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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
96.49 | $C_2^3:C_{12}$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $33$ | $C_6$ | Nilpotent - 3 |
96.50 | $\OD_{16}:C_6$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $33$ | $C_6$ | Nilpotent - 3 |
96.51 | $C_{12}.D_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $33$ | $C_6$ | Nilpotent - 3 |
96.52 | $D_4:C_{12}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $42$ | $C_2\times C_6$ | Nilpotent - 3 |
96.53 | $Q_8:C_{12}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $42$ | $C_2\times C_6$ | Nilpotent - 3 |
96.54 | $D_4:C_{12}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $42$ | $C_{12}$ | Nilpotent - 3 |
96.56 | $C_8:C_{12}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $42$ | $C_2\times C_6$ | Nilpotent - 3 |
96.57 | $C_8:C_{12}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $42$ | $C_2\times C_6$ | Nilpotent - 3 |
96.58 | $C_8.C_{12}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $42$ | $C_{12}$ | Nilpotent - 3 |
96.179 | $C_6\times D_8$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $42$ | $C_2\times C_6$ | Nilpotent - 3 |
96.180 | $C_6\times \SD_{16}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $42$ | $C_2\times C_6$ | Nilpotent - 3 |
96.181 | $C_6\times Q_{16}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $42$ | $C_2\times C_6$ | Nilpotent - 3 |
96.182 | $D_8:C_6$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $42$ | $C_{12}$ | Nilpotent - 3 |
96.183 | $D_8:C_6$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $33$ | $C_6$ | Nilpotent - 3 |
96.184 | $Q_{16}:C_6$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $33$ | $C_6$ | Nilpotent - 3 |
160.49 | $C_2^3:C_{20}$ | $2^{5} \cdot 5$ | $2^{2} \cdot 5$ | $55$ | $C_{10}$ | Nilpotent - 3 |
160.50 | $\OD_{16}:C_{10}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $55$ | $C_{10}$ | Nilpotent - 3 |
160.51 | $C_{20}.D_4$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $55$ | $C_{10}$ | Nilpotent - 3 |
160.52 | $D_4:C_{20}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $70$ | $C_2\times C_{10}$ | Nilpotent - 3 |
160.53 | $Q_8:C_{20}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $70$ | $C_2\times C_{10}$ | Nilpotent - 3 |
160.54 | $D_4:C_{20}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $70$ | $C_{20}$ | Nilpotent - 3 |
160.56 | $C_8:C_{20}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $70$ | $C_2\times C_{10}$ | Nilpotent - 3 |
160.57 | $C_8:C_{20}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $70$ | $C_2\times C_{10}$ | Nilpotent - 3 |
160.58 | $C_8.C_{20}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $70$ | $C_{20}$ | Nilpotent - 3 |
160.193 | $C_{10}\times D_8$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $70$ | $C_2\times C_{10}$ | Nilpotent - 3 |
160.194 | $C_{10}\times \SD_{16}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $70$ | $C_2\times C_{10}$ | Nilpotent - 3 |
160.195 | $C_{10}\times Q_{16}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $70$ | $C_2\times C_{10}$ | Nilpotent - 3 |
160.196 | $D_8:C_{10}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $70$ | $C_{20}$ | Nilpotent - 3 |
160.197 | $D_8:C_{10}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $55$ | $C_{10}$ | Nilpotent - 3 |
160.198 | $Q_{16}:C_{10}$ | $2^{5} \cdot 5$ | $2^{3} \cdot 5$ | $55$ | $C_{10}$ | Nilpotent - 3 |
192.129 | $C_2^3:C_{24}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $66$ | $C_2\times C_6$ | Nilpotent - 3 |
192.130 | $(C_2\times C_4):C_{24}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $66$ | $C_2\times C_6$ | Nilpotent - 3 |
192.131 | $D_4:C_{24}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $84$ | $C_2\times C_{12}$ | Nilpotent - 3 |
192.132 | $Q_8:C_{24}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $84$ | $C_2\times C_{12}$ | Nilpotent - 3 |
192.133 | $(C_2\times D_4):C_{12}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $57$ | $C_2\times C_6$ | Nilpotent - 3 |
192.134 | $(C_2\times Q_8):C_{12}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $57$ | $C_2\times C_6$ | Nilpotent - 3 |
192.135 | $C_3\times C_4^2.C_2^2$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $57$ | $C_2\times C_6$ | Nilpotent - 3 |
192.136 | $C_3\times C_4^2.C_2^2$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $57$ | $C_2\times C_6$ | Nilpotent - 3 |
192.137 | $C_{12}.D_8$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $57$ | $C_2\times C_6$ | Nilpotent - 3 |
192.138 | $C_{12}.D_8$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $57$ | $C_2\times C_6$ | Nilpotent - 3 |
192.139 | $C_{12}.Q_{16}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $57$ | $C_2\times C_6$ | Nilpotent - 3 |
192.140 | $C_8:C_{24}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $84$ | $C_2\times C_{12}$ | Nilpotent - 3 |
192.141 | $C_8:C_{24}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $84$ | $C_2\times C_{12}$ | Nilpotent - 3 |
192.145 | $C_4^2:C_{12}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $84$ | $C_2\times C_{12}$ | Nilpotent - 3 |
192.146 | $C_{12}.C_4^2$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $84$ | $C_2^2\times C_6$ | Nilpotent - 3 |
192.147 | $C_{12}.C_4^2$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $84$ | $C_2\times C_{12}$ | Nilpotent - 3 |
192.148 | $(C_2^2\times C_{12}):C_4$ | $2^{6} \cdot 3$ | $2^{2} \cdot 3$ | $66$ | $C_2\times C_6$ | Nilpotent - 3 |
192.149 | $\OD_{16}:C_{12}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $66$ | $C_2\times C_6$ | Nilpotent - 3 |
192.150 | $\OD_{16}:C_{12}$ | $2^{6} \cdot 3$ | $2^{3} \cdot 3$ | $66$ | $C_{12}$ | Nilpotent - 3 |
192.155 | $\OD_{32}:C_6$ | $2^{6} \cdot 3$ | $2^{4} \cdot 3$ | $66$ | $C_{12}$ | Nilpotent - 3 |