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Elements of the group are displayed as permutations of degree 16.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $A_4^2:\POPlus(4,3).C_2^3$ | 1A | $1$ | $1$ | $A_4^2:\POPlus(4,3).C_2^3$ | 1A | 1A | $()$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2A | $2$ | $12$ | $C_2^6.C_3^3.C_2^4.C_2$ | 1A | 2A | $(9,10)(11,12)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2B | $2$ | $18$ | $(C_2^3\times S_4^2).D_4$ | 1A | 2B | $(9,11)(10,12)(13,15)(14,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2C | $2$ | $18$ | $(C_2^3\times S_4^2).D_4$ | 1A | 2C | $(5,7)(6,8)(13,15)(14,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2D | $2$ | $18$ | $(C_2^3\times S_4^2).D_4$ | 1A | 2D | $(5,7)(6,8)(9,11)(10,12)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2E | $2$ | $72$ | not computed | 1A | 2E | $(10,12)(13,15)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2F | $2$ | $72$ | not computed | 1A | 2F | $(1,2)(14,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2G | $2$ | $72$ | not computed | 1A | 2G | $(1,4)(10,11)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2H | $2$ | $81$ | $C_2\wr D_4.C_2^2$ | 1A | 2H | $(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,16)(14,15)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2I | $2$ | $108$ | not computed | 1A | 2I | $(5,7)(6,8)(9,11)(10,12)(13,14)(15,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2J | $2$ | $288$ | not computed | 1A | 2J | $(1,16)(2,14)(3,13)(4,15)(5,9)(6,12)(7,11)(8,10)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2K | $2$ | $288$ | not computed | 1A | 2K | $(1,9)(2,10)(3,12)(4,11)(5,14)(6,15)(7,13)(8,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2L | $2$ | $288$ | not computed | 1A | 2L | $(1,9)(2,12)(3,11)(4,10)(5,14)(6,16)(7,13)(8,15)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2M | $2$ | $288$ | not computed | 1A | 2M | $(1,6)(2,8)(3,5)(4,7)(9,16)(10,14)(11,13)(12,15)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2N | $2$ | $288$ | not computed | 1A | 2N | $(1,8)(2,7)(3,5)(4,6)(9,13)(10,16)(11,15)(12,14)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2O | $2$ | $288$ | not computed | 1A | 2O | $(1,15)(2,13)(3,16)(4,14)(5,10)(6,11)(7,12)(8,9)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2P | $2$ | $432$ | not computed | 1A | 2P | $(1,2)(6,7)(9,10)(11,12)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2Q | $2$ | $432$ | not computed | 1A | 2Q | $(2,3)(9,10)(13,15)(14,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2R | $2$ | $432$ | not computed | 1A | 2R | $(6,7)(11,12)(13,14)(15,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2S | $2$ | $648$ | not computed | 1A | 2S | $(3,4)(7,8)(9,10)(11,12)(13,14)(15,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2T | $2$ | $648$ | not computed | 1A | 2T | $(3,4)(5,6)(7,8)(11,12)(13,14)(15,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2U | $2$ | $648$ | not computed | 1A | 2U | $(3,4)(5,6)(7,8)(9,10)(11,12)(15,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 2V | $2$ | $1296$ | not computed | 1A | 2V | $(3,4)(5,8)(9,10)(14,15)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 3A | $3$ | $32$ | $C_3\times A_4:S_4^2$ | 3A | 1A | $(13,16,15)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 3B | $3$ | $128$ | not computed | 3B | 1A | $(5,6,7)(13,14,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 3C | $3$ | $128$ | not computed | 3C | 1A | $(1,3,4)(13,14,15)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 3D | $3$ | $128$ | not computed | 3D | 1A | $(2,4,3)(5,7,8)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 3E | $3$ | $2048$ | not computed | 3E | 1A | $(1,4,2)(5,7,8)(9,11,10)(14,16,15)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 3F | $3$ | $2048$ | not computed | 3F | 1A | $(2,4,3)(5,7,8)(10,11,12)(13,15,14)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 3G | $3$ | $2048$ | not computed | 3G | 1A | $(5,8,6)(9,11,12)(13,15,14)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4A | $4$ | $72$ | not computed | 2B | 4A | $(9,11,12,10)(13,16,15,14)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4B | $4$ | $72$ | not computed | 2D | 4B | $(1,3,4,2)(13,16,15,14)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4C | $4$ | $72$ | not computed | 2C | 4C | $(1,4,2,3)(9,12,10,11)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4D | $4$ | $144$ | not computed | 2A | 4D | $(1,4)(9,11,10,12)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4E | $4$ | $144$ | not computed | 2A | 4E | $(5,7)(9,11,10,12)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4F | $4$ | $144$ | not computed | 2A | 4F | $(1,3,4,2)(7,8)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4G | $4$ | $432$ | not computed | 2D | 4G | $(1,2)(3,4)(5,7,8,6)(9,11,12,10)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4H | $4$ | $432$ | not computed | 2A | 4H | $(1,2)(3,4)(5,8)(13,16,14,15)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4I | $4$ | $432$ | not computed | 2A | 4I | $(1,4,2,3)(9,10)(11,12)(15,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4J | $4$ | $432$ | not computed | 2C | 4J | $(1,4,2,3)(9,11,12,10)(13,14)(15,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4K | $4$ | $432$ | not computed | 2B | 4K | $(1,4)(2,3)(9,10,12,11)(13,16,15,14)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4L | $4$ | $432$ | not computed | 2A | 4L | $(5,6)(7,8)(9,11,12,10)(14,15)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4M | $4$ | $432$ | not computed | 2A | 4M | $(1,4)(2,3)(9,12,11,10)(13,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4N | $4$ | $432$ | not computed | 2A | 4N | $(1,3)(2,4)(5,8,7,6)(14,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4O | $4$ | $432$ | not computed | 2A | 4O | $(5,6)(9,12,10,11)(13,16)(14,15)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4P | $4$ | $648$ | not computed | 2B | 4P | $(1,2)(3,4)(5,6)(7,8)(9,10,11,12)(13,14,15,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4Q | $4$ | $648$ | not computed | 2C | 4Q | $(1,2)(3,4)(5,6,7,8)(9,10)(11,12)(13,14,15,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4R | $4$ | $648$ | not computed | 2D | 4R | $(1,2)(3,4)(5,6,7,8)(9,10,11,12)(13,14)(15,16)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4S | $4$ | $1296$ | not computed | 2H | 4S | $(1,2,3,4)(5,8,7,6)(9,10,11,12)(13,15,16,14)$ |
| $A_4^2:\POPlus(4,3).C_2^3$ | 4T | $4$ | $1296$ | not computed | 2A | 4T | $(1,3)(5,8,6,7)(9,10)(11,12)(13,14)(15,16)$ |