Elements of the group are displayed as permutations of degree 15.
| Group |
Label |
Order |
Size |
Centralizer |
Powers |
Representative |
| 2P |
3P |
| $C_3^5:(S_3\times D_4)$ |
1A |
$1$ |
$1$ |
$C_3^5:(S_3\times D_4)$ |
1A |
1A |
$()$ |
| $C_3^5:(S_3\times D_4)$ |
2A |
$2$ |
$6$ |
$C_3\wr S_3\times D_6$ |
1A |
2A |
$(12,13)$ |
| $C_3^5:(S_3\times D_4)$ |
2B |
$2$ |
$6$ |
$C_3\wr S_3\times D_6$ |
1A |
2B |
$(10,14)(11,13)(12,15)$ |
| $C_3^5:(S_3\times D_4)$ |
2C |
$2$ |
$9$ |
$S_3^2:C_6^2$ |
1A |
2C |
$(2,4)(3,7)(6,8)$ |
| $C_3^5:(S_3\times D_4)$ |
2D |
$2$ |
$9$ |
$C_3\wr S_3\times D_4$ |
1A |
2D |
$(12,13)(14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
2E |
$2$ |
$54$ |
$S_3\times C_6^2$ |
1A |
2E |
$(2,4)(3,7)(6,8)(14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
2F |
$2$ |
$54$ |
$S_3\times C_6^2$ |
1A |
2F |
$(2,4)(3,7)(6,8)(10,11)(12,14)(13,15)$ |
| $C_3^5:(S_3\times D_4)$ |
2G |
$2$ |
$81$ |
$C_4:C_6^2$ |
1A |
2G |
$(2,4)(3,7)(6,8)(12,13)(14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
3A1 |
$3$ |
$1$ |
$C_3^5:(S_3\times D_4)$ |
3A-1 |
1A |
$(1,5,9)(2,7,6)(3,8,4)$ |
| $C_3^5:(S_3\times D_4)$ |
3A-1 |
$3$ |
$1$ |
$C_3^5:(S_3\times D_4)$ |
3A1 |
1A |
$(1,9,5)(2,6,7)(3,4,8)$ |
| $C_3^5:(S_3\times D_4)$ |
3B1 |
$3$ |
$3$ |
$C_3\times S_3^3:C_6$ |
3B-1 |
1A |
$(2,6,7)(3,4,8)$ |
| $C_3^5:(S_3\times D_4)$ |
3B-1 |
$3$ |
$3$ |
$C_3\times S_3^3:C_6$ |
3B1 |
1A |
$(2,7,6)(3,8,4)$ |
| $C_3^5:(S_3\times D_4)$ |
3C1 |
$3$ |
$3$ |
$C_3\times S_3^3:C_6$ |
3C-1 |
1A |
$(3,8,4)$ |
| $C_3^5:(S_3\times D_4)$ |
3C-1 |
$3$ |
$3$ |
$C_3\times S_3^3:C_6$ |
3C1 |
1A |
$(3,4,8)$ |
| $C_3^5:(S_3\times D_4)$ |
3D1 |
$3$ |
$3$ |
$C_3\times S_3^3:C_6$ |
3D-1 |
1A |
$(1,5,9)(2,7,6)(3,4,8)$ |
| $C_3^5:(S_3\times D_4)$ |
3D-1 |
$3$ |
$3$ |
$C_3\times S_3^3:C_6$ |
3D1 |
1A |
$(1,9,5)(2,6,7)(3,8,4)$ |
| $C_3^5:(S_3\times D_4)$ |
3E |
$3$ |
$4$ |
$C_3^5:D_6$ |
3E |
1A |
$(11,15,14)$ |
| $C_3^5:(S_3\times D_4)$ |
3F |
$3$ |
$4$ |
$C_3^5:D_6$ |
3F |
1A |
$(10,12,13)(11,14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
3G1 |
$3$ |
$4$ |
$C_3^5:D_6$ |
3G-1 |
1A |
$(1,9,5)(2,6,7)(3,4,8)(11,15,14)$ |
| $C_3^5:(S_3\times D_4)$ |
3G-1 |
$3$ |
$4$ |
$C_3^5:D_6$ |
3G1 |
1A |
$(1,5,9)(2,7,6)(3,8,4)(11,14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
3H1 |
$3$ |
$4$ |
$C_3^5:D_6$ |
3H-1 |
1A |
$(1,9,5)(2,6,7)(3,4,8)(10,12,13)(11,14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
3H-1 |
$3$ |
$4$ |
$C_3^5:D_6$ |
3H1 |
1A |
$(1,5,9)(2,7,6)(3,8,4)(10,13,12)(11,15,14)$ |
| $C_3^5:(S_3\times D_4)$ |
3I |
$3$ |
$6$ |
$C_3^5:D_4$ |
3I |
1A |
$(2,7,6)(3,4,8)$ |
| $C_3^5:(S_3\times D_4)$ |
3J1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3J-1 |
1A |
$(3,8,4)(11,15,14)$ |
| $C_3^5:(S_3\times D_4)$ |
3J-1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3J1 |
1A |
$(3,4,8)(11,14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
3K1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3K-1 |
1A |
$(3,8,4)(10,12,13)(11,14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
3K-1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3K1 |
1A |
$(3,4,8)(10,13,12)(11,15,14)$ |
| $C_3^5:(S_3\times D_4)$ |
3L1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3L-1 |
1A |
$(2,6,7)(3,4,8)(11,15,14)$ |
| $C_3^5:(S_3\times D_4)$ |
3L-1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3L1 |
1A |
$(2,7,6)(3,8,4)(11,14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
3M1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3M-1 |
1A |
$(2,6,7)(3,4,8)(10,13,12)(11,15,14)$ |
| $C_3^5:(S_3\times D_4)$ |
3M-1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3M1 |
1A |
$(2,7,6)(3,8,4)(10,12,13)(11,14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
3N1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3N-1 |
1A |
$(1,5,9)(2,7,6)(3,4,8)(11,15,14)$ |
| $C_3^5:(S_3\times D_4)$ |
3N-1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3N1 |
1A |
$(1,9,5)(2,6,7)(3,8,4)(11,14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
3O1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3O-1 |
1A |
$(1,5,9)(2,7,6)(3,4,8)(10,13,12)(11,15,14)$ |
| $C_3^5:(S_3\times D_4)$ |
3O-1 |
$3$ |
$12$ |
$C_3^3\times S_3^2$ |
3O1 |
1A |
$(1,9,5)(2,6,7)(3,8,4)(10,12,13)(11,14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
3P |
$3$ |
$18$ |
$C_3^4:D_4$ |
3P |
1A |
$(1,3,2)(4,6,9)(5,8,7)$ |
| $C_3^5:(S_3\times D_4)$ |
3Q |
$3$ |
$24$ |
$S_3\times C_3^4$ |
3Q |
1A |
$(2,7,6)(3,4,8)(11,15,14)$ |
| $C_3^5:(S_3\times D_4)$ |
3R |
$3$ |
$24$ |
$S_3\times C_3^4$ |
3R |
1A |
$(2,7,6)(3,4,8)(10,12,13)(11,14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
3S |
$3$ |
$72$ |
$S_3\times C_3^3$ |
3S |
1A |
$(1,3,7)(2,9,4)(5,8,6)(11,15,14)$ |
| $C_3^5:(S_3\times D_4)$ |
3T |
$3$ |
$72$ |
$S_3\times C_3^3$ |
3T |
1A |
$(1,2,8)(3,9,6)(4,5,7)(10,12,13)(11,14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
4A |
$4$ |
$18$ |
$C_4\times C_3\wr S_3$ |
2D |
4A |
$(10,11)(12,15,13,14)$ |
| $C_3^5:(S_3\times D_4)$ |
4B |
$4$ |
$162$ |
$C_6\times C_{12}$ |
2D |
4B |
$(2,3)(4,6)(7,8)(10,15,12,14)(11,13)$ |
| $C_3^5:(S_3\times D_4)$ |
6A1 |
$6$ |
$6$ |
$C_3\wr S_3\times D_6$ |
3A-1 |
2A |
$(1,5,9)(2,7,6)(3,8,4)(14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
6A-1 |
$6$ |
$6$ |
$C_3\wr S_3\times D_6$ |
3A1 |
2A |
$(1,9,5)(2,6,7)(3,4,8)(14,15)$ |
| $C_3^5:(S_3\times D_4)$ |
6B1 |
$6$ |
$6$ |
$C_3\wr S_3\times D_6$ |
3A-1 |
2B |
$(1,5,9)(2,7,6)(3,8,4)(10,11)(12,14)(13,15)$ |
| $C_3^5:(S_3\times D_4)$ |
6B-1 |
$6$ |
$6$ |
$C_3\wr S_3\times D_6$ |
3A1 |
2B |
$(1,9,5)(2,6,7)(3,4,8)(10,11)(12,14)(13,15)$ |
| $C_3^5:(S_3\times D_4)$ |
6C1 |
$6$ |
$9$ |
$S_3^2:C_6^2$ |
3B1 |
2C |
$(2,3,6,4,7,8)$ |
| $C_3^5:(S_3\times D_4)$ |
6C-1 |
$6$ |
$9$ |
$S_3^2:C_6^2$ |
3B-1 |
2C |
$(2,3,7,8,6,4)$ |
| $C_3^5:(S_3\times D_4)$ |
6D1 |
$6$ |
$9$ |
$S_3^2:C_6^2$ |
3C1 |
2C |
$(1,2)(3,4,8)(5,7)(6,9)$ |
| $C_3^5:(S_3\times D_4)$ |
6D-1 |
$6$ |
$9$ |
$S_3^2:C_6^2$ |
3C-1 |
2C |
$(1,2)(3,8,4)(5,7)(6,9)$ |
