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Elements of the group are displayed as permutations of degree 14.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $D_6^2:C_2^2:A_4$ | 1A | $1$ | $1$ | $D_6^2:C_2^2:A_4$ | 1A | 1A | $()$ |
| $D_6^2:C_2^2:A_4$ | 2A | $2$ | $1$ | $D_6^2:C_2^2:A_4$ | 1A | 2A | $(7,14)(8,13)(9,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 2B | $2$ | $6$ | $D_6^2.C_2^3$ | 1A | 2B | $(8,13)(9,12)$ |
| $D_6^2:C_2^2:A_4$ | 2C | $2$ | $9$ | $(D_4\times C_2^3):A_4$ | 1A | 2C | $(1,5)(4,6)(7,14)(8,13)(9,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 2D | $2$ | $9$ | $(D_4\times C_2^3):A_4$ | 1A | 2D | $(2,4)(3,5)$ |
| $D_6^2:C_2^2:A_4$ | 2E | $2$ | $12$ | $C_6^2:(C_2^2\times C_4)$ | 1A | 2E | $(7,8)(9,10)(11,12)(13,14)$ |
| $D_6^2:C_2^2:A_4$ | 2F | $2$ | $24$ | $C_2\times A_4\times D_6$ | 1A | 2F | $(3,5)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 2G | $2$ | $24$ | $C_2\times A_4\times D_6$ | 1A | 2G | $(3,5)(8,13)(9,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 2H | $2$ | $24$ | $C_2\times A_4\times D_6$ | 1A | 2H | $(1,4)(2,5)(3,6)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 2I | $2$ | $24$ | $C_2\times A_4\times D_6$ | 1A | 2I | $(1,4)(2,5)(3,6)(8,13)(9,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 2J | $2$ | $54$ | $C_2.D_4^2$ | 1A | 2J | $(3,5)(4,6)(9,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 2K | $2$ | $108$ | $C_4^2:C_2^2$ | 1A | 2K | $(1,5)(2,4)(7,10)(8,9)(11,14)(12,13)$ |
| $D_6^2:C_2^2:A_4$ | 3A | $3$ | $4$ | $C_3^2:C_2\wr A_4$ | 3A | 1A | $(2,6,4)$ |
| $D_6^2:C_2^2:A_4$ | 3B | $3$ | $4$ | $C_3^2:C_2\wr A_4$ | 3B | 1A | $(1,3,5)(2,4,6)$ |
| $D_6^2:C_2^2:A_4$ | 3C1 | $3$ | $16$ | $C_6\times \SOPlus(4,2)$ | 3C-1 | 1A | $(7,9,13)(8,14,12)$ |
| $D_6^2:C_2^2:A_4$ | 3C-1 | $3$ | $16$ | $C_6\times \SOPlus(4,2)$ | 3C1 | 1A | $(7,13,9)(8,12,14)$ |
| $D_6^2:C_2^2:A_4$ | 3D1 | $3$ | $64$ | $C_3^2\times D_6$ | 3D-1 | 1A | $(2,6,4)(7,9,13)(8,14,12)$ |
| $D_6^2:C_2^2:A_4$ | 3D-1 | $3$ | $64$ | $C_3^2\times D_6$ | 3D1 | 1A | $(2,4,6)(7,13,9)(8,12,14)$ |
| $D_6^2:C_2^2:A_4$ | 3E1 | $3$ | $64$ | $C_3^2\times D_6$ | 3E-1 | 1A | $(1,5,3)(2,6,4)(7,9,13)(8,14,12)$ |
| $D_6^2:C_2^2:A_4$ | 3E-1 | $3$ | $64$ | $C_3^2\times D_6$ | 3E1 | 1A | $(1,3,5)(2,4,6)(7,13,9)(8,12,14)$ |
| $D_6^2:C_2^2:A_4$ | 4A | $4$ | $12$ | $C_6^2.(C_2^2\times C_4)$ | 2A | 4A | $(7,13,14,8)(9,11,12,10)$ |
| $D_6^2:C_2^2:A_4$ | 4B | $4$ | $18$ | $C_4\times Q_8:A_4$ | 2D | 4B | $(1,6)(2,5,4,3)(7,14)(8,13)(9,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 4C | $4$ | $18$ | $C_4\times Q_8:A_4$ | 2D | 4C | $(1,2)(3,4,5,6)$ |
| $D_6^2:C_2^2:A_4$ | 4D | $4$ | $108$ | $C_4^2:C_2^2$ | 2D | 4D | $(1,4,5,6)(2,3)(8,13)(9,12)$ |
| $D_6^2:C_2^2:A_4$ | 4E | $4$ | $108$ | $C_4^2.C_2^2$ | 2A | 4E | $(1,5)(2,6)(7,12,14,9)(8,11,13,10)$ |
| $D_6^2:C_2^2:A_4$ | 4F1 | $4$ | $108$ | $C_4^2.C_2^2$ | 2C | 4F-1 | $(1,2,5,6)(3,4)(7,13,14,8)(9,10,12,11)$ |
| $D_6^2:C_2^2:A_4$ | 4F-1 | $4$ | $108$ | $C_4^2.C_2^2$ | 2C | 4F1 | $(1,6,5,2)(3,4)(7,8,14,13)(9,11,12,10)$ |
| $D_6^2:C_2^2:A_4$ | 4G1 | $4$ | $108$ | $C_4^2:C_2^2$ | 2D | 4G-1 | $(1,2,5,6)(3,4)(7,9)(8,11)(10,13)(12,14)$ |
| $D_6^2:C_2^2:A_4$ | 4G-1 | $4$ | $108$ | $C_4^2:C_2^2$ | 2D | 4G1 | $(1,6,5,2)(3,4)(7,9)(8,11)(10,13)(12,14)$ |
| $D_6^2:C_2^2:A_4$ | 4H | $4$ | $144$ | $C_4\times D_6$ | 2B | 4H | $(1,5)(7,11)(8,9,13,12)(10,14)$ |
| $D_6^2:C_2^2:A_4$ | 4I | $4$ | $144$ | $C_4\times D_6$ | 2B | 4I | $(1,2)(3,4)(5,6)(7,11)(8,12,13,9)(10,14)$ |
| $D_6^2:C_2^2:A_4$ | 6A | $6$ | $4$ | $C_3^2:C_2\wr A_4$ | 3A | 2A | $(2,6,4)(7,14)(8,13)(9,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 6B | $6$ | $4$ | $C_3^2:C_2\wr A_4$ | 3B | 2A | $(1,5,3)(2,6,4)(7,14)(8,13)(9,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 6C1 | $6$ | $16$ | $C_6\times \SOPlus(4,2)$ | 3C1 | 2A | $(7,8,9,14,13,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 6C-1 | $6$ | $16$ | $C_6\times \SOPlus(4,2)$ | 3C-1 | 2A | $(7,8,10,14,13,11)(9,12)$ |
| $D_6^2:C_2^2:A_4$ | 6D | $6$ | $24$ | $C_6^2:D_4$ | 3A | 2B | $(2,6,4)(8,13)(9,12)$ |
| $D_6^2:C_2^2:A_4$ | 6E | $6$ | $24$ | $C_6^2:D_4$ | 3B | 2B | $(1,5,3)(2,6,4)(8,13)(9,12)$ |
| $D_6^2:C_2^2:A_4$ | 6F | $6$ | $48$ | $C_4:C_6^2$ | 3A | 2E | $(2,4,6)(7,8)(9,10)(11,12)(13,14)$ |
| $D_6^2:C_2^2:A_4$ | 6G | $6$ | $48$ | $C_2^2:C_6^2$ | 3A | 2F | $(2,4,6)(3,5)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 6H | $6$ | $48$ | $C_2^2:C_6^2$ | 3A | 2G | $(2,4,6)(3,5)(8,13)(9,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 6I | $6$ | $48$ | $C_2^2:C_6^2$ | 3B | 2H | $(1,2,3,4,5,6)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 6J | $6$ | $48$ | $C_2^2:C_6^2$ | 3B | 2I | $(1,2,3,4,5,6)(8,13)(9,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 6K | $6$ | $48$ | $C_4:C_6^2$ | 3B | 2E | $(1,3,5)(2,4,6)(7,8)(9,10)(11,12)(13,14)$ |
| $D_6^2:C_2^2:A_4$ | 6L1 | $6$ | $64$ | $C_3^2\times D_6$ | 3D1 | 2A | $(2,4,6)(7,8,9,14,13,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 6L-1 | $6$ | $64$ | $C_3^2\times D_6$ | 3D-1 | 2A | $(2,4,6)(7,8,10,14,13,11)(9,12)$ |
| $D_6^2:C_2^2:A_4$ | 6M1 | $6$ | $64$ | $C_3^2\times D_6$ | 3E1 | 2A | $(1,3,5)(2,4,6)(7,8,9,14,13,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 6M-1 | $6$ | $64$ | $C_3^2\times D_6$ | 3E-1 | 2A | $(1,3,5)(2,4,6)(7,8,10,14,13,11)(9,12)$ |
| $D_6^2:C_2^2:A_4$ | 6N1 | $6$ | $96$ | $C_6\times D_6$ | 3C-1 | 2F | $(2,4)(7,9,13)(8,14,12)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 6N-1 | $6$ | $96$ | $C_6\times D_6$ | 3C1 | 2F | $(2,4)(7,13,9)(8,12,14)(10,11)$ |
| $D_6^2:C_2^2:A_4$ | 6O1 | $6$ | $96$ | $C_6\times D_6$ | 3C1 | 2I | $(1,6)(2,5)(3,4)(7,12,10,14,9,11)$ |