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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
64.52 | $D_{32}$ | $2^{6}$ | $2^{5}$ | $19$ | $C_2$ | Nilpotent - 5 |
64.53 | $\SD_{64}$ | $2^{6}$ | $2^{5}$ | $19$ | $C_2$ | Nilpotent - 5 |
64.54 | $Q_{64}$ | $2^{6}$ | $2^{5}$ | $19$ | $C_2$ | Nilpotent - 5 |
128.134 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $17$ | $C_2$ | Nilpotent - 5 |
128.135 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $17$ | $C_2$ | Nilpotent - 5 |
128.136 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $17$ | $C_2$ | Nilpotent - 5 |
128.137 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $17$ | $C_2$ | Nilpotent - 5 |
128.138 | $C_4^2.(C_2\times C_4)$ | $2^{7}$ | $2^{3}$ | $14$ | $C_2$ | Nilpotent - 5 |
128.139 | $C_4^2.(C_2\times C_4)$ | $2^{7}$ | $2^{3}$ | $14$ | $C_2$ | Nilpotent - 5 |
128.140 | $(C_4\times C_8):C_4$ | $2^{7}$ | $2^{3}$ | $17$ | $C_2$ | Nilpotent - 5 |
128.141 | $(C_4\times C_8):C_4$ | $2^{7}$ | $2^{3}$ | $17$ | $C_2$ | Nilpotent - 5 |
128.142 | $(C_4\times C_8).C_4$ | $2^{7}$ | $2^{3}$ | $17$ | $C_2$ | Nilpotent - 5 |
128.143 | $(C_4\times C_8).C_4$ | $2^{7}$ | $2^{3}$ | $17$ | $C_2$ | Nilpotent - 5 |
128.144 | $C_4^2.(C_2\times C_4)$ | $2^{7}$ | $2^{3}$ | $14$ | $C_2$ | Nilpotent - 5 |
128.145 | $C_4^2.(C_2\times C_4)$ | $2^{7}$ | $2^{3}$ | $14$ | $C_2$ | Nilpotent - 5 |
128.146 | $(C_4\times C_8):C_4$ | $2^{7}$ | $2^{3}$ | $17$ | $C_2$ | Nilpotent - 5 |
128.147 | $D_{16}:C_4$ | $2^{7}$ | $2^{5}$ | $38$ | $C_2^2$ | Nilpotent - 5 |
128.148 | $Q_{32}:C_4$ | $2^{7}$ | $2^{5}$ | $38$ | $C_2^2$ | Nilpotent - 5 |
128.149 | $C_4.D_{16}$ | $2^{7}$ | $2^{5}$ | $38$ | $C_4$ | Nilpotent - 5 |
128.150 | $D_{16}:C_4$ | $2^{7}$ | $2^{5}$ | $26$ | $C_2$ | Nilpotent - 5 |
128.151 | $\OD_{64}:C_2$ | $2^{7}$ | $2^{5}$ | $26$ | $C_2$ | Nilpotent - 5 |
128.152 | $C_4.D_{16}$ | $2^{7}$ | $2^{5}$ | $26$ | $C_2$ | Nilpotent - 5 |
128.155 | $C_{32}:C_4$ | $2^{7}$ | $2^{5}$ | $38$ | $C_2^2$ | Nilpotent - 5 |
128.156 | $C_{32}:C_4$ | $2^{7}$ | $2^{5}$ | $38$ | $C_2^2$ | Nilpotent - 5 |
128.157 | $C_{32}.C_4$ | $2^{7}$ | $2^{5}$ | $38$ | $C_4$ | Nilpotent - 5 |
128.158 | $C_{32}:C_4$ | $2^{7}$ | $2^{5}$ | $26$ | $C_2$ | Nilpotent - 5 |
128.991 | $C_2\times D_{32}$ | $2^{7}$ | $2^{5}$ | $38$ | $C_2^2$ | Nilpotent - 5 |
128.992 | $C_2\times \SD_{64}$ | $2^{7}$ | $2^{5}$ | $38$ | $C_2^2$ | Nilpotent - 5 |
128.993 | $C_2\times Q_{64}$ | $2^{7}$ | $2^{5}$ | $38$ | $C_2^2$ | Nilpotent - 5 |
128.994 | $D_{32}:C_2$ | $2^{7}$ | $2^{5}$ | $38$ | $C_4$ | Nilpotent - 5 |
128.995 | $D_{32}:C_2$ | $2^{7}$ | $2^{5}$ | $26$ | $C_2$ | Nilpotent - 5 |
128.996 | $Q_{64}:C_2$ | $2^{7}$ | $2^{5}$ | $26$ | $C_2$ | Nilpotent - 5 |
192.177 | $C_3\times D_{32}$ | $2^{6} \cdot 3$ | $2^{5} \cdot 3$ | $57$ | $C_6$ | Nilpotent - 5 |
192.178 | $C_3\times \SD_{64}$ | $2^{6} \cdot 3$ | $2^{5} \cdot 3$ | $57$ | $C_6$ | Nilpotent - 5 |
192.179 | $C_3\times Q_{64}$ | $2^{6} \cdot 3$ | $2^{5} \cdot 3$ | $57$ | $C_6$ | Nilpotent - 5 |
256.326 | $C_2^5:C_8$ | $2^{8}$ | $2^{3}$ | $28$ | $C_2$ | Nilpotent - 5 |
256.327 | $(C_2^2\times D_4):C_8$ | $2^{8}$ | $2^{3}$ | $28$ | $C_2$ | Nilpotent - 5 |
256.328 | $C_2^5.C_8$ | $2^{8}$ | $2^{4}$ | $28$ | $C_2$ | Nilpotent - 5 |
256.329 | $C_2^4.(C_2\times C_8)$ | $2^{8}$ | $2^{4}$ | $28$ | $C_2$ | Nilpotent - 5 |
256.330 | $C_2^4.\OD_{16}$ | $2^{8}$ | $2^{4}$ | $28$ | $C_2$ | Nilpotent - 5 |
256.331 | $C_2^4.\OD_{16}$ | $2^{8}$ | $2^{4}$ | $28$ | $C_2$ | Nilpotent - 5 |
256.332 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $34$ | $C_2^2$ | Nilpotent - 5 |
256.333 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $34$ | $C_2^2$ | Nilpotent - 5 |
256.334 | $(C_2^2\times C_8).D_4$ | $2^{8}$ | $2^{4}$ | $34$ | $C_4$ | Nilpotent - 5 |
256.335 | $(C_2^2\times C_8).D_4$ | $2^{8}$ | $2^{4}$ | $34$ | $C_4$ | Nilpotent - 5 |
256.336 | $(C_2\times C_4^2):C_8$ | $2^{8}$ | $2^{3}$ | $28$ | $C_2$ | Nilpotent - 5 |
256.337 | $C_2^4.\OD_{16}$ | $2^{8}$ | $2^{3}$ | $28$ | $C_2$ | Nilpotent - 5 |
256.338 | $C_2^4.\OD_{16}$ | $2^{8}$ | $2^{4}$ | $28$ | $C_2$ | Nilpotent - 5 |
256.339 | $C_2^4.(C_2\times C_8)$ | $2^{8}$ | $2^{4}$ | $28$ | $C_2$ | Nilpotent - 5 |
256.340 | $C_4^2.\OD_{16}$ | $2^{8}$ | $2^{3}$ | $28$ | $C_2^2$ | Nilpotent - 5 |