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Elements of the group are displayed as permutations of degree 20.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $C_6^4:D_6$ | 1A | $1$ | $1$ | $C_6^4:D_6$ | 1A | 1A | $()$ |
| $C_6^4:D_6$ | 2A | $2$ | $3$ | $C_3^4.C_2\wr C_2^2$ | 1A | 2A | $(1,4)(2,3)(5,8)(6,7)$ |
| $C_6^4:D_6$ | 2B | $2$ | $6$ | $C_6^2.C_6^2.C_2$ | 1A | 2B | $(2,3)(5,8)$ |
| $C_6^4:D_6$ | 2C | $2$ | $6$ | $C_6^4.C_2$ | 1A | 2C | $(1,4)(2,5)(3,8)(6,7)$ |
| $C_6^4:D_6$ | 2D | $2$ | $108$ | $C_6^2:C_2^2$ | 1A | 2D | $(3,5)(4,6)(10,11)(13,18)(14,16)(15,20)$ |
| $C_6^4:D_6$ | 2E | $2$ | $108$ | $C_6:S_4$ | 1A | 2E | $(1,2)(3,4)(5,6)(7,8)(12,19)(14,20)(15,18)$ |
| $C_6^4:D_6$ | 2F | $2$ | $324$ | $C_6:D_4$ | 1A | 2F | $(1,5)(2,6)(3,4)(7,8)(10,11)(12,15)(13,20)(16,19)(17,18)$ |
| $C_6^4:D_6$ | 3A | $3$ | $2$ | $C_6^4:C_6$ | 3A | 1A | $(9,11,10)$ |
| $C_6^4:D_6$ | 3B | $3$ | $2$ | $C_6^4:S_3$ | 3B | 1A | $(12,19,17)(13,14,20)(15,18,16)$ |
| $C_6^4:D_6$ | 3C | $3$ | $4$ | $C_3\times C_3.C_2^4:\He_3$ | 3C | 1A | $(9,11,10)(12,19,17)(13,14,20)(15,18,16)$ |
| $C_6^4:D_6$ | 3D | $3$ | $6$ | $C_6^4.C_2$ | 3D | 1A | $(12,19,17)(13,20,14)$ |
| $C_6^4:D_6$ | 3E | $3$ | $6$ | $C_6^2.C_6^2.C_2$ | 3E | 1A | $(13,20,14)$ |
| $C_6^4:D_6$ | 3F | $3$ | $6$ | $C_6^2.C_6^2.C_2$ | 3F | 1A | $(13,20,14)(15,16,18)$ |
| $C_6^4:D_6$ | 3G | $3$ | $6$ | $C_6^2.C_6^2.C_2$ | 3G | 1A | $(12,19,17)(13,20,14)(15,18,16)$ |
| $C_6^4:D_6$ | 3H | $3$ | $12$ | $C_6^4$ | 3H | 1A | $(9,11,10)(12,19,17)(13,20,14)$ |
| $C_6^4:D_6$ | 3I | $3$ | $12$ | $C_6^4$ | 3I | 1A | $(9,11,10)(15,18,16)$ |
| $C_6^4:D_6$ | 3J | $3$ | $12$ | $C_6^4$ | 3J | 1A | $(9,11,10)(12,19,17)(13,14,20)$ |
| $C_6^4:D_6$ | 3K | $3$ | $12$ | $C_6^4$ | 3K | 1A | $(9,11,10)(12,19,17)(13,14,20)(15,16,18)$ |
| $C_6^4:D_6$ | 3L | $3$ | $288$ | $S_3\times C_3^2$ | 3L | 1A | $(1,6,4)(2,5,3)(9,11,10)(12,15,14)(13,17,16)(18,20,19)$ |
| $C_6^4:D_6$ | 3M | $3$ | $288$ | $S_3\times C_3^2$ | 3M | 1A | $(1,7,6)(3,5,8)(9,10,11)(12,15,13)(14,19,18)(16,20,17)$ |
| $C_6^4:D_6$ | 3N | $3$ | $288$ | $S_3\times C_3^2$ | 3N | 1A | $(1,6,4)(2,5,3)(12,16,13)(14,19,15)(17,18,20)$ |
| $C_6^4:D_6$ | 4A | $4$ | $108$ | $C_{12}.D_6$ | 2A | 4A | $(1,6,4,7)(2,8,3,5)(9,11)(12,14)(13,17)(19,20)$ |
| $C_6^4:D_6$ | 4B | $4$ | $216$ | $C_6\times C_{12}$ | 2B | 4B | $(2,5,8,3)(4,6)(9,11)(13,18)(14,16)(15,20)$ |
| $C_6^4:D_6$ | 4C | $4$ | $324$ | $D_{12}:C_2$ | 2A | 4C | $(1,2,4,3)(5,7,8,6)(12,17)(14,20)(16,18)$ |
| $C_6^4:D_6$ | 4D | $4$ | $324$ | $D_{12}:C_2$ | 2A | 4D | $(1,5,4,8)(2,6,3,7)(9,10)(12,13)(14,17)(15,18)(19,20)$ |
| $C_6^4:D_6$ | 4E | $4$ | $648$ | $C_2\times C_{12}$ | 2C | 4E | $(1,2,6,3)(4,5,7,8)(9,11)(13,15)(14,16)(17,19)(18,20)$ |
| $C_6^4:D_6$ | 6A | $6$ | $6$ | $C_3\times C_6^3.C_2^2$ | 3A | 2A | $(1,4)(2,3)(5,8)(6,7)(9,11,10)$ |
| $C_6^4:D_6$ | 6B | $6$ | $6$ | $C_6^4.C_2$ | 3D | 2A | $(1,4)(2,3)(5,8)(6,7)(12,17,19)(13,14,20)$ |
| $C_6^4:D_6$ | 6C | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3F | 2A | $(1,4)(2,3)(5,8)(6,7)(12,17,19)(13,20,14)$ |
| $C_6^4:D_6$ | 6D | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3B | 2A | $(1,7)(2,8)(3,5)(4,6)(12,19,17)(13,14,20)(15,18,16)$ |
| $C_6^4:D_6$ | 6E | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3G | 2A | $(1,7)(2,8)(3,5)(4,6)(12,19,17)(13,20,14)(15,16,18)$ |
| $C_6^4:D_6$ | 6F | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3E | 2A | $(1,7)(2,8)(3,5)(4,6)(12,17,19)$ |
| $C_6^4:D_6$ | 6G1 | $6$ | $6$ | $C_6^4.C_2$ | 3D | 2C | $(1,6)(2,3)(4,7)(5,8)(13,14,20)(15,16,18)$ |
| $C_6^4:D_6$ | 6G-1 | $6$ | $6$ | $C_6^4.C_2$ | 3D | 2C | $(1,6)(2,3)(4,7)(5,8)(13,20,14)(15,18,16)$ |
| $C_6^4:D_6$ | 6H1 | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3F | 2B | $(2,8)(3,5)(13,20,14)(15,16,18)$ |
| $C_6^4:D_6$ | 6H-1 | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3F | 2B | $(2,8)(3,5)(13,14,20)(15,18,16)$ |
| $C_6^4:D_6$ | 6I1 | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3G | 2B | $(2,5)(3,8)(12,19,17)(13,20,14)(15,18,16)$ |
| $C_6^4:D_6$ | 6I-1 | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3G | 2B | $(2,5)(3,8)(12,17,19)(13,14,20)(15,16,18)$ |
| $C_6^4:D_6$ | 6J1 | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3E | 2B | $(1,7)(4,6)(12,19,17)$ |
| $C_6^4:D_6$ | 6J-1 | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3E | 2B | $(1,7)(4,6)(12,17,19)$ |
| $C_6^4:D_6$ | 6K1 | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3B | 2B | $(1,4)(6,7)(12,17,19)(13,20,14)(15,16,18)$ |
| $C_6^4:D_6$ | 6K-1 | $6$ | $6$ | $C_6^2.C_6^2.C_2$ | 3B | 2B | $(1,4)(6,7)(12,19,17)(13,14,20)(15,18,16)$ |
| $C_6^4:D_6$ | 6L | $6$ | $12$ | $C_6^4$ | 3D | 2B | $(2,3)(5,8)(12,17,19)(13,14,20)$ |
| $C_6^4:D_6$ | 6M | $6$ | $12$ | $C_6^4$ | 3A | 2B | $(2,3)(5,8)(9,10,11)$ |
| $C_6^4:D_6$ | 6N | $6$ | $12$ | $C_6^4$ | 3H | 2B | $(2,3)(5,8)(9,10,11)(12,17,19)(13,14,20)$ |
| $C_6^4:D_6$ | 6O | $6$ | $12$ | $C_6^4$ | 3H | 2B | $(2,3)(5,8)(9,10,11)(12,19,17)(13,20,14)$ |
| $C_6^4:D_6$ | 6P | $6$ | $12$ | $C_6^4$ | 3E | 2A | $(1,4)(2,3)(5,8)(6,7)(13,14,20)$ |
| $C_6^4:D_6$ | 6Q | $6$ | $12$ | $C_6^4$ | 3D | 2A | $(1,4)(2,3)(5,8)(6,7)(13,14,20)(15,16,18)$ |
| $C_6^4:D_6$ | 6R | $6$ | $12$ | $C_6^4$ | 3F | 2A | $(1,4)(2,3)(5,8)(6,7)(13,14,20)(15,18,16)$ |
| $C_6^4:D_6$ | 6S | $6$ | $12$ | $C_6^4$ | 3G | 2A | $(1,4)(2,3)(5,8)(6,7)(12,17,19)(13,14,20)(15,16,18)$ |