Elements of the group are displayed as permutations of degree 12.
| Group |
Label |
Order |
Size |
Centralizer |
Powers |
Representative |
| 2P |
3P |
5P |
| $S_3\times F_5\times S_4$ |
1A |
$1$ |
$1$ |
$S_3\times F_5\times S_4$ |
1A |
1A |
1A |
$()$ |
| $S_3\times F_5\times S_4$ |
2A |
$2$ |
$3$ |
$S_3\times D_4\times F_5$ |
1A |
2A |
2A |
$(9,11)(10,12)$ |
| $S_3\times F_5\times S_4$ |
2B |
$2$ |
$3$ |
$C_2\times F_5\times S_4$ |
1A |
2B |
2B |
$(6,8)$ |
| $S_3\times F_5\times S_4$ |
2C |
$2$ |
$5$ |
$C_4\times S_3\times S_4$ |
1A |
2C |
2C |
$(2,3)(4,5)$ |
| $S_3\times F_5\times S_4$ |
2D |
$2$ |
$6$ |
$C_2\times D_6\times F_5$ |
1A |
2D |
2D |
$(11,12)$ |
| $S_3\times F_5\times S_4$ |
2E |
$2$ |
$9$ |
$D_{10}.C_2^4$ |
1A |
2E |
2E |
$(7,8)(9,10)(11,12)$ |
| $S_3\times F_5\times S_4$ |
2F |
$2$ |
$15$ |
$C_2^4.D_6$ |
1A |
2F |
2F |
$(1,3)(2,4)(7,8)$ |
| $S_3\times F_5\times S_4$ |
2G |
$2$ |
$15$ |
$C_4^2:D_6$ |
1A |
2G |
2G |
$(2,3)(4,5)(9,10)(11,12)$ |
| $S_3\times F_5\times S_4$ |
2H |
$2$ |
$18$ |
$C_2^3\times F_5$ |
1A |
2H |
2H |
$(6,7)(11,12)$ |
| $S_3\times F_5\times S_4$ |
2I |
$2$ |
$30$ |
$C_{12}:C_2^3$ |
1A |
2I |
2I |
$(1,3)(2,4)(10,11)$ |
| $S_3\times F_5\times S_4$ |
2J |
$2$ |
$45$ |
$C_4^2:C_2^2$ |
1A |
2J |
2J |
$(2,3)(4,5)(7,8)(9,10)(11,12)$ |
| $S_3\times F_5\times S_4$ |
2K |
$2$ |
$90$ |
$C_2^3\times C_4$ |
1A |
2K |
2K |
$(2,3)(4,5)(6,7)(10,12)$ |
| $S_3\times F_5\times S_4$ |
3A |
$3$ |
$2$ |
$C_3\times F_5\times S_4$ |
3A |
1A |
3A |
$(6,7,8)$ |
| $S_3\times F_5\times S_4$ |
3B |
$3$ |
$8$ |
$D_{15}:C_{12}$ |
3B |
1A |
3B |
$(10,11,12)$ |
| $S_3\times F_5\times S_4$ |
3C |
$3$ |
$16$ |
$C_3^2\times F_5$ |
3C |
1A |
3C |
$(6,8,7)(9,11,12)$ |
| $S_3\times F_5\times S_4$ |
4A1 |
$4$ |
$5$ |
$C_4\times S_3\times S_4$ |
2C |
4A-1 |
4A1 |
$(2,5,3,4)$ |
| $S_3\times F_5\times S_4$ |
4A-1 |
$4$ |
$5$ |
$C_4\times S_3\times S_4$ |
2C |
4A1 |
4A-1 |
$(2,4,3,5)$ |
| $S_3\times F_5\times S_4$ |
4B |
$4$ |
$6$ |
$D_{15}:C_4^2$ |
2A |
4B |
4B |
$(9,12,11,10)$ |
| $S_3\times F_5\times S_4$ |
4C1 |
$4$ |
$15$ |
$C_4^2:D_6$ |
2C |
4C-1 |
4C1 |
$(2,5,3,4)(9,10)(11,12)$ |
| $S_3\times F_5\times S_4$ |
4C-1 |
$4$ |
$15$ |
$C_4^2:D_6$ |
2C |
4C1 |
4C-1 |
$(2,4,3,5)(9,10)(11,12)$ |
| $S_3\times F_5\times S_4$ |
4D1 |
$4$ |
$15$ |
$C_2^4.D_6$ |
2C |
4D-1 |
4D1 |
$(1,2,3,4)(6,7)$ |
| $S_3\times F_5\times S_4$ |
4D-1 |
$4$ |
$15$ |
$C_2^4.D_6$ |
2C |
4D1 |
4D-1 |
$(1,4,3,2)(6,7)$ |
| $S_3\times F_5\times S_4$ |
4E |
$4$ |
$18$ |
$C_{10}:C_4^2$ |
2A |
4E |
4E |
$(6,8)(9,12,10,11)$ |
| $S_3\times F_5\times S_4$ |
4F |
$4$ |
$30$ |
$S_3\times C_4^2$ |
2A |
4F |
4F |
$(1,3)(2,4)(9,10,11,12)$ |
| $S_3\times F_5\times S_4$ |
4G1 |
$4$ |
$30$ |
$S_3\times C_4^2$ |
2G |
4G-1 |
4G1 |
$(2,4,3,5)(9,12,11,10)$ |
| $S_3\times F_5\times S_4$ |
4G-1 |
$4$ |
$30$ |
$S_3\times C_4^2$ |
2G |
4G1 |
4G-1 |
$(2,5,3,4)(9,10,11,12)$ |
| $S_3\times F_5\times S_4$ |
4H1 |
$4$ |
$30$ |
$C_{12}:C_2^3$ |
2C |
4H-1 |
4H1 |
$(1,4,5,3)(10,12)$ |
| $S_3\times F_5\times S_4$ |
4H-1 |
$4$ |
$30$ |
$C_{12}:C_2^3$ |
2C |
4H1 |
4H-1 |
$(1,3,5,4)(10,12)$ |
| $S_3\times F_5\times S_4$ |
4I1 |
$4$ |
$45$ |
$C_4^2:C_2^2$ |
2C |
4I-1 |
4I1 |
$(2,4,3,5)(7,8)(9,10)(11,12)$ |
| $S_3\times F_5\times S_4$ |
4I-1 |
$4$ |
$45$ |
$C_4^2:C_2^2$ |
2C |
4I1 |
4I-1 |
$(2,5,3,4)(7,8)(9,10)(11,12)$ |
| $S_3\times F_5\times S_4$ |
4J |
$4$ |
$90$ |
$C_2\times C_4^2$ |
2A |
4J |
4J |
$(2,3)(4,5)(6,7)(9,12,10,11)$ |
| $S_3\times F_5\times S_4$ |
4K1 |
$4$ |
$90$ |
$C_2^3\times C_4$ |
2C |
4K-1 |
4K1 |
$(2,4,3,5)(6,8)(9,11)$ |
| $S_3\times F_5\times S_4$ |
4K-1 |
$4$ |
$90$ |
$C_2^3\times C_4$ |
2C |
4K1 |
4K-1 |
$(2,5,3,4)(6,8)(9,11)$ |
| $S_3\times F_5\times S_4$ |
4L1 |
$4$ |
$90$ |
$C_2\times C_4^2$ |
2G |
4L-1 |
4L1 |
$(2,4,3,5)(7,8)(9,12,10,11)$ |
| $S_3\times F_5\times S_4$ |
4L-1 |
$4$ |
$90$ |
$C_2\times C_4^2$ |
2G |
4L1 |
4L-1 |
$(2,5,3,4)(7,8)(9,11,10,12)$ |
| $S_3\times F_5\times S_4$ |
5A |
$5$ |
$4$ |
$C_5\times S_3\times S_4$ |
5A |
5A |
1A |
$(1,5,3,2,4)$ |
| $S_3\times F_5\times S_4$ |
6A |
$6$ |
$6$ |
$D_{20}:C_{12}$ |
3A |
2A |
6A |
$(6,7,8)(9,11)(10,12)$ |
| $S_3\times F_5\times S_4$ |
6B |
$6$ |
$10$ |
$C_{12}\times S_4$ |
3A |
2C |
6B |
$(2,3)(4,5)(6,8,7)$ |
| $S_3\times F_5\times S_4$ |
6C |
$6$ |
$12$ |
$D_{10}:C_{12}$ |
3A |
2D |
6C |
$(6,8,7)(11,12)$ |
| $S_3\times F_5\times S_4$ |
6D |
$6$ |
$24$ |
$C_6\times F_5$ |
3B |
2B |
6D |
$(6,8)(9,11,10)$ |
| $S_3\times F_5\times S_4$ |
6E |
$6$ |
$30$ |
$D_4\times C_{12}$ |
3A |
2G |
6E |
$(2,3)(4,5)(6,8,7)(9,11)(10,12)$ |
| $S_3\times F_5\times S_4$ |
6F |
$6$ |
$40$ |
$S_3\times C_{12}$ |
3B |
2C |
6F |
$(2,3)(4,5)(10,12,11)$ |
| $S_3\times F_5\times S_4$ |
6G |
$6$ |
$60$ |
$C_2^2\times C_{12}$ |
3A |
2I |
6G |
$(1,3)(2,4)(6,7,8)(10,11)$ |
| $S_3\times F_5\times S_4$ |
6H |
$6$ |
$80$ |
$C_3\times C_{12}$ |
3C |
2C |
6H |
$(2,3)(4,5)(6,8,7)(9,10,11)$ |
| $S_3\times F_5\times S_4$ |
6I |
$6$ |
$120$ |
$C_2\times C_{12}$ |
3B |
2F |
6I |
$(1,3)(2,4)(7,8)(9,12,10)$ |
| $S_3\times F_5\times S_4$ |
10A |
$10$ |
$12$ |
$C_{20}:D_6$ |
5A |
10A |
2A |
$(1,2,5,4,3)(9,11)(10,12)$ |
| $S_3\times F_5\times S_4$ |
10B |
$10$ |
$12$ |
$C_{10}\times S_4$ |
5A |
10B |
2B |
$(1,2,5,4,3)(6,8)$ |
| $S_3\times F_5\times S_4$ |
10C |
$10$ |
$24$ |
$C_{10}\times D_6$ |
5A |
10C |
2D |
$(1,4,2,3,5)(11,12)$ |
| $S_3\times F_5\times S_4$ |
10D |
$10$ |
$36$ |
$D_4\times C_{10}$ |
5A |
10D |
2E |
$(1,2,5,4,3)(7,8)(9,10)(11,12)$ |
| $S_3\times F_5\times S_4$ |
10E |
$10$ |
$72$ |
$C_2^2\times C_{10}$ |
5A |
10E |
2H |
$(1,3,4,5,2)(6,7)(11,12)$ |
