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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
128.161 | $D_{64}$ | $2^{7}$ | $2^{6}$ | $35$ | $C_2$ | Nilpotent - 6 |
128.162 | $\SD_{128}$ | $2^{7}$ | $2^{6}$ | $35$ | $C_2$ | Nilpotent - 6 |
128.163 | $Q_{128}$ | $2^{7}$ | $2^{6}$ | $35$ | $C_2$ | Nilpotent - 6 |
256.503 | $D_4^2:C_4$ | $2^{8}$ | $2^{4}$ | $22$ | $C_2$ | Nilpotent - 6 |
256.504 | $(C_4\times C_8).D_4$ | $2^{8}$ | $2^{4}$ | $22$ | $C_2$ | Nilpotent - 6 |
256.505 | $D_4^2.C_4$ | $2^{8}$ | $2^{4}$ | $22$ | $C_2$ | Nilpotent - 6 |
256.506 | $(C_4\times C_8).D_4$ | $2^{8}$ | $2^{4}$ | $22$ | $C_2$ | Nilpotent - 6 |
256.507 | $(C_4\times C_8).D_4$ | $2^{8}$ | $2^{4}$ | $22$ | $C_2$ | Nilpotent - 6 |
256.508 | $Q_8^2:C_4$ | $2^{8}$ | $2^{4}$ | $22$ | $C_2$ | Nilpotent - 6 |
256.509 | $(C_4\times C_8).D_4$ | $2^{8}$ | $2^{4}$ | $22$ | $C_2$ | Nilpotent - 6 |
256.510 | $Q_8^2.C_4$ | $2^{8}$ | $2^{4}$ | $22$ | $C_2$ | Nilpotent - 6 |
256.511 | $C_2^2.C_2\wr C_4$ | $2^{8}$ | $2^{4}$ | $19$ | $C_2$ | Nilpotent - 6 |
256.512 | $C_2^2.C_2\wr C_4$ | $2^{8}$ | $2^{4}$ | $19$ | $C_2$ | Nilpotent - 6 |
256.513 | $C_2^2.C_2\wr C_4$ | $2^{8}$ | $2^{4}$ | $19$ | $C_2$ | Nilpotent - 6 |
256.514 | $C_2^2.C_2\wr C_4$ | $2^{8}$ | $2^{4}$ | $19$ | $C_2$ | Nilpotent - 6 |
256.515 | $C_8:C_8:C_4$ | $2^{8}$ | $2^{3}$ | $19$ | $C_2$ | Nilpotent - 6 |
256.516 | $C_8:C_8:C_4$ | $2^{8}$ | $2^{3}$ | $19$ | $C_2$ | Nilpotent - 6 |
256.517 | $C_8^2:C_4$ | $2^{8}$ | $2^{3}$ | $25$ | $C_2$ | Nilpotent - 6 |
256.518 | $C_8^2:C_4$ | $2^{8}$ | $2^{3}$ | $25$ | $C_2$ | Nilpotent - 6 |
256.519 | $C_8^2.C_4$ | $2^{8}$ | $2^{3}$ | $25$ | $C_2$ | Nilpotent - 6 |
256.520 | $C_8^2.C_4$ | $2^{8}$ | $2^{3}$ | $25$ | $C_2$ | Nilpotent - 6 |
256.521 | $C_8:C_8:C_4$ | $2^{8}$ | $2^{3}$ | $19$ | $C_2$ | Nilpotent - 6 |
256.522 | $C_8:C_8.C_4$ | $2^{8}$ | $2^{3}$ | $19$ | $C_2$ | Nilpotent - 6 |
256.523 | $C_8^2:C_4$ | $2^{8}$ | $2^{3}$ | $25$ | $C_2$ | Nilpotent - 6 |
256.524 | $C_8^2:C_4$ | $2^{8}$ | $2^{3}$ | $25$ | $C_2$ | Nilpotent - 6 |
256.525 | $D_{32}:C_4$ | $2^{8}$ | $2^{6}$ | $70$ | $C_2^2$ | Nilpotent - 6 |
256.526 | $Q_{64}:C_4$ | $2^{8}$ | $2^{6}$ | $70$ | $C_2^2$ | Nilpotent - 6 |
256.527 | $C_4.D_{32}$ | $2^{8}$ | $2^{6}$ | $70$ | $C_4$ | Nilpotent - 6 |
256.528 | $D_{32}:C_4$ | $2^{8}$ | $2^{6}$ | $46$ | $C_2$ | Nilpotent - 6 |
256.529 | $\OD_{128}:C_2$ | $2^{8}$ | $2^{6}$ | $46$ | $C_2$ | Nilpotent - 6 |
256.530 | $C_4.D_{32}$ | $2^{8}$ | $2^{6}$ | $46$ | $C_2$ | Nilpotent - 6 |
256.533 | $C_{64}:C_4$ | $2^{8}$ | $2^{6}$ | $70$ | $C_2^2$ | Nilpotent - 6 |
256.534 | $C_{64}:C_4$ | $2^{8}$ | $2^{6}$ | $70$ | $C_2^2$ | Nilpotent - 6 |
256.535 | $C_{64}.C_4$ | $2^{8}$ | $2^{6}$ | $70$ | $C_4$ | Nilpotent - 6 |
256.536 | $C_{64}:C_4$ | $2^{8}$ | $2^{6}$ | $46$ | $C_2$ | Nilpotent - 6 |
256.6726 | $C_2\times D_{64}$ | $2^{8}$ | $2^{6}$ | $70$ | $C_2^2$ | Nilpotent - 6 |
256.6727 | $C_2\times \SD_{128}$ | $2^{8}$ | $2^{6}$ | $70$ | $C_2^2$ | Nilpotent - 6 |
256.6728 | $C_2\times Q_{128}$ | $2^{8}$ | $2^{6}$ | $70$ | $C_2^2$ | Nilpotent - 6 |
256.6729 | $D_{64}:C_2$ | $2^{8}$ | $2^{6}$ | $70$ | $C_4$ | Nilpotent - 6 |
256.6730 | $D_{64}:C_2$ | $2^{8}$ | $2^{6}$ | $46$ | $C_2$ | Nilpotent - 6 |
256.6731 | $Q_{128}:C_2$ | $2^{8}$ | $2^{6}$ | $46$ | $C_2$ | Nilpotent - 6 |
384.565 | $C_3\times D_{64}$ | $2^{7} \cdot 3$ | $2^{6} \cdot 3$ | $105$ | $C_6$ | Nilpotent - 6 |
384.566 | $C_3\times \SD_{128}$ | $2^{7} \cdot 3$ | $2^{6} \cdot 3$ | $105$ | $C_6$ | Nilpotent - 6 |
384.567 | $C_3\times Q_{128}$ | $2^{7} \cdot 3$ | $2^{6} \cdot 3$ | $105$ | $C_6$ | Nilpotent - 6 |
512.1710 | $C_2^6:C_8$ | $2^{9}$ | $2^{3}$ | $32$ | $C_2$ | Nilpotent - 6 |
512.1712 | $C_2^5.\OD_{16}$ | $2^{9}$ | $2^{3}$ | $32$ | $C_2$ | Nilpotent - 6 |
512.1714 | $C_2^6.C_8$ | $2^{9}$ | $2^{4}$ | $32$ | $C_2$ | Nilpotent - 6 |
512.1716 | $(C_2^2\times C_4^2).C_8$ | $2^{9}$ | $2^{4}$ | $32$ | $C_2$ | Nilpotent - 6 |
512.1718 | $C_2^3.C_2\wr C_4$ | $2^{9}$ | $2^{3}$ | $32$ | $C_2$ | Nilpotent - 6 |
512.1719 | $C_2^3.C_2\wr C_4$ | $2^{9}$ | $2^{3}$ | $32$ | $C_2$ | Nilpotent - 6 |