Elements of the group are displayed as permutations of degree 14.
| Group |
Label |
Order |
Size |
Centralizer |
Powers |
Representative |
| 2P |
3P |
5P |
| $A_5\times S_3\wr S_3$ |
1A |
$1$ |
$1$ |
$A_5\times S_3\wr S_3$ |
1A |
1A |
1A |
$()$ |
| $A_5\times S_3\wr S_3$ |
2A |
$2$ |
$9$ |
$S_3^2:C_2^2\times A_5$ |
1A |
2A |
2A |
$(7,9)$ |
| $A_5\times S_3\wr S_3$ |
2B |
$2$ |
$15$ |
$C_2^2\times S_3\wr S_3$ |
1A |
2B |
2B |
$(11,12)(13,14)$ |
| $A_5\times S_3\wr S_3$ |
2C |
$2$ |
$18$ |
$S_3\times D_6\times A_5$ |
1A |
2C |
2C |
$(2,3)(5,7)(8,9)$ |
| $A_5\times S_3\wr S_3$ |
2D |
$2$ |
$27$ |
$C_2\times S_4\times A_5$ |
1A |
2D |
2D |
$(1,4)(3,8)(7,9)$ |
| $A_5\times S_3\wr S_3$ |
2E |
$2$ |
$27$ |
$S_3\times D_4\times A_5$ |
1A |
2E |
2E |
$(2,9)(3,8)$ |
| $A_5\times S_3\wr S_3$ |
2F |
$2$ |
$54$ |
$\GL(2,4):C_2^3$ |
1A |
2F |
2F |
$(1,9)(2,4)(3,8)(6,7)$ |
| $A_5\times S_3\wr S_3$ |
2G |
$2$ |
$135$ |
$D_6^2:C_2^2$ |
1A |
2G |
2G |
$(1,4)(10,11)(12,13)$ |
| $A_5\times S_3\wr S_3$ |
2H |
$2$ |
$270$ |
$C_2\times D_6^2$ |
1A |
2H |
2H |
$(1,7)(2,4)(6,9)(11,14)(12,13)$ |
| $A_5\times S_3\wr S_3$ |
2I |
$2$ |
$405$ |
$C_2^3\times S_4$ |
1A |
2I |
2I |
$(1,4)(2,7)(3,5)(10,13)(11,12)$ |
| $A_5\times S_3\wr S_3$ |
2J |
$2$ |
$405$ |
$C_{12}:C_2^4$ |
1A |
2J |
2J |
$(1,4)(2,7)(11,14)(12,13)$ |
| $A_5\times S_3\wr S_3$ |
2K |
$2$ |
$810$ |
$C_2^3\times D_6$ |
1A |
2K |
2K |
$(1,6)(2,3)(5,9)(7,8)(10,12)(11,13)$ |
| $A_5\times S_3\wr S_3$ |
3A |
$3$ |
$6$ |
$\GL(2,4)\times \SOPlus(4,2)$ |
3A |
1A |
3A |
$(3,8,5)$ |
| $A_5\times S_3\wr S_3$ |
3B |
$3$ |
$8$ |
$A_5\times C_3\wr S_3$ |
3B |
1A |
3B |
$(1,4,6)(2,7,9)(3,5,8)$ |
| $A_5\times S_3\wr S_3$ |
3C |
$3$ |
$12$ |
$S_3^2\times \GL(2,4)$ |
3C |
1A |
3C |
$(2,9,7)(3,8,5)$ |
| $A_5\times S_3\wr S_3$ |
3D |
$3$ |
$20$ |
$C_3\times S_3\wr S_3$ |
3D |
1A |
3D |
$(12,14,13)$ |
| $A_5\times S_3\wr S_3$ |
3E |
$3$ |
$72$ |
$S_3\times \GL(2,4)$ |
3E |
1A |
3E |
$(1,8,2)(3,7,6)(4,5,9)$ |
| $A_5\times S_3\wr S_3$ |
3F |
$3$ |
$120$ |
$C_3^4:D_4$ |
3F |
1A |
3F |
$(2,9,7)(10,12,14)$ |
| $A_5\times S_3\wr S_3$ |
3G |
$3$ |
$160$ |
$C_3^4:S_3$ |
3G |
1A |
3G |
$(1,6,4)(2,9,7)(3,5,8)(11,12,13)$ |
| $A_5\times S_3\wr S_3$ |
3H |
$3$ |
$240$ |
$C_3^2\times S_3^2$ |
3H |
1A |
3H |
$(1,4,6)(3,5,8)(10,13,12)$ |
| $A_5\times S_3\wr S_3$ |
3I |
$3$ |
$1440$ |
$S_3\times C_3^2$ |
3I |
1A |
3I |
$(1,3,7)(2,6,5)(4,8,9)(11,12,14)$ |
| $A_5\times S_3\wr S_3$ |
4A |
$4$ |
$54$ |
$C_4\times S_3\times A_5$ |
2E |
4A |
4A |
$(1,3,6,5)(4,8)$ |
| $A_5\times S_3\wr S_3$ |
4B |
$4$ |
$162$ |
$C_2\times C_4\times A_5$ |
2E |
4B |
4B |
$(1,5,6,3)(2,9)(4,8)$ |
| $A_5\times S_3\wr S_3$ |
4C |
$4$ |
$810$ |
$C_{12}:C_2^3$ |
2E |
4C |
4C |
$(1,5,6,8)(3,4)(11,13)(12,14)$ |
| $A_5\times S_3\wr S_3$ |
4D |
$4$ |
$2430$ |
$C_2^3\times C_4$ |
2E |
4D |
4D |
$(2,8,9,3)(4,6)(5,7)(10,12)(11,14)$ |
| $A_5\times S_3\wr S_3$ |
5A1 |
$5$ |
$12$ |
$C_5\times S_3\wr S_3$ |
5A2 |
5A2 |
1A |
$(10,11,14,12,13)$ |
| $A_5\times S_3\wr S_3$ |
5A2 |
$5$ |
$12$ |
$C_5\times S_3\wr S_3$ |
5A1 |
5A1 |
1A |
$(10,14,13,11,12)$ |
| $A_5\times S_3\wr S_3$ |
6A |
$6$ |
$36$ |
$D_6\times \GL(2,4)$ |
3C |
2C |
6A |
$(1,2,6,9,4,7)$ |
| $A_5\times S_3\wr S_3$ |
6B |
$6$ |
$36$ |
$D_6\times \GL(2,4)$ |
3C |
2A |
6B |
$(1,4,6)(2,7,9)(3,5)$ |
| $A_5\times S_3\wr S_3$ |
6C |
$6$ |
$36$ |
$D_6\times \GL(2,4)$ |
3A |
2A |
6C |
$(3,5,8)(4,6)$ |
| $A_5\times S_3\wr S_3$ |
6D |
$6$ |
$36$ |
$D_6\times \GL(2,4)$ |
3A |
2C |
6D |
$(1,8)(2,7,9)(3,6)(4,5)$ |
| $A_5\times S_3\wr S_3$ |
6E |
$6$ |
$54$ |
$D_4\times \GL(2,4)$ |
3A |
2E |
6E |
$(3,8,5)(4,6)(7,9)$ |
| $A_5\times S_3\wr S_3$ |
6F |
$6$ |
$72$ |
$C_6\times \GL(2,4)$ |
3B |
2C |
6F |
$(1,6,4)(2,8,7,3,9,5)$ |
| $A_5\times S_3\wr S_3$ |
6G |
$6$ |
$90$ |
$D_6^2:C_6$ |
3A |
2B |
6G |
$(3,5,8)(11,12)(13,14)$ |
| $A_5\times S_3\wr S_3$ |
6H |
$6$ |
$108$ |
$C_2^2\times \GL(2,4)$ |
3C |
2F |
6H |
$(1,7,4,9,6,2)(3,8)$ |
| $A_5\times S_3\wr S_3$ |
6I |
$6$ |
$120$ |
$C_2^2\times C_3\wr S_3$ |
3B |
2B |
6I |
$(1,4,6)(2,7,9)(3,8,5)(11,14)(12,13)$ |
| $A_5\times S_3\wr S_3$ |
6J |
$6$ |
$180$ |
$C_6\times \SOPlus(4,2)$ |
3D |
2A |
6J |
$(7,9)(12,13,14)$ |
| $A_5\times S_3\wr S_3$ |
6K |
$6$ |
$180$ |
$C_3\times D_6^2$ |
3C |
2B |
6K |
$(2,7,9)(3,5,8)(11,12)(13,14)$ |
| $A_5\times S_3\wr S_3$ |
6L |
$6$ |
$216$ |
$C_6\times A_5$ |
3E |
2D |
6L |
$(1,3,9,4,8,7)(2,6,5)$ |
| $A_5\times S_3\wr S_3$ |
6M |
$6$ |
$360$ |
$C_6\times S_3^2$ |
3D |
2C |
6M |
$(1,3)(4,8)(5,6)(11,14,13)$ |
| $A_5\times S_3\wr S_3$ |
6N |
$6$ |
$540$ |
$C_6^2:C_2^2$ |
3C |
2H |
6N |
$(1,9,4,7,6,2)(11,14)(12,13)$ |
| $A_5\times S_3\wr S_3$ |
6O |
$6$ |
$540$ |
$C_{12}:D_6$ |
3D |
2E |
6O |
$(1,6)(3,5)(10,13,12)$ |
| $A_5\times S_3\wr S_3$ |
6P |
$6$ |
$540$ |
$C_6^2:C_2^2$ |
3A |
2G |
6P |
$(1,4)(2,9,7)(10,11)(12,13)$ |
| $A_5\times S_3\wr S_3$ |
6Q |
$6$ |
$540$ |
$C_6^2:C_2^2$ |
3A |
2H |
6Q |
$(1,9)(2,4)(3,5,8)(6,7)(10,11)(12,13)$ |
| $A_5\times S_3\wr S_3$ |
6R |
$6$ |
$540$ |
$C_6\times S_4$ |
3D |
2D |
6R |
$(1,4)(2,7)(3,8)(11,14,12)$ |
| $A_5\times S_3\wr S_3$ |
6S |
$6$ |
$540$ |
$C_6^2:C_2^2$ |
3C |
2G |
6S |
$(1,4,6)(2,9,7)(5,8)(10,14)(11,13)$ |
| $A_5\times S_3\wr S_3$ |
6T |
$6$ |
$720$ |
$C_3^2\times D_6$ |
3H |
2C |
6T |
$(1,8,4,3,6,5)(10,12,13)$ |
| $A_5\times S_3\wr S_3$ |
6U |
$6$ |
$720$ |
$C_3^2\times D_6$ |
3F |
2A |
6U |
$(2,7)(3,8,5)(11,12,14)$ |
| $A_5\times S_3\wr S_3$ |
6V |
$6$ |
$720$ |
$C_3^2\times D_6$ |
3H |
2A |
6V |
$(1,4,6)(2,7,9)(3,5)(12,13,14)$ |
| $A_5\times S_3\wr S_3$ |
6W |
$6$ |
$720$ |
$C_3^2\times D_6$ |
3F |
2C |
6W |
$(1,5)(2,7,9)(3,6)(4,8)(10,11,12)$ |
