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Elements of the group are displayed as permutations of degree 36.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_3^6.C_3\wr C_2^2$ | 1A | $1$ | $1$ | $C_3^6.C_3\wr C_2^2$ | 1A | 1A | $()$ |
| $C_3^6.C_3\wr C_2^2$ | 2A | $2$ | $243$ | not computed | 1A | 2A | $(1,7)(2,8)(3,9)(4,12)(5,11)(6,10)(13,19)(14,20)(15,21)(16,22)(17,24)(18,23)(25,31)(26,32)(27,33)(28,36)(29,35)(30,34)$ |
| $C_3^6.C_3\wr C_2^2$ | 2B | $2$ | $243$ | not computed | 1A | 2B | $(1,12)(2,11)(3,10)(4,7)(5,8)(6,9)(13,24)(14,23)(15,22)(16,21)(17,19)(18,20)(25,36)(26,35)(27,34)(28,31)(29,32)(30,33)$ |
| $C_3^6.C_3\wr C_2^2$ | 2C | $2$ | $729$ | not computed | 1A | 2C | $(1,6)(2,4)(3,5)(7,11)(8,10)(9,12)(13,18)(14,16)(15,17)(19,23)(20,22)(21,24)(25,28)(26,29)(27,30)(31,35)(32,34)(33,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3A1 | $3$ | $1$ | $C_3^6.C_3\wr C_2^2$ | 3A-1 | 1A | $(1,2,3)(4,5,6)(7,8,9)(10,12,11)(13,14,15)(16,17,18)(19,20,21)(22,24,23)(25,26,27)(28,29,30)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3A-1 | $3$ | $1$ | $C_3^6.C_3\wr C_2^2$ | 3A1 | 1A | $(1,3,2)(4,6,5)(7,9,8)(10,11,12)(13,15,14)(16,18,17)(19,21,20)(22,23,24)(25,27,26)(28,30,29)(31,33,32)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3B | $3$ | $2$ | $C_3^6.C_3^4.C_2$ | 3B | 1A | $(1,3,2)(4,5,6)(7,9,8)(10,12,11)(13,15,14)(16,17,18)(19,21,20)(22,24,23)(25,27,26)(28,29,30)(31,33,32)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3C | $3$ | $2$ | $C_3^6.C_3^4.C_2$ | 3C | 1A | $(1,3,2)(4,5,6)(7,8,9)(10,11,12)(13,15,14)(16,17,18)(19,20,21)(22,23,24)(25,27,26)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3D | $3$ | $2$ | $C_3^6.C_3^4.C_2$ | 3D | 1A | $(1,3,2)(4,6,5)(7,8,9)(10,12,11)(13,15,14)(16,18,17)(19,20,21)(22,24,23)(25,27,26)(28,30,29)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3E1 | $3$ | $2$ | $C_3^6.C_3^4.C_2$ | 3E-1 | 1A | $(4,5,6)(10,12,11)(16,17,18)(22,24,23)(28,29,30)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3E-1 | $3$ | $2$ | $C_3^6.C_3^4.C_2$ | 3E1 | 1A | $(4,6,5)(10,11,12)(16,18,17)(22,23,24)(28,30,29)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3F1 | $3$ | $2$ | $C_3^6.C_3^4.C_2$ | 3F-1 | 1A | $(1,2,3)(10,12,11)(13,14,15)(22,24,23)(25,26,27)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3F-1 | $3$ | $2$ | $C_3^6.C_3^4.C_2$ | 3F1 | 1A | $(1,3,2)(10,11,12)(13,15,14)(22,23,24)(25,27,26)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3G1 | $3$ | $2$ | $C_3^6.C_3^4.C_2$ | 3G-1 | 1A | $(7,8,9)(10,12,11)(19,20,21)(22,24,23)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3G-1 | $3$ | $2$ | $C_3^6.C_3^4.C_2$ | 3G1 | 1A | $(7,9,8)(10,11,12)(19,21,20)(22,23,24)(31,33,32)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3H | $3$ | $4$ | $C_3^6.C_3^4$ | 3H | 1A | $(4,5,6)(10,11,12)(16,17,18)(22,23,24)(28,29,30)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3I | $3$ | $4$ | $C_3^6.C_3^4$ | 3I | 1A | $(4,5,6)(7,9,8)(16,17,18)(19,21,20)(28,29,30)(31,33,32)$ |
| $C_3^6.C_3\wr C_2^2$ | 3J | $3$ | $4$ | $C_3^6.C_3^4$ | 3J | 1A | $(7,9,8)(10,12,11)(19,21,20)(22,24,23)(31,33,32)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3K1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3K-1 | 1A | $(10,11,12)(22,23,24)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3K-1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3K1 | 1A | $(10,12,11)(22,24,23)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3L1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3L-1 | 1A | $(4,5,6)(7,8,9)(10,11,12)(16,17,18)(19,20,21)(22,23,24)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3L-1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3L1 | 1A | $(4,6,5)(7,9,8)(10,12,11)(16,18,17)(19,21,20)(22,24,23)(28,30,29)(31,33,32)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3M1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3M-1 | 1A | $(4,5,6)(7,8,9)(10,12,11)(16,17,18)(19,20,21)(22,24,23)(28,29,30)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3M-1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3M1 | 1A | $(4,6,5)(7,9,8)(10,11,12)(16,18,17)(19,21,20)(22,23,24)(28,30,29)(31,33,32)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3N1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3N-1 | 1A | $(4,5,6)(7,9,8)(10,11,12)(16,17,18)(19,21,20)(22,23,24)(28,29,30)(31,33,32)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3N-1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3N1 | 1A | $(4,6,5)(7,8,9)(10,12,11)(16,18,17)(19,20,21)(22,24,23)(28,30,29)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3O1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3O-1 | 1A | $(4,5,6)(7,9,8)(10,12,11)(16,17,18)(19,21,20)(22,24,23)(28,29,30)(31,33,32)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3O-1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3O1 | 1A | $(4,6,5)(7,8,9)(10,11,12)(16,18,17)(19,20,21)(22,23,24)(28,30,29)(31,32,33)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3P1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3P-1 | 1A | $(1,2,3)(4,5,6)(7,9,8)(10,12,11)(13,14,15)(16,17,18)(19,21,20)(22,24,23)(25,26,27)(28,29,30)(31,33,32)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3P-1 | $3$ | $4$ | $C_3^6.C_3^4$ | 3P1 | 1A | $(1,3,2)(4,6,5)(7,8,9)(10,11,12)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(25,27,26)(28,30,29)(31,32,33)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3Q | $3$ | $36$ | not computed | 3Q | 1A | $(19,20,21)(22,23,24)(31,33,32)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3R | $3$ | $36$ | not computed | 3R | 1A | $(7,8,9)(10,11,12)(13,14,15)(16,18,17)(19,20,21)(22,23,24)(25,27,26)(28,29,30)(31,32,33)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3S | $3$ | $36$ | not computed | 3S | 1A | $(7,8,9)(10,11,12)(13,15,14)(16,17,18)(19,20,21)(22,23,24)(25,26,27)(28,30,29)(31,32,33)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3T1 | $3$ | $36$ | not computed | 3T-1 | 1A | $(10,11,12)(13,14,15)(16,18,17)(22,23,24)(25,27,26)(28,29,30)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3T-1 | $3$ | $36$ | not computed | 3T1 | 1A | $(10,12,11)(13,15,14)(16,17,18)(22,24,23)(25,26,27)(28,30,29)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3U1 | $3$ | $36$ | not computed | 3U-1 | 1A | $(10,11,12)(13,15,14)(16,17,18)(22,23,24)(25,26,27)(28,30,29)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3U-1 | $3$ | $36$ | not computed | 3U1 | 1A | $(10,12,11)(13,14,15)(16,18,17)(22,24,23)(25,27,26)(28,29,30)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3V1 | $3$ | $36$ | not computed | 3V-1 | 1A | $(10,22,34)(11,23,35)(12,24,36)(31,32,33)$ |
| $C_3^6.C_3\wr C_2^2$ | 3V-1 | $3$ | $36$ | not computed | 3V1 | 1A | $(10,34,22)(11,35,23)(12,36,24)(31,33,32)$ |
| $C_3^6.C_3\wr C_2^2$ | 3W1 | $3$ | $36$ | not computed | 3W-1 | 1A | $(10,22,36)(11,23,34)(12,24,35)(19,21,20)(31,33,32)$ |
| $C_3^6.C_3\wr C_2^2$ | 3W-1 | $3$ | $36$ | not computed | 3W1 | 1A | $(10,34,24)(11,35,22)(12,36,23)(19,20,21)(31,32,33)$ |
| $C_3^6.C_3\wr C_2^2$ | 3X1 | $3$ | $36$ | not computed | 3X-1 | 1A | $(7,8,9)(10,12,11)(13,14,15)(16,18,17)(19,20,21)(22,24,23)(25,27,26)(28,29,30)(31,32,33)(34,36,35)$ |
| $C_3^6.C_3\wr C_2^2$ | 3X-1 | $3$ | $36$ | not computed | 3X1 | 1A | $(7,9,8)(10,11,12)(13,14,15)(16,18,17)(19,21,20)(22,23,24)(25,27,26)(28,29,30)(31,33,32)(34,35,36)$ |
| $C_3^6.C_3\wr C_2^2$ | 3Y1 | $3$ | $36$ | not computed | 3Y-1 | 1A | $(7,8,9)(10,22,34)(11,23,35)(12,24,36)(19,20,21)(31,33,32)$ |
| $C_3^6.C_3\wr C_2^2$ | 3Y-1 | $3$ | $36$ | not computed | 3Y1 | 1A | $(7,8,9)(10,34,24)(11,35,22)(12,36,23)(19,21,20)(31,33,32)$ |
| $C_3^6.C_3\wr C_2^2$ | 3Z1 | $3$ | $36$ | not computed | 3Z-1 | 1A | $(4,5,6)(10,22,34)(11,23,35)(12,24,36)(16,17,18)(28,29,30)(31,32,33)$ |
| $C_3^6.C_3\wr C_2^2$ | 3Z-1 | $3$ | $36$ | not computed | 3Z1 | 1A | $(4,6,5)(10,34,22)(11,35,23)(12,36,24)(16,18,17)(28,30,29)(31,33,32)$ |
| $C_3^6.C_3\wr C_2^2$ | 3AA1 | $3$ | $36$ | not computed | 3AA-1 | 1A | $(4,5,6)(10,22,36)(11,23,34)(12,24,35)(16,17,18)(19,21,20)(28,29,30)(31,33,32)$ |
| $C_3^6.C_3\wr C_2^2$ | 3AA-1 | $3$ | $36$ | not computed | 3AA1 | 1A | $(4,6,5)(10,34,24)(11,35,22)(12,36,23)(16,18,17)(19,20,21)(28,30,29)(31,32,33)$ |
| $C_3^6.C_3\wr C_2^2$ | 3AB1 | $3$ | $36$ | not computed | 3AB-1 | 1A | $(4,5,6)(10,34,22)(11,35,23)(12,36,24)(16,17,18)(28,29,30)(31,33,32)$ |