Elements of the group are displayed as permutations of degree 14.
| Group |
Label |
Order |
Size |
Centralizer |
Powers |
Representative |
| 2P |
3P |
| $C_3^2\times Q_8:A_4$ |
1A |
$1$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
1A |
1A |
$()$ |
| $C_3^2\times Q_8:A_4$ |
2A |
$2$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
1A |
2A |
$(1,4)(2,6)(3,7)(5,8)$ |
| $C_3^2\times Q_8:A_4$ |
2B |
$2$ |
$6$ |
$C_4:C_6^2$ |
1A |
2B |
$(3,7)(5,8)$ |
| $C_3^2\times Q_8:A_4$ |
2C |
$2$ |
$6$ |
$C_4:C_6^2$ |
1A |
2C |
$(1,2)(3,5)(4,6)(7,8)$ |
| $C_3^2\times Q_8:A_4$ |
2D |
$2$ |
$6$ |
$C_4:C_6^2$ |
1A |
2D |
$(1,2)(3,8)(4,6)(5,7)$ |
| $C_3^2\times Q_8:A_4$ |
3A1 |
$3$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3A-1 |
1A |
$(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
3A-1 |
$3$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3A1 |
1A |
$(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
3B1 |
$3$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3B-1 |
1A |
$(9,11,10)$ |
| $C_3^2\times Q_8:A_4$ |
3B-1 |
$3$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3B1 |
1A |
$(9,10,11)$ |
| $C_3^2\times Q_8:A_4$ |
3C1 |
$3$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3C-1 |
1A |
$(9,11,10)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
3C-1 |
$3$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3C1 |
1A |
$(9,10,11)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
3D1 |
$3$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3D-1 |
1A |
$(9,11,10)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
3D-1 |
$3$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3D1 |
1A |
$(9,10,11)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
3E1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3E-1 |
1A |
$(1,3,6)(2,4,7)$ |
| $C_3^2\times Q_8:A_4$ |
3E-1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3E1 |
1A |
$(1,6,3)(2,7,4)$ |
| $C_3^2\times Q_8:A_4$ |
3F1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3F-1 |
1A |
$(1,3,6)(2,4,7)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
3F-1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3F1 |
1A |
$(1,6,3)(2,7,4)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
3G1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3G-1 |
1A |
$(1,3,6)(2,4,7)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
3G-1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3G1 |
1A |
$(1,6,3)(2,7,4)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
3H1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3H-1 |
1A |
$(1,3,6)(2,4,7)(9,11,10)$ |
| $C_3^2\times Q_8:A_4$ |
3H-1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3H1 |
1A |
$(1,6,3)(2,7,4)(9,10,11)$ |
| $C_3^2\times Q_8:A_4$ |
3I1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3I-1 |
1A |
$(1,3,6)(2,4,7)(9,11,10)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
3I-1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3I1 |
1A |
$(1,6,3)(2,7,4)(9,10,11)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
3J1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3J-1 |
1A |
$(1,3,6)(2,4,7)(9,11,10)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
3J-1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3J1 |
1A |
$(1,6,3)(2,7,4)(9,10,11)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
3K1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3K-1 |
1A |
$(1,3,6)(2,4,7)(9,10,11)$ |
| $C_3^2\times Q_8:A_4$ |
3K-1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3K1 |
1A |
$(1,6,3)(2,7,4)(9,11,10)$ |
| $C_3^2\times Q_8:A_4$ |
3L1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3L-1 |
1A |
$(1,3,6)(2,4,7)(9,10,11)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
3L-1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3L1 |
1A |
$(1,6,3)(2,7,4)(9,11,10)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
3M1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3M-1 |
1A |
$(1,3,6)(2,4,7)(9,10,11)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
3M-1 |
$3$ |
$16$ |
$C_3^2\times C_6$ |
3M1 |
1A |
$(1,6,3)(2,7,4)(9,11,10)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
4A |
$4$ |
$6$ |
$C_4.C_6^2$ |
2A |
4A |
$(1,6,4,2)(3,8,7,5)$ |
| $C_3^2\times Q_8:A_4$ |
4B |
$4$ |
$6$ |
$C_4.C_6^2$ |
2A |
4B |
$(1,6,4,2)(3,5,7,8)$ |
| $C_3^2\times Q_8:A_4$ |
6A1 |
$6$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3A-1 |
2A |
$(1,4)(2,6)(3,7)(5,8)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
6A-1 |
$6$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3A1 |
2A |
$(1,4)(2,6)(3,7)(5,8)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
6B1 |
$6$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3B-1 |
2A |
$(1,4)(2,6)(3,7)(5,8)(9,11,10)$ |
| $C_3^2\times Q_8:A_4$ |
6B-1 |
$6$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3B1 |
2A |
$(1,4)(2,6)(3,7)(5,8)(9,10,11)$ |
| $C_3^2\times Q_8:A_4$ |
6C1 |
$6$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3C-1 |
2A |
$(1,4)(2,6)(3,7)(5,8)(9,11,10)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
6C-1 |
$6$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3C1 |
2A |
$(1,4)(2,6)(3,7)(5,8)(9,10,11)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
6D1 |
$6$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3D-1 |
2A |
$(1,4)(2,6)(3,7)(5,8)(9,11,10)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
6D-1 |
$6$ |
$1$ |
$C_3^2\times Q_8:A_4$ |
3D1 |
2A |
$(1,4)(2,6)(3,7)(5,8)(9,10,11)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
6E1 |
$6$ |
$6$ |
$C_4:C_6^2$ |
3A1 |
2B |
$(3,7)(5,8)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
6E-1 |
$6$ |
$6$ |
$C_4:C_6^2$ |
3A-1 |
2B |
$(3,7)(5,8)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
6F1 |
$6$ |
$6$ |
$C_4:C_6^2$ |
3B1 |
2B |
$(3,7)(5,8)(9,10,11)$ |
| $C_3^2\times Q_8:A_4$ |
6F-1 |
$6$ |
$6$ |
$C_4:C_6^2$ |
3B-1 |
2B |
$(3,7)(5,8)(9,11,10)$ |
| $C_3^2\times Q_8:A_4$ |
6G1 |
$6$ |
$6$ |
$C_4:C_6^2$ |
3C1 |
2B |
$(3,7)(5,8)(9,10,11)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
6G-1 |
$6$ |
$6$ |
$C_4:C_6^2$ |
3C-1 |
2B |
$(3,7)(5,8)(9,11,10)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
6H1 |
$6$ |
$6$ |
$C_4:C_6^2$ |
3D1 |
2B |
$(3,7)(5,8)(9,10,11)(12,14,13)$ |
| $C_3^2\times Q_8:A_4$ |
6H-1 |
$6$ |
$6$ |
$C_4:C_6^2$ |
3D-1 |
2B |
$(3,7)(5,8)(9,11,10)(12,13,14)$ |
| $C_3^2\times Q_8:A_4$ |
6I1 |
$6$ |
$6$ |
$C_4:C_6^2$ |
3A1 |
2C |
$(1,2)(3,5)(4,6)(7,8)(12,13,14)$ |
