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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
216.10 | $D_4\times C_{27}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $135$ | $C_{54}$ | Nilpotent - 2 |
216.11 | $Q_8\times C_{27}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $135$ | $C_{54}$ | Nilpotent - 2 |
216.20 | $C_9:C_{24}$ | $2^{3} \cdot 3^{3}$ | $2^{3} \cdot 3^{2}$ | $88$ | $C_{24}$ | Nilpotent - 2 |
216.75 | $C_{18}:C_{12}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $88$ | $C_2\times C_{12}$ | Nilpotent - 2 |
216.76 | $C_{12}:C_{18}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $135$ | $C_3\times C_{18}$ | Nilpotent - 2 |
216.78 | $C_{36}:C_6$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $55$ | $C_6$ | Nilpotent - 2 |
216.79 | $C_{12}.C_{18}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $135$ | $C_3\times C_{18}$ | Nilpotent - 2 |
216.81 | $C_{36}.C_6$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $55$ | $C_6$ | Nilpotent - 2 |
432.22 | $C_4:C_{108}$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $270$ | $C_2\times C_{54}$ | Nilpotent - 2 |
432.24 | $\OD_{16}\times C_{27}$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $270$ | $C_{108}$ | Nilpotent - 2 |
432.25 | $D_8\times C_{27}$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $189$ | $C_{54}$ | Nilpotent - 3 |
432.26 | $\SD_{16}\times C_{27}$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $189$ | $C_{54}$ | Nilpotent - 3 |
432.27 | $Q_{16}\times C_{27}$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $189$ | $C_{54}$ | Nilpotent - 3 |
432.36 | $C_9:C_{48}$ | $2^{4} \cdot 3^{3}$ | $2^{4} \cdot 3^{2}$ | $176$ | $C_{48}$ | Nilpotent - 2 |
432.202 | $C_{36}:C_{12}$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $176$ | $C_4\times C_{12}$ | Nilpotent - 2 |
432.206 | $C_{12}:C_{36}$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $270$ | $C_6\times C_{18}$ | Nilpotent - 2 |
432.208 | $C_{36}:C_{12}$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $110$ | $C_2\times C_6$ | Nilpotent - 2 |
432.211 | $C_{18}:C_{24}$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{2}$ | $176$ | $C_2\times C_{24}$ | Nilpotent - 2 |
432.212 | $C_{24}:C_{18}$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{2}$ | $270$ | $C_3\times C_{36}$ | Nilpotent - 2 |
432.214 | $C_{72}:C_6$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{2}$ | $110$ | $C_{12}$ | Nilpotent - 2 |
432.215 | $C_{24}:C_{18}$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{2}$ | $189$ | $C_3\times C_{18}$ | Nilpotent - 3 |
432.217 | $C_{72}:C_6$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{2}$ | $77$ | $C_6$ | Nilpotent - 3 |
432.218 | $C_{24}:C_{18}$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{2}$ | $189$ | $C_3\times C_{18}$ | Nilpotent - 3 |
432.220 | $C_{72}:C_6$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{2}$ | $77$ | $C_6$ | Nilpotent - 3 |
432.221 | $C_{24}.C_{18}$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{2}$ | $189$ | $C_3\times C_{18}$ | Nilpotent - 3 |
432.223 | $C_{72}.C_6$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3^{2}$ | $77$ | $C_6$ | Nilpotent - 3 |
648.10 | $D_4\times C_{81}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{4}$ | $405$ | $C_{162}$ | Nilpotent - 2 |
648.11 | $Q_8\times C_{81}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{4}$ | $405$ | $C_{162}$ | Nilpotent - 2 |
648.34 | $C_9:C_{72}$ | $2^{3} \cdot 3^{4}$ | $2^{3} \cdot 3^{2}$ | $264$ | $C_3\times C_{24}$ | Nilpotent - 2 |
648.36 | $C_{216}:C_3$ | $2^{3} \cdot 3^{4}$ | $2^{3} \cdot 3^{3}$ | $264$ | $C_{72}$ | Nilpotent - 2 |
648.207 | $C_{18}:C_{36}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $264$ | $C_6\times C_{12}$ | Nilpotent - 2 |
648.209 | $C_{108}:C_6$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{3}$ | $264$ | $C_2\times C_{36}$ | Nilpotent - 2 |
648.214 | $D_4\times C_9^2$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $405$ | $C_9\times C_{18}$ | Nilpotent - 2 |
648.216 | $C_{36}:C_{18}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $165$ | $C_3\times C_6$ | Nilpotent - 2 |
648.217 | $C_{12}:C_{54}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{3}$ | $405$ | $C_3\times C_{54}$ | Nilpotent - 2 |
648.218 | $C_{108}:C_6$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{3}$ | $165$ | $C_{18}$ | Nilpotent - 2 |
648.223 | $Q_8\times C_9^2$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $405$ | $C_9\times C_{18}$ | Nilpotent - 2 |
648.225 | $C_{36}.C_{18}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $165$ | $C_3\times C_6$ | Nilpotent - 2 |
648.226 | $C_{12}.C_{54}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{3}$ | $405$ | $C_3\times C_{54}$ | Nilpotent - 2 |
648.227 | $C_{108}.C_6$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{3}$ | $165$ | $C_{18}$ | Nilpotent - 2 |
864.47 | $C_8:C_{108}$ | $2^{5} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $540$ | $C_2\times C_{108}$ | Nilpotent - 2 |
864.55 | $C_4:C_{216}$ | $2^{5} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $540$ | $C_2\times C_{108}$ | Nilpotent - 2 |
864.56 | $C_8:C_{108}$ | $2^{5} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $378$ | $C_2\times C_{54}$ | Nilpotent - 3 |
864.57 | $C_8:C_{108}$ | $2^{5} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $378$ | $C_2\times C_{54}$ | Nilpotent - 3 |
864.58 | $C_8.C_{108}$ | $2^{5} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $378$ | $C_{108}$ | Nilpotent - 3 |
864.60 | $C_{27}\times \OD_{32}$ | $2^{5} \cdot 3^{3}$ | $2^{4} \cdot 3^{3}$ | $540$ | $C_{216}$ | Nilpotent - 2 |
864.61 | $C_{27}\times D_{16}$ | $2^{5} \cdot 3^{3}$ | $2^{4} \cdot 3^{3}$ | $297$ | $C_{54}$ | Nilpotent - 4 |
864.62 | $C_{27}\times \SD_{32}$ | $2^{5} \cdot 3^{3}$ | $2^{4} \cdot 3^{3}$ | $297$ | $C_{54}$ | Nilpotent - 4 |
864.63 | $C_{27}\times Q_{32}$ | $2^{5} \cdot 3^{3}$ | $2^{4} \cdot 3^{3}$ | $297$ | $C_{54}$ | Nilpotent - 4 |
864.72 | $C_9:C_{96}$ | $2^{5} \cdot 3^{3}$ | $2^{5} \cdot 3^{2}$ | $352$ | $C_{96}$ | Nilpotent - 2 |