Elements of the group are displayed as permutations of degree 15.
| Group |
Label |
Order |
Size |
Centralizer |
Powers |
Representative |
| 2P |
3P |
| $C_3^4:(D_4\times D_6)$ |
1A |
$1$ |
$1$ |
$C_3^4:(D_4\times D_6)$ |
1A |
1A |
$()$ |
| $C_3^4:(D_4\times D_6)$ |
2A |
$2$ |
$6$ |
$C_3^2:D_6^2$ |
1A |
2A |
$(11,14)$ |
| $C_3^4:(D_4\times D_6)$ |
2B |
$2$ |
$6$ |
$C_3^2:D_6^2$ |
1A |
2B |
$(10,13)(11,15)(12,14)$ |
| $C_3^4:(D_4\times D_6)$ |
2C |
$2$ |
$9$ |
$S_3^3:C_2^2$ |
1A |
2C |
$(2,9)(3,8)(4,6)(5,7)$ |
| $C_3^4:(D_4\times D_6)$ |
2D |
$2$ |
$9$ |
$S_3^3:C_2^2$ |
1A |
2D |
$(1,5)(2,6)(3,4)$ |
| $C_3^4:(D_4\times D_6)$ |
2E |
$2$ |
$9$ |
$S_3^3:C_2^2$ |
1A |
2E |
$(1,6)(2,5)(7,8)$ |
| $C_3^4:(D_4\times D_6)$ |
2F |
$2$ |
$9$ |
$C_6.D_6^2$ |
1A |
2F |
$(11,14)(13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
2G |
$2$ |
$54$ |
$D_6^2$ |
1A |
2G |
$(1,4)(2,5)(8,9)(11,14)$ |
| $C_3^4:(D_4\times D_6)$ |
2H |
$2$ |
$54$ |
$D_6^2$ |
1A |
2H |
$(1,2)(3,4)(5,6)(7,8)(10,12)(11,13)(14,15)$ |
| $C_3^4:(D_4\times D_6)$ |
2I |
$2$ |
$54$ |
$D_6^2$ |
1A |
2I |
$(2,7)(3,8)(5,9)(13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
2J |
$2$ |
$54$ |
$D_6^2$ |
1A |
2J |
$(2,8)(3,9)(5,7)(10,12)(11,13)(14,15)$ |
| $C_3^4:(D_4\times D_6)$ |
2K |
$2$ |
$54$ |
$D_6^2$ |
1A |
2K |
$(1,4)(2,8)(3,7)(5,9)(11,14)$ |
| $C_3^4:(D_4\times D_6)$ |
2L |
$2$ |
$54$ |
$D_6^2$ |
1A |
2L |
$(2,3)(4,6)(8,9)(10,12)(11,13)(14,15)$ |
| $C_3^4:(D_4\times D_6)$ |
2M |
$2$ |
$81$ |
$D_4\times D_6$ |
1A |
2M |
$(1,8)(2,5)(4,9)(6,7)(11,14)(13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
2N |
$2$ |
$81$ |
$D_4\times D_6$ |
1A |
2N |
$(3,5)(4,6)(7,8)(10,14)(12,13)$ |
| $C_3^4:(D_4\times D_6)$ |
2O |
$2$ |
$81$ |
$D_4\times D_6$ |
1A |
2O |
$(1,8)(4,7)(6,9)(10,14)(12,15)$ |
| $C_3^4:(D_4\times D_6)$ |
3A |
$3$ |
$2$ |
$C_3^4:(S_3\times D_4)$ |
3A |
1A |
$(1,6,4)(2,3,5)(7,8,9)$ |
| $C_3^4:(D_4\times D_6)$ |
3B |
$3$ |
$4$ |
$C_3^2.S_3^3$ |
3B |
1A |
$(12,15,13)$ |
| $C_3^4:(D_4\times D_6)$ |
3C |
$3$ |
$4$ |
$C_3^2.S_3^3$ |
3C |
1A |
$(10,11,14)(12,13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
3D |
$3$ |
$6$ |
$S_3^3:C_6$ |
3D |
1A |
$(2,3,5)(7,9,8)$ |
| $C_3^4:(D_4\times D_6)$ |
3E |
$3$ |
$6$ |
$S_3^3:C_6$ |
3E |
1A |
$(1,7,5)(2,6,8)(3,4,9)$ |
| $C_3^4:(D_4\times D_6)$ |
3F |
$3$ |
$8$ |
$C_3^3:S_3^2$ |
3F |
1A |
$(1,6,4)(2,3,5)(7,8,9)(12,15,13)$ |
| $C_3^4:(D_4\times D_6)$ |
3G |
$3$ |
$8$ |
$C_3^3:S_3^2$ |
3G |
1A |
$(1,6,4)(2,3,5)(7,8,9)(10,11,14)(12,13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
3H |
$3$ |
$12$ |
$C_3^4:D_4$ |
3H |
1A |
$(1,7,2)(3,6,8)(4,9,5)$ |
| $C_3^4:(D_4\times D_6)$ |
3I |
$3$ |
$24$ |
$C_3^2\times S_3^2$ |
3I |
1A |
$(2,5,3)(7,8,9)(12,15,13)$ |
| $C_3^4:(D_4\times D_6)$ |
3J |
$3$ |
$24$ |
$C_3^2\times S_3^2$ |
3J |
1A |
$(2,5,3)(7,8,9)(10,11,14)(12,13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
3K |
$3$ |
$24$ |
$C_3^2\times S_3^2$ |
3K |
1A |
$(1,7,5)(2,6,8)(3,4,9)(12,15,13)$ |
| $C_3^4:(D_4\times D_6)$ |
3L |
$3$ |
$24$ |
$C_3^2\times S_3^2$ |
3L |
1A |
$(1,7,5)(2,6,8)(3,4,9)(10,14,11)(12,15,13)$ |
| $C_3^4:(D_4\times D_6)$ |
3M |
$3$ |
$48$ |
$S_3\times C_3^3$ |
3M |
1A |
$(1,5,8)(2,9,6)(3,7,4)(10,11,14)$ |
| $C_3^4:(D_4\times D_6)$ |
3N |
$3$ |
$48$ |
$S_3\times C_3^3$ |
3N |
1A |
$(1,3,9)(2,8,4)(5,7,6)(10,14,11)(12,13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
4A |
$4$ |
$18$ |
$C_{12}.S_3^2$ |
2F |
4A |
$(10,12)(11,15,14,13)$ |
| $C_3^4:(D_4\times D_6)$ |
4B |
$4$ |
$162$ |
$C_4\times D_6$ |
2F |
4B |
$(2,3)(4,6)(8,9)(10,13,11,15)(12,14)$ |
| $C_3^4:(D_4\times D_6)$ |
4C |
$4$ |
$162$ |
$C_4\times D_6$ |
2F |
4C |
$(2,9)(3,8)(4,6)(5,7)(10,13)(11,12,14,15)$ |
| $C_3^4:(D_4\times D_6)$ |
4D |
$4$ |
$162$ |
$C_4\times D_6$ |
2F |
4D |
$(2,7)(3,8)(5,9)(10,15,11,13)(12,14)$ |
| $C_3^4:(D_4\times D_6)$ |
6A |
$6$ |
$12$ |
$C_6\times C_3^2:D_6$ |
3B |
2A |
$(11,14)(12,13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6B |
$6$ |
$12$ |
$C_6\times C_3^2:D_6$ |
3C |
2B |
$(10,12,11,13,14,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6C |
$6$ |
$12$ |
$S_3\times C_3^2:D_6$ |
3A |
2A |
$(1,4,6)(2,5,3)(7,9,8)(13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6D |
$6$ |
$12$ |
$S_3\times C_3^2:D_6$ |
3A |
2B |
$(1,4,6)(2,5,3)(7,9,8)(10,12)(11,13)(14,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6E |
$6$ |
$18$ |
$C_6\times \SOPlus(4,2)$ |
3D |
2C |
$(2,7,3,9,5,8)(4,6)$ |
| $C_3^4:(D_4\times D_6)$ |
6F |
$6$ |
$18$ |
$C_6\times \SOPlus(4,2)$ |
3A |
2D |
$(1,2,4,5,6,3)(7,8,9)$ |
| $C_3^4:(D_4\times D_6)$ |
6G |
$6$ |
$18$ |
$C_6\times \SOPlus(4,2)$ |
3E |
2E |
$(1,2,7,6,5,8)(3,9,4)$ |
| $C_3^4:(D_4\times D_6)$ |
6H |
$6$ |
$18$ |
$C_6^2:D_6$ |
3A |
2F |
$(1,6,4)(2,3,5)(7,8,9)(11,14)(13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6I |
$6$ |
$24$ |
$C_3^3:D_6$ |
3F |
2A |
$(1,4,6)(2,5,3)(7,9,8)(11,14)(12,13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6J |
$6$ |
$24$ |
$C_3^3:D_6$ |
3G |
2B |
$(1,4,6)(2,5,3)(7,9,8)(10,12,11,13,14,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6K |
$6$ |
$36$ |
$C_6\times S_3^2$ |
3B |
2E |
$(3,5)(4,6)(7,8)(12,13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6L |
$6$ |
$36$ |
$C_6\times S_3^2$ |
3C |
2E |
$(3,5)(4,6)(7,8)(10,11,14)(12,13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6M |
$6$ |
$36$ |
$C_6\times S_3^2$ |
3D |
2A |
$(2,3,5)(7,9,8)(13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6N |
$6$ |
$36$ |
$C_6\times S_3^2$ |
3D |
2B |
$(2,3,5)(7,9,8)(10,12)(11,13)(14,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6O |
$6$ |
$36$ |
$C_6\times S_3^2$ |
3B |
2D |
$(2,7)(3,8)(5,9)(12,13,15)$ |
| $C_3^4:(D_4\times D_6)$ |
6P |
$6$ |
$36$ |
$C_6\times S_3^2$ |
3C |
2D |
$(2,7)(3,8)(5,9)(10,11,14)(12,13,15)$ |
