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Elements of the group are displayed as permutations of degree 36.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_3^6.C_3^3:(C_4\times S_3)$ | 1A | $1$ | $1$ | $C_3^6.C_3^3:(C_4\times S_3)$ | 1A | 1A | $()$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 2A | $2$ | $729$ | not computed | 1A | 2A | $(1,20)(2,19)(3,21)(4,34)(5,35)(6,36)(7,13)(8,15)(9,14)(10,29)(11,30)(12,28)(16,22)(17,23)(18,24)(25,33)(26,32)(27,31)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 2B | $2$ | $729$ | not computed | 1A | 2B | $(1,8)(2,9)(3,7)(4,36)(5,35)(6,34)(10,17)(11,16)(12,18)(13,19)(14,20)(15,21)(22,28)(23,30)(24,29)(25,32)(26,33)(27,31)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 2C | $2$ | $6561$ | not computed | 1A | 2C | $(1,2)(4,17)(5,16)(6,18)(7,20)(8,19)(9,21)(10,11)(13,25)(14,27)(15,26)(22,34)(23,36)(24,35)(28,29)(31,33)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3A | $3$ | $2$ | $C_3^6.C_3\wr C_4$ | 3A | 1A | $(1,2,3)(4,5,6)(7,8,9)(10,12,11)(13,14,15)(16,17,18)(19,20,21)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3B | $3$ | $2$ | $C_3^6.C_3\wr C_4$ | 3B | 1A | $(1,2,3)(4,6,5)(7,8,9)(10,11,12)(13,14,15)(16,18,17)(19,20,21)(22,23,24)(25,26,27)(28,30,29)(31,32,33)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3C | $3$ | $4$ | $C_3^5.C_3^4.C_6$ | 3C | 1A | $(4,5,6)(10,12,11)(16,17,18)(22,24,23)(28,29,30)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3D | $3$ | $4$ | $C_3^5.C_3^4.C_6$ | 3D | 1A | $(4,6,5)(10,12,11)(16,18,17)(22,24,23)(28,30,29)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3E | $3$ | $4$ | $C_3^6.C_3^4.C_2$ | 3E | 1A | $(1,2,3)(4,5,6)(7,9,8)(10,11,12)(13,14,15)(16,17,18)(19,21,20)(22,23,24)(25,26,27)(28,29,30)(31,33,32)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3F | $3$ | $8$ | $C_3^6.C_3^4$ | 3F | 1A | $(10,11,12)(22,23,24)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3G | $3$ | $8$ | $C_3^6.C_3^4$ | 3G | 1A | $(7,8,9)(10,11,12)(19,20,21)(22,23,24)(31,32,33)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3H | $3$ | $8$ | $C_3^6.C_3^4$ | 3H | 1A | $(7,8,9)(10,12,11)(19,20,21)(22,24,23)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3I | $3$ | $8$ | $C_3^6.C_3^4$ | 3I | 1A | $(4,5,6)(7,8,9)(10,11,12)(16,17,18)(19,20,21)(22,23,24)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3J | $3$ | $8$ | $C_3^6.C_3^4$ | 3J | 1A | $(4,5,6)(7,8,9)(10,12,11)(16,17,18)(19,20,21)(22,24,23)(28,29,30)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3K | $3$ | $8$ | $C_3^6.C_3^4$ | 3K | 1A | $(4,5,6)(7,9,8)(10,11,12)(16,17,18)(19,21,20)(22,23,24)(28,29,30)(31,33,32)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3L | $3$ | $8$ | $C_3^6.C_3^4$ | 3L | 1A | $(4,5,6)(7,9,8)(10,12,11)(16,17,18)(19,21,20)(22,24,23)(28,29,30)(31,33,32)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3M | $3$ | $8$ | $C_3^6.C_3^4$ | 3M | 1A | $(1,2,3)(4,6,5)(7,8,9)(10,12,11)(13,14,15)(16,18,17)(19,20,21)(22,24,23)(25,26,27)(28,30,29)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3N | $3$ | $36$ | not computed | 3N | 1A | $(4,6,5)(16,17,18)(22,24,23)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3O | $3$ | $72$ | not computed | 3O | 1A | $(10,22,36)(11,23,34)(12,24,35)(28,29,30)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3P | $3$ | $72$ | not computed | 3P | 1A | $(10,22,35)(11,23,36)(12,24,34)(16,18,17)(28,30,29)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3Q | $3$ | $72$ | not computed | 3Q | 1A | $(7,8,9)(10,22,36)(11,23,34)(12,24,35)(19,20,21)(28,29,30)(31,32,33)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3R | $3$ | $72$ | not computed | 3R | 1A | $(7,8,9)(10,22,35)(11,23,36)(12,24,34)(16,18,17)(19,20,21)(28,30,29)(31,32,33)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3S | $3$ | $72$ | not computed | 3S | 1A | $(7,8,9)(10,34,24)(11,35,22)(12,36,23)(19,20,21)(28,30,29)(31,32,33)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3T | $3$ | $72$ | not computed | 3T | 1A | $(7,8,9)(10,34,23)(11,35,24)(12,36,22)(16,17,18)(19,20,21)(28,29,30)(31,32,33)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3U | $3$ | $72$ | not computed | 3U | 1A | $(7,19,32)(8,20,33)(9,21,31)(10,11,12)(22,23,24)(25,26,27)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3V | $3$ | $72$ | not computed | 3V | 1A | $(7,19,33)(8,20,31)(9,21,32)(10,11,12)(13,15,14)(22,23,24)(25,27,26)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3W | $3$ | $72$ | not computed | 3W | 1A | $(7,19,32)(8,20,33)(9,21,31)(10,12,11)(22,24,23)(25,26,27)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3X | $3$ | $72$ | not computed | 3X | 1A | $(7,19,33)(8,20,31)(9,21,32)(10,12,11)(13,15,14)(22,24,23)(25,27,26)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3Y | $3$ | $72$ | not computed | 3Y | 1A | $(4,5,6)(10,11,12)(13,14,15)(16,17,18)(19,21,20)(22,23,24)(25,27,26)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3Z | $3$ | $72$ | not computed | 3Z | 1A | $(4,5,6)(10,12,11)(13,14,15)(16,17,18)(19,21,20)(22,24,23)(25,27,26)(28,29,30)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AA | $3$ | $72$ | not computed | 3AA | 1A | $(4,5,6)(10,22,36)(11,23,34)(12,24,35)(16,17,18)(28,30,29)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AB | $3$ | $72$ | not computed | 3AB | 1A | $(4,5,6)(7,8,9)(10,22,36)(11,23,34)(12,24,35)(16,17,18)(19,20,21)(28,30,29)(31,32,33)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AC | $3$ | $72$ | not computed | 3AC | 1A | $(4,5,6)(7,8,9)(10,34,23)(11,35,24)(12,36,22)(16,18,17)(19,20,21)(28,30,29)(31,32,33)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AD | $3$ | $72$ | not computed | 3AD | 1A | $(4,5,6)(7,19,32)(8,20,33)(9,21,31)(10,11,12)(16,17,18)(22,23,24)(25,26,27)(28,29,30)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AE | $3$ | $72$ | not computed | 3AE | 1A | $(4,5,6)(7,19,33)(8,20,31)(9,21,32)(10,11,12)(13,15,14)(16,17,18)(22,23,24)(25,27,26)(28,29,30)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AF | $3$ | $72$ | not computed | 3AF | 1A | $(4,5,6)(7,19,32)(8,20,33)(9,21,31)(10,12,11)(16,17,18)(22,24,23)(25,26,27)(28,29,30)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AG | $3$ | $72$ | not computed | 3AG | 1A | $(4,5,6)(7,19,33)(8,20,31)(9,21,32)(10,12,11)(13,15,14)(16,17,18)(22,24,23)(25,27,26)(28,29,30)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AH | $3$ | $72$ | not computed | 3AH | 1A | $(4,5,6)(7,31,20)(8,32,21)(9,33,19)(10,11,12)(16,17,18)(22,23,24)(25,27,26)(28,29,30)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AI | $3$ | $72$ | not computed | 3AI | 1A | $(4,5,6)(7,31,21)(8,32,19)(9,33,20)(10,11,12)(13,14,15)(16,17,18)(22,23,24)(25,26,27)(28,29,30)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AJ | $3$ | $72$ | not computed | 3AJ | 1A | $(4,5,6)(7,31,20)(8,32,21)(9,33,19)(10,12,11)(16,17,18)(22,24,23)(25,27,26)(28,29,30)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AK | $3$ | $72$ | not computed | 3AK | 1A | $(4,5,6)(7,31,21)(8,32,19)(9,33,20)(10,12,11)(13,14,15)(16,17,18)(22,24,23)(25,26,27)(28,29,30)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AL | $3$ | $72$ | not computed | 3AL | 1A | $(4,16,28)(5,17,29)(6,18,30)(7,8,9)(10,11,12)(19,20,21)(22,24,23)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AM | $3$ | $72$ | not computed | 3AM | 1A | $(4,16,28)(5,17,29)(6,18,30)(7,9,8)(10,11,12)(19,21,20)(22,24,23)(31,33,32)(34,36,35)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AN | $3$ | $72$ | not computed | 3AN | 1A | $(1,2,3)(4,5,6)(7,8,9)(10,22,36)(11,23,34)(12,24,35)(13,14,15)(16,17,18)(19,20,21)(25,26,27)(28,30,29)(31,32,33)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AO | $3$ | $72$ | not computed | 3AO | 1A | $(1,2,3)(4,5,6)(7,8,9)(10,34,23)(11,35,24)(12,36,22)(13,14,15)(16,18,17)(19,20,21)(25,26,27)(28,30,29)(31,32,33)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AP | $3$ | $72$ | not computed | 3AP | 1A | $(1,2,3)(4,5,6)(7,9,8)(10,22,36)(11,23,34)(12,24,35)(13,14,15)(16,17,18)(19,21,20)(25,26,27)(28,30,29)(31,33,32)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AQ | $3$ | $72$ | not computed | 3AQ | 1A | $(1,2,3)(4,5,6)(7,9,8)(10,34,23)(11,35,24)(12,36,22)(13,14,15)(16,18,17)(19,21,20)(25,26,27)(28,30,29)(31,33,32)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AR1 | $3$ | $72$ | not computed | 3AR-1 | 1A | $(10,11,12)(13,14,15)(19,21,20)(22,23,24)(25,27,26)(31,32,33)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AR-1 | $3$ | $72$ | not computed | 3AR1 | 1A | $(10,11,12)(13,15,14)(19,20,21)(22,23,24)(25,26,27)(31,33,32)(34,35,36)$ |
| $C_3^6.C_3^3:(C_4\times S_3)$ | 3AS | $3$ | $324$ | not computed | 3AS | 1A | $(1,2,3)(4,6,5)(16,17,18)(19,20,21)(22,24,23)(25,27,26)(31,33,32)(34,35,36)$ |