Elements of the group are displayed as permutations of degree 13.
| Group |
Label |
Order |
Size |
Centralizer |
Powers |
Representative |
| 2P |
3P |
| $C_2^2:A_4\times D_6$ |
1A |
$1$ |
$1$ |
$C_2^2:A_4\times D_6$ |
1A |
1A |
$()$ |
| $C_2^2:A_4\times D_6$ |
2A |
$2$ |
$1$ |
$C_2^2:A_4\times D_6$ |
1A |
2A |
$(12,13)$ |
| $C_2^2:A_4\times D_6$ |
2B |
$2$ |
$3$ |
$D_6\times C_2^4$ |
1A |
2B |
$(5,6)(7,8)$ |
| $C_2^2:A_4\times D_6$ |
2C |
$2$ |
$3$ |
$D_6\times C_2^4$ |
1A |
2C |
$(5,6)(7,8)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
2D |
$2$ |
$3$ |
$D_6\times C_2^4$ |
1A |
2D |
$(1,2)(3,4)$ |
| $C_2^2:A_4\times D_6$ |
2E |
$2$ |
$3$ |
$D_6\times C_2^4$ |
1A |
2E |
$(1,2)(3,4)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
2F |
$2$ |
$3$ |
$D_6\times C_2^4$ |
1A |
2F |
$(1,2)(3,4)(5,6)(7,8)$ |
| $C_2^2:A_4\times D_6$ |
2G |
$2$ |
$3$ |
$D_6\times C_2^4$ |
1A |
2G |
$(1,2)(3,4)(5,6)(7,8)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
2H |
$2$ |
$3$ |
$D_6\times C_2^4$ |
1A |
2H |
$(1,2)(3,4)(5,7)(6,8)$ |
| $C_2^2:A_4\times D_6$ |
2I |
$2$ |
$3$ |
$D_6\times C_2^4$ |
1A |
2I |
$(1,2)(3,4)(5,7)(6,8)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
2J |
$2$ |
$3$ |
$D_6\times C_2^4$ |
1A |
2J |
$(1,2)(3,4)(5,8)(6,7)$ |
| $C_2^2:A_4\times D_6$ |
2K |
$2$ |
$3$ |
$D_6\times C_2^4$ |
1A |
2K |
$(1,2)(3,4)(5,8)(6,7)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
2L |
$2$ |
$3$ |
$C_2^2\wr C_3$ |
1A |
2L |
$(10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
2M |
$2$ |
$3$ |
$C_2^2\wr C_3$ |
1A |
2M |
$(9,10)$ |
| $C_2^2:A_4\times D_6$ |
2N |
$2$ |
$9$ |
$C_2^6$ |
1A |
2N |
$(5,6)(7,8)(10,11)$ |
| $C_2^2:A_4\times D_6$ |
2O |
$2$ |
$9$ |
$C_2^6$ |
1A |
2O |
$(5,6)(7,8)(10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
2P |
$2$ |
$9$ |
$C_2^6$ |
1A |
2P |
$(1,2)(3,4)(10,11)$ |
| $C_2^2:A_4\times D_6$ |
2Q |
$2$ |
$9$ |
$C_2^6$ |
1A |
2Q |
$(1,2)(3,4)(10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
2R |
$2$ |
$9$ |
$C_2^6$ |
1A |
2R |
$(1,2)(3,4)(5,6)(7,8)(10,11)$ |
| $C_2^2:A_4\times D_6$ |
2S |
$2$ |
$9$ |
$C_2^6$ |
1A |
2S |
$(1,2)(3,4)(5,6)(7,8)(10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
2T |
$2$ |
$9$ |
$C_2^6$ |
1A |
2T |
$(1,2)(3,4)(5,7)(6,8)(10,11)$ |
| $C_2^2:A_4\times D_6$ |
2U |
$2$ |
$9$ |
$C_2^6$ |
1A |
2U |
$(1,2)(3,4)(5,7)(6,8)(10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
2V |
$2$ |
$9$ |
$C_2^6$ |
1A |
2V |
$(1,2)(3,4)(5,8)(6,7)(10,11)$ |
| $C_2^2:A_4\times D_6$ |
2W |
$2$ |
$9$ |
$C_2^6$ |
1A |
2W |
$(1,2)(3,4)(5,8)(6,7)(10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
3A |
$3$ |
$2$ |
$C_2^5:C_3^2$ |
3A |
1A |
$(9,11,10)$ |
| $C_2^2:A_4\times D_6$ |
3B1 |
$3$ |
$16$ |
$C_6\times S_3$ |
3B-1 |
1A |
$(2,4,3)(6,8,7)$ |
| $C_2^2:A_4\times D_6$ |
3B-1 |
$3$ |
$16$ |
$C_6\times S_3$ |
3B1 |
1A |
$(2,3,4)(6,7,8)$ |
| $C_2^2:A_4\times D_6$ |
3C1 |
$3$ |
$32$ |
$C_3\times C_6$ |
3C-1 |
1A |
$(1,2,4)(5,6,8)(9,11,10)$ |
| $C_2^2:A_4\times D_6$ |
3C-1 |
$3$ |
$32$ |
$C_3\times C_6$ |
3C1 |
1A |
$(1,4,2)(5,8,6)(9,10,11)$ |
| $C_2^2:A_4\times D_6$ |
6A |
$6$ |
$2$ |
$C_2^5:C_3^2$ |
3A |
2A |
$(9,10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6B |
$6$ |
$6$ |
$C_2^4\times C_6$ |
3A |
2B |
$(5,6)(7,8)(9,10,11)$ |
| $C_2^2:A_4\times D_6$ |
6C |
$6$ |
$6$ |
$C_2^4\times C_6$ |
3A |
2C |
$(5,6)(7,8)(9,10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6D |
$6$ |
$6$ |
$C_2^4\times C_6$ |
3A |
2D |
$(1,2)(3,4)(9,10,11)$ |
| $C_2^2:A_4\times D_6$ |
6E |
$6$ |
$6$ |
$C_2^4\times C_6$ |
3A |
2E |
$(1,2)(3,4)(9,10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6F |
$6$ |
$6$ |
$C_2^4\times C_6$ |
3A |
2F |
$(1,2)(3,4)(5,6)(7,8)(9,10,11)$ |
| $C_2^2:A_4\times D_6$ |
6G |
$6$ |
$6$ |
$C_2^4\times C_6$ |
3A |
2G |
$(1,2)(3,4)(5,6)(7,8)(9,10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6H |
$6$ |
$6$ |
$C_2^4\times C_6$ |
3A |
2H |
$(1,2)(3,4)(5,7)(6,8)(9,10,11)$ |
| $C_2^2:A_4\times D_6$ |
6I |
$6$ |
$6$ |
$C_2^4\times C_6$ |
3A |
2I |
$(1,2)(3,4)(5,7)(6,8)(9,10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6J |
$6$ |
$6$ |
$C_2^4\times C_6$ |
3A |
2J |
$(1,2)(3,4)(5,8)(6,7)(9,10,11)$ |
| $C_2^2:A_4\times D_6$ |
6K |
$6$ |
$6$ |
$C_2^4\times C_6$ |
3A |
2K |
$(1,2)(3,4)(5,8)(6,7)(9,10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6L1 |
$6$ |
$16$ |
$C_6\times S_3$ |
3B1 |
2A |
$(2,3,4)(6,7,8)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6L-1 |
$6$ |
$16$ |
$C_6\times S_3$ |
3B-1 |
2A |
$(2,4,3)(6,8,7)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6M1 |
$6$ |
$32$ |
$C_3\times C_6$ |
3C1 |
2A |
$(1,4,2)(5,8,6)(9,10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6M-1 |
$6$ |
$32$ |
$C_3\times C_6$ |
3C-1 |
2A |
$(1,2,4)(5,6,8)(9,11,10)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6N1 |
$6$ |
$48$ |
$C_2\times C_6$ |
3B1 |
2L |
$(1,4,3)(5,8,7)(10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6N-1 |
$6$ |
$48$ |
$C_2\times C_6$ |
3B-1 |
2L |
$(1,3,4)(5,7,8)(10,11)(12,13)$ |
| $C_2^2:A_4\times D_6$ |
6O1 |
$6$ |
$48$ |
$C_2\times C_6$ |
3B-1 |
2M |
$(1,4,2)(5,8,6)(9,10)$ |
| $C_2^2:A_4\times D_6$ |
6O-1 |
$6$ |
$48$ |
$C_2\times C_6$ |
3B1 |
2M |
$(1,2,4)(5,6,8)(9,10)$ |
