30,29)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AH | $3$ | $1296$ | not computed | 3AH | 1A | $(1,26,14)(2,27,15)(3,25,13)(4,6,5)(10,22,36)(11,23,34)(12,24,35)(16,18,17)(28,29,30)(31,33,32)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AI | $3$ | $1296$ | not computed | 3AI | 1A | $(1,3,2)(4,17,30)(5,18,28)(6,16,29)(7,20,33)(8,21,31)(9,19,32)(10,11,12)(13,15,14)(22,23,24)(25,26,27)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AJ | $3$ | $1296$ | not computed | 3AJ | 1A | $(4,17,30)(5,18,28)(6,16,29)(7,19,32)(8,20,33)(9,21,31)(10,12,11)(13,14,15)(22,24,23)(25,26,27)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AK | $3$ | $1296$ | not computed | 3AK | 1A | $(1,14,27)(2,15,25)(3,13,26)(4,6,5)(7,9,8)(10,36,22)(11,34,23)(12,35,24)(16,18,17)(31,33,32)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AL | $3$ | $1296$ | not computed | 3AL | 1A | $(1,2,3)(4,18,30)(5,16,28)(6,17,29)(7,32,19)(8,33,20)(9,31,21)(22,24,23)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AM | $3$ | $1296$ | not computed | 3AM | 1A | $(1,15,25)(2,13,26)(3,14,27)(7,9,8)(10,36,22)(11,34,23)(12,35,24)(19,21,20)(28,29,30)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AN | $3$ | $1296$ | not computed | 3AN | 1A | $(1,3,2)(4,30,16)(5,28,17)(6,29,18)(7,19,33)(8,20,31)(9,21,32)(10,12,11)(13,14,15)(22,23,24)(25,27,26)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AO | $3$ | $1296$ | not computed | 3AO | 1A | $(1,14,25)(2,15,26)(3,13,27)(4,17,29)(5,18,30)(6,16,28)(7,9,8)(10,12,11)(19,20,21)(31,32,33)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AP | $3$ | $1296$ | not computed | 3AP | 1A | $(1,13,27)(2,14,25)(3,15,26)(4,6,5)(22,24,23)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AQ | $3$ | $1296$ | not computed | 3AQ | 1A | $(1,26,14)(2,27,15)(3,25,13)(7,9,8)(16,18,17)(19,21,20)(22,23,24)(28,29,30)(31,32,33)(34,36,35)$ |
| $C_3^6.(C_3^2\times S_3^2):C_4$ | 3AR | $3$ | $1296$ | not computed | 3AR | 1A | $(1,3,2)(7,9,8)(10,24,36)(11,22,34)(12,23,35)(13,14,15)(16,17,18)(19,20,21)(28,29,30)$ |