Elements of the group are displayed as permutations of degree 14.
| Group |
Label |
Order |
Size |
Centralizer |
Powers |
Representative |
| 2P |
3P |
| $(C_6\times C_{12}):D_4^2$ |
1A |
$1$ |
$1$ |
$(C_6\times C_{12}):D_4^2$ |
1A |
1A |
$()$ |
| $(C_6\times C_{12}):D_4^2$ |
2A |
$2$ |
$1$ |
$(C_6\times C_{12}):D_4^2$ |
1A |
2A |
$(5,10)(8,12)(9,13)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2B |
$2$ |
$2$ |
$C_6^2:D_4^2$ |
1A |
2B |
$(9,13)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2C |
$2$ |
$2$ |
$C_6^2:D_4^2$ |
1A |
2C |
$(5,8)(9,11)(10,12)(13,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2D |
$2$ |
$2$ |
$C_6^2:D_4^2$ |
1A |
2D |
$(5,8)(9,14)(10,12)(11,13)$ |
| $(C_6\times C_{12}):D_4^2$ |
2E |
$2$ |
$4$ |
$D_6^2:C_2^3$ |
1A |
2E |
$(9,11)(13,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2F |
$2$ |
$4$ |
$D_6^2:C_2^3$ |
1A |
2F |
$(8,12)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2G |
$2$ |
$4$ |
$D_6^2:C_2^3$ |
1A |
2G |
$(5,8)(9,13)(10,12)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2H |
$2$ |
$4$ |
$D_6^2:C_2^3$ |
1A |
2H |
$(5,9)(8,11)(10,13)(12,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2I |
$2$ |
$4$ |
$D_6^2:C_2^3$ |
1A |
2I |
$(5,9)(8,14)(10,13)(11,12)$ |
| $(C_6\times C_{12}):D_4^2$ |
2J |
$2$ |
$6$ |
$C_2\wr C_2^2\times D_6$ |
1A |
2J |
$(4,7)$ |
| $(C_6\times C_{12}):D_4^2$ |
2K |
$2$ |
$6$ |
$C_2\wr C_2^2\times D_6$ |
1A |
2K |
$(4,7)(5,10)(8,12)(9,13)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2L |
$2$ |
$6$ |
$C_2\wr C_2^2\times D_6$ |
1A |
2L |
$(1,6)(2,7)(3,4)$ |
| $(C_6\times C_{12}):D_4^2$ |
2M |
$2$ |
$6$ |
$C_2\wr C_2^2\times D_6$ |
1A |
2M |
$(1,6)(2,7)(3,4)(5,10)(8,12)(9,13)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2N |
$2$ |
$9$ |
$C_2^3:D_4^2$ |
1A |
2N |
$(3,6)(4,7)$ |
| $(C_6\times C_{12}):D_4^2$ |
2O |
$2$ |
$9$ |
$C_2^3:D_4^2$ |
1A |
2O |
$(1,4)(2,3)(5,10)(8,12)(9,13)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2P |
$2$ |
$12$ |
$C_2^5:D_6$ |
1A |
2P |
$(4,7)(9,13)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2Q |
$2$ |
$12$ |
$C_2^5:D_6$ |
1A |
2Q |
$(4,7)(5,8)(9,11)(10,12)(13,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2R |
$2$ |
$12$ |
$C_2^5:D_6$ |
1A |
2R |
$(4,7)(5,8)(9,14)(10,12)(11,13)$ |
| $(C_6\times C_{12}):D_4^2$ |
2S |
$2$ |
$12$ |
$C_2^5:D_6$ |
1A |
2S |
$(1,6)(2,7)(3,4)(9,13)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2T |
$2$ |
$12$ |
$C_2^5:D_6$ |
1A |
2T |
$(1,6)(2,7)(3,4)(5,8)(9,11)(10,12)(13,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2U |
$2$ |
$12$ |
$C_2^5:D_6$ |
1A |
2U |
$(1,6)(2,7)(3,4)(5,8)(9,14)(10,12)(11,13)$ |
| $(C_6\times C_{12}):D_4^2$ |
2V |
$2$ |
$18$ |
$C_2^2:D_4^2$ |
1A |
2V |
$(1,4)(3,6)(5,8)(9,11)(10,12)(13,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2W |
$2$ |
$18$ |
$C_2^2:D_4^2$ |
1A |
2W |
$(3,6)(4,7)(5,10)(8,12)$ |
| $(C_6\times C_{12}):D_4^2$ |
2X |
$2$ |
$18$ |
$C_2^2:D_4^2$ |
1A |
2X |
$(1,7)(2,3)(5,12)(8,10)(9,11)(13,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2Y |
$2$ |
$24$ |
$D_6\times C_2^4$ |
1A |
2Y |
$(4,7)(9,11)(13,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2Z |
$2$ |
$24$ |
$C_{12}:C_2^4$ |
1A |
2Z |
$(4,7)(8,12)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AA |
$2$ |
$24$ |
$D_6\times C_2^4$ |
1A |
2AA |
$(4,7)(5,8)(9,13)(10,12)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AB |
$2$ |
$24$ |
$C_{12}:C_2^4$ |
1A |
2AB |
$(4,7)(5,9)(8,11)(10,13)(12,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AC |
$2$ |
$24$ |
$C_{12}:C_2^4$ |
1A |
2AC |
$(4,7)(5,9)(8,14)(10,13)(11,12)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AD |
$2$ |
$24$ |
$D_6\times C_2^4$ |
1A |
2AD |
$(1,6)(2,7)(3,4)(9,11)(13,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AE |
$2$ |
$24$ |
$C_{12}:C_2^4$ |
1A |
2AE |
$(1,6)(2,7)(3,4)(8,12)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AF |
$2$ |
$24$ |
$D_6\times C_2^4$ |
1A |
2AF |
$(1,6)(2,7)(3,4)(5,8)(9,13)(10,12)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AG |
$2$ |
$24$ |
$C_{12}:C_2^4$ |
1A |
2AG |
$(1,6)(2,7)(3,4)(5,9)(8,11)(10,13)(12,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AH |
$2$ |
$24$ |
$C_{12}:C_2^4$ |
1A |
2AH |
$(1,6)(2,7)(3,4)(5,9)(8,14)(10,13)(11,12)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AI |
$2$ |
$36$ |
$D_4\times C_2^4$ |
1A |
2AI |
$(3,6)(4,7)(9,11)(13,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AJ |
$2$ |
$36$ |
$C_2\times D_4^2$ |
1A |
2AJ |
$(3,6)(4,7)(8,12)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AK |
$2$ |
$36$ |
$D_4\times C_2^4$ |
1A |
2AK |
$(3,6)(4,7)(5,8)(9,13)(10,12)(11,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AL |
$2$ |
$36$ |
$C_2\times D_4^2$ |
1A |
2AL |
$(3,6)(4,7)(5,9)(8,11)(10,13)(12,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
2AM |
$2$ |
$36$ |
$C_2\times D_4^2$ |
1A |
2AM |
$(3,6)(4,7)(5,9)(8,14)(10,13)(11,12)$ |
| $(C_6\times C_{12}):D_4^2$ |
3A |
$3$ |
$4$ |
$(C_6\times D_{12}):D_4$ |
3A |
1A |
$(2,6,3)$ |
| $(C_6\times C_{12}):D_4^2$ |
3B |
$3$ |
$4$ |
$(C_6\times D_{12}):D_4$ |
3B |
1A |
$(1,4,7)(2,6,3)$ |
| $(C_6\times C_{12}):D_4^2$ |
4A |
$4$ |
$4$ |
$D_6^2.C_2^3$ |
2A |
4A |
$(5,12,10,8)(9,14,13,11)$ |
| $(C_6\times C_{12}):D_4^2$ |
4B |
$4$ |
$4$ |
$D_6^2.C_2^3$ |
2A |
4B |
$(5,13,10,9)(8,14,12,11)$ |
| $(C_6\times C_{12}):D_4^2$ |
4C |
$4$ |
$4$ |
$D_6^2.C_2^3$ |
2A |
4C |
$(5,13,10,9)(8,11,12,14)$ |
| $(C_6\times C_{12}):D_4^2$ |
4D |
$4$ |
$8$ |
$D_6^2.C_2^2$ |
2B |
4D |
$(8,12)(9,14,13,11)$ |
| $(C_6\times C_{12}):D_4^2$ |
4E |
$4$ |
$8$ |
$D_6^2.C_2^2$ |
2C |
4E |
$(5,11,8,9)(10,14,12,13)$ |
| $(C_6\times C_{12}):D_4^2$ |
4F |
$4$ |
$8$ |
$D_6^2.C_2^2$ |
2D |
4F |
$(5,14,8,9)(10,11,12,13)$ |
| $(C_6\times C_{12}):D_4^2$ |
4G |
$4$ |
$18$ |
$C_2^4.C_2^4$ |
2N |
4G |
$(1,2)(3,4,6,7)$ |
| $(C_6\times C_{12}):D_4^2$ |
4H |
$4$ |
$18$ |
$C_2^4.C_2^4$ |
2N |
4H |
$(1,2)(3,4,6,7)(5,10)(8,12)(9,13)(11,14)$ |
