Elements of the group are displayed as permutations of degree 15.
| Group |
Label |
Order |
Size |
Centralizer |
Powers |
Representative |
| 2P |
3P |
| $A_4\times D_4^2:S_3$ |
1A |
$1$ |
$1$ |
$A_4\times D_4^2:S_3$ |
1A |
1A |
$()$ |
| $A_4\times D_4^2:S_3$ |
2A |
$2$ |
$1$ |
$A_4\times D_4^2:S_3$ |
1A |
2A |
$(8,15)(9,10)(11,13)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
2B |
$2$ |
$2$ |
$C_2^6:C_6^2$ |
1A |
2B |
$(9,10)(11,13)$ |
| $A_4\times D_4^2:S_3$ |
2C |
$2$ |
$3$ |
$C_2\times D_4^2:D_6$ |
1A |
2C |
$(4,5)(6,7)$ |
| $A_4\times D_4^2:S_3$ |
2D |
$2$ |
$3$ |
$C_2\times D_4^2:D_6$ |
1A |
2D |
$(4,5)(6,7)(8,15)(9,10)(11,13)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
2E |
$2$ |
$4$ |
$C_2^5:C_6^2$ |
1A |
2E |
$(12,14)$ |
| $A_4\times D_4^2:S_3$ |
2F |
$2$ |
$4$ |
$C_2^5:C_6^2$ |
1A |
2F |
$(9,10)(11,13)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
2G |
$2$ |
$4$ |
$C_2^5:C_6^2$ |
1A |
2G |
$(9,11)(10,13)$ |
| $A_4\times D_4^2:S_3$ |
2H |
$2$ |
$4$ |
$C_2^5:C_6^2$ |
1A |
2H |
$(8,12)(9,10)(11,13)(14,15)$ |
| $A_4\times D_4^2:S_3$ |
2I |
$2$ |
$4$ |
$A_4\times C_2^4:S_3$ |
1A |
2I |
$(11,13)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
2J |
$2$ |
$4$ |
$A_4\times C_2^4:S_3$ |
1A |
2J |
$(8,12)(9,11)(10,13)(14,15)$ |
| $A_4\times D_4^2:S_3$ |
2K |
$2$ |
$6$ |
$C_2\times C_6\times D_4^2$ |
1A |
2K |
$(4,5)(6,7)(9,10)(11,13)$ |
| $A_4\times D_4^2:S_3$ |
2L |
$2$ |
$8$ |
$C_2^4:C_6^2$ |
1A |
2L |
$(9,11)(10,13)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
2M |
$2$ |
$12$ |
$C_{12}:C_2^5$ |
1A |
2M |
$(4,5)(6,7)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
2N |
$2$ |
$12$ |
$C_{12}:C_2^5$ |
1A |
2N |
$(4,5)(6,7)(9,10)(11,13)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
2O |
$2$ |
$12$ |
$C_{12}:C_2^5$ |
1A |
2O |
$(4,5)(6,7)(9,11)(10,13)$ |
| $A_4\times D_4^2:S_3$ |
2P |
$2$ |
$12$ |
$C_{12}:C_2^5$ |
1A |
2P |
$(4,5)(6,7)(8,12)(9,10)(11,13)(14,15)$ |
| $A_4\times D_4^2:S_3$ |
2Q |
$2$ |
$12$ |
$C_2^5:D_6$ |
1A |
2Q |
$(4,5)(6,7)(11,13)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
2R |
$2$ |
$12$ |
$C_2^5:D_6$ |
1A |
2R |
$(4,5)(6,7)(8,12)(9,11)(10,13)(14,15)$ |
| $A_4\times D_4^2:S_3$ |
2S |
$2$ |
$24$ |
$C_2^5\times C_6$ |
1A |
2S |
$(4,5)(6,7)(9,11)(10,13)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
2T |
$2$ |
$24$ |
$C_2^5:C_6$ |
1A |
2T |
$(2,3)(8,11)(9,12)(10,14)(13,15)$ |
| $A_4\times D_4^2:S_3$ |
2U |
$2$ |
$72$ |
$D_4\times C_2^3$ |
1A |
2U |
$(2,3)(4,7)(5,6)(8,9)(10,15)(11,12)(13,14)$ |
| $A_4\times D_4^2:S_3$ |
3A |
$3$ |
$2$ |
$C_2^6:C_6^2$ |
3A |
1A |
$(1,3,2)$ |
| $A_4\times D_4^2:S_3$ |
3B1 |
$3$ |
$4$ |
$C_{12}^2:D_4$ |
3B-1 |
1A |
$(5,7,6)$ |
| $A_4\times D_4^2:S_3$ |
3B-1 |
$3$ |
$4$ |
$C_{12}^2:D_4$ |
3B1 |
1A |
$(5,6,7)$ |
| $A_4\times D_4^2:S_3$ |
3C1 |
$3$ |
$8$ |
$C_3^2\times D_4^2$ |
3C-1 |
1A |
$(1,3,2)(5,7,6)$ |
| $A_4\times D_4^2:S_3$ |
3C-1 |
$3$ |
$8$ |
$C_3^2\times D_4^2$ |
3C1 |
1A |
$(1,2,3)(5,6,7)$ |
| $A_4\times D_4^2:S_3$ |
4A |
$4$ |
$4$ |
$C_2^5.C_6^2$ |
2B |
4A |
$(9,13,10,11)$ |
| $A_4\times D_4^2:S_3$ |
4B |
$4$ |
$4$ |
$C_2^5.C_6^2$ |
2B |
4B |
$(8,14,15,12)(9,10)(11,13)$ |
| $A_4\times D_4^2:S_3$ |
4C |
$4$ |
$4$ |
$A_4\times D_{12}:C_4$ |
2A |
4C |
$(8,14,15,12)(9,13,10,11)$ |
| $A_4\times D_4^2:S_3$ |
4D |
$4$ |
$8$ |
$C_2^4.C_6^2$ |
2B |
4D |
$(9,13,10,11)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
4E |
$4$ |
$8$ |
$C_2^4.C_6^2$ |
2B |
4E |
$(8,14,15,12)(9,11)(10,13)$ |
| $A_4\times D_4^2:S_3$ |
4F |
$4$ |
$12$ |
$C_2^2\times D_4\times C_{12}$ |
2B |
4F |
$(4,5)(6,7)(9,13,10,11)$ |
| $A_4\times D_4^2:S_3$ |
4G |
$4$ |
$12$ |
$C_2^2\times D_4\times C_{12}$ |
2B |
4G |
$(4,5)(6,7)(8,14,15,12)(9,10)(11,13)$ |
| $A_4\times D_4^2:S_3$ |
4H |
$4$ |
$12$ |
$C_2\times C_4^2:D_6$ |
2A |
4H |
$(4,5)(6,7)(8,14,15,12)(9,13,10,11)$ |
| $A_4\times D_4^2:S_3$ |
4I |
$4$ |
$24$ |
$C_2^4\times C_{12}$ |
2B |
4I |
$(4,5)(6,7)(9,13,10,11)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
4J |
$4$ |
$24$ |
$C_2^4\times C_{12}$ |
2B |
4J |
$(4,5)(6,7)(8,14,15,12)(9,11)(10,13)$ |
| $A_4\times D_4^2:S_3$ |
4K |
$4$ |
$24$ |
$A_4\times D_4:C_2$ |
2A |
4K |
$(1,2)(8,9,15,10)(11,14,13,12)$ |
| $A_4\times D_4^2:S_3$ |
4L |
$4$ |
$48$ |
$C_2^3:C_{12}$ |
2I |
4L |
$(1,2)(8,9)(10,15)(11,14,13,12)$ |
| $A_4\times D_4^2:S_3$ |
4M |
$4$ |
$48$ |
$C_2^3:C_{12}$ |
2J |
4M |
$(2,3)(8,10,14,11)(9,12,13,15)$ |
| $A_4\times D_4^2:S_3$ |
4N |
$4$ |
$72$ |
$D_4:C_2^3$ |
2A |
4N |
$(1,2)(4,7)(5,6)(8,10,15,9)(11,14,13,12)$ |
| $A_4\times D_4^2:S_3$ |
4O |
$4$ |
$144$ |
$C_2^3\times C_4$ |
2J |
4O |
$(1,2)(4,5)(6,7)(8,13,12,10)(9,15,11,14)$ |
| $A_4\times D_4^2:S_3$ |
4P |
$4$ |
$144$ |
$C_2^3\times C_4$ |
2I |
4P |
$(1,3)(4,7)(5,6)(8,9,15,10)(11,14)(12,13)$ |
| $A_4\times D_4^2:S_3$ |
6A |
$6$ |
$2$ |
$C_2^6:C_6^2$ |
3A |
2A |
$(1,3,2)(8,15)(9,10)(11,13)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
6B1 |
$6$ |
$2$ |
$C_2^6:C_6^2$ |
3A |
2B |
$(1,3,2)(9,10)(11,13)$ |
| $A_4\times D_4^2:S_3$ |
6B-1 |
$6$ |
$2$ |
$C_2^6:C_6^2$ |
3A |
2B |
$(1,2,3)(9,10)(11,13)$ |
| $A_4\times D_4^2:S_3$ |
6C1 |
$6$ |
$4$ |
$C_2^5:C_6^2$ |
3A |
2E |
$(1,2,3)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
6C-1 |
$6$ |
$4$ |
$C_2^5:C_6^2$ |
3A |
2E |
$(1,2,3)(11,13)$ |
| $A_4\times D_4^2:S_3$ |
6D1 |
$6$ |
$4$ |
$C_2^5:C_6^2$ |
3A |
2F |
$(1,2,3)(9,10)(11,13)(12,14)$ |
| $A_4\times D_4^2:S_3$ |
6D-1 |
$6$ |
$4$ |
$C_2^5:C_6^2$ |
3A |
2F |
$(1,2,3)(8,15)(11,13)(12,14)$ |
