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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
216.24 | $C_2^2\times C_{54}$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3^{3}$ | $216$ | $C_2^2\times C_{54}$ | Abelian - 3 |
216.85 | $C_3^2\times C_{24}$ | $2^{3} \cdot 3^{3}$ | $2^{3} \cdot 3$ | $216$ | $C_3^2\times C_{24}$ | Abelian - 3 |
216.114 | $C_2\times C_6\times C_{18}$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $216$ | $C_2\times C_6\times C_{18}$ | Abelian - 3 |
216.150 | $C_3\times C_6\times C_{12}$ | $2^{3} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $216$ | $C_3\times C_6\times C_{12}$ | Abelian - 3 |
216.177 | $C_6^3$ | $2^{3} \cdot 3^{3}$ | $2 \cdot 3$ | $216$ | $C_6^3$ | Abelian - 3 |
432.53 | $C_2^2\times C_{108}$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $432$ | $C_2^2\times C_{108}$ | Abelian - 3 |
432.228 | $C_2^3\times C_{54}$ | $2^{4} \cdot 3^{3}$ | $2 \cdot 3^{3}$ | $432$ | $C_2^3\times C_{54}$ | Abelian - 4 |
432.232 | $C_3^2\times C_{48}$ | $2^{4} \cdot 3^{3}$ | $2^{4} \cdot 3$ | $432$ | $C_3^2\times C_{48}$ | Abelian - 3 |
432.400 | $C_2\times C_6\times C_{36}$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $432$ | $C_2\times C_6\times C_{36}$ | Abelian - 3 |
432.512 | $C_3\times C_{12}^2$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $432$ | $C_3\times C_{12}^2$ | Abelian - 3 |
432.515 | $C_3\times C_6\times C_{24}$ | $2^{4} \cdot 3^{3}$ | $2^{3} \cdot 3$ | $432$ | $C_3\times C_6\times C_{24}$ | Abelian - 3 |
432.562 | $C_2^2\times C_6\times C_{18}$ | $2^{4} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $432$ | $C_2^2\times C_6\times C_{18}$ | Abelian - 4 |
432.730 | $C_6^2\times C_{12}$ | $2^{4} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $432$ | $C_6^2\times C_{12}$ | Abelian - 3 |
432.775 | $C_2\times C_6^3$ | $2^{4} \cdot 3^{3}$ | $2 \cdot 3$ | $432$ | $C_2\times C_6^3$ | Abelian - 4 |
648.44 | $C_2^2\times C_{162}$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{4}$ | $648$ | $C_2^2\times C_{162}$ | Abelian - 3 |
648.247 | $C_3^2\times C_{72}$ | $2^{3} \cdot 3^{4}$ | $2^{3} \cdot 3^{2}$ | $648$ | $C_3^2\times C_{72}$ | Abelian - 3 |
648.341 | $C_2\times C_{18}^2$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{2}$ | $648$ | $C_2\times C_{18}^2$ | Abelian - 3 |
648.344 | $C_2\times C_6\times C_{54}$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{3}$ | $648$ | $C_2\times C_6\times C_{54}$ | Abelian - 3 |
648.514 | $C_3\times C_6\times C_{36}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $648$ | $C_3\times C_6\times C_{36}$ | Abelian - 3 |
648.530 | $C_3^3\times C_{24}$ | $2^{3} \cdot 3^{4}$ | $2^{3} \cdot 3$ | $648$ | $C_3^3\times C_{24}$ | Abelian - 4 |
648.637 | $C_6^2\times C_{18}$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3^{2}$ | $648$ | $C_6^2\times C_{18}$ | Abelian - 3 |
648.699 | $C_3^2\times C_6\times C_{12}$ | $2^{3} \cdot 3^{4}$ | $2^{2} \cdot 3$ | $648$ | $C_3^2\times C_6\times C_{12}$ | Abelian - 4 |
648.757 | $C_3\times C_6^3$ | $2^{3} \cdot 3^{4}$ | $2 \cdot 3$ | $648$ | $C_3\times C_6^3$ | Abelian - 4 |
864.170 | $C_2\times C_4\times C_{108}$ | $2^{5} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $864$ | $C_2\times C_4\times C_{108}$ | Abelian - 3 |
864.185 | $C_2^2\times C_{216}$ | $2^{5} \cdot 3^{3}$ | $2^{3} \cdot 3^{3}$ | $864$ | $C_2^2\times C_{216}$ | Abelian - 3 |
864.646 | $C_2^3\times C_{108}$ | $2^{5} \cdot 3^{3}$ | $2^{2} \cdot 3^{3}$ | $864$ | $C_2^3\times C_{108}$ | Abelian - 4 |
864.655 | $C_3^2\times C_{96}$ | $2^{5} \cdot 3^{3}$ | $2^{5} \cdot 3$ | $864$ | $C_3^2\times C_{96}$ | Abelian - 3 |
864.1844 | $C_2\times C_{12}\times C_{36}$ | $2^{5} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $864$ | $C_2\times C_{12}\times C_{36}$ | Abelian - 3 |
864.1889 | $C_2\times C_6\times C_{72}$ | $2^{5} \cdot 3^{3}$ | $2^{3} \cdot 3^{2}$ | $864$ | $C_2\times C_6\times C_{72}$ | Abelian - 3 |
864.1921 | $C_2^4\times C_{54}$ | $2^{5} \cdot 3^{3}$ | $2 \cdot 3^{3}$ | $864$ | $C_2^4\times C_{54}$ | Abelian - 5 |
864.2176 | $C_3\times C_{12}\times C_{24}$ | $2^{5} \cdot 3^{3}$ | $2^{3} \cdot 3$ | $864$ | $C_3\times C_{12}\times C_{24}$ | Abelian - 3 |
864.2189 | $C_3\times C_6\times C_{48}$ | $2^{5} \cdot 3^{3}$ | $2^{4} \cdot 3$ | $864$ | $C_3\times C_6\times C_{48}$ | Abelian - 3 |
864.2648 | $C_2^2\times C_6\times C_{36}$ | $2^{5} \cdot 3^{3}$ | $2^{2} \cdot 3^{2}$ | $864$ | $C_2^2\times C_6\times C_{36}$ | Abelian - 4 |
864.3962 | $C_6\times C_{12}^2$ | $2^{5} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $864$ | $C_6\times C_{12}^2$ | Abelian - 3 |
864.3977 | $C_6^2\times C_{24}$ | $2^{5} \cdot 3^{3}$ | $2^{3} \cdot 3$ | $864$ | $C_6^2\times C_{24}$ | Abelian - 3 |
864.4050 | $C_2^3\times C_6\times C_{18}$ | $2^{5} \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $864$ | $C_2^3\times C_6\times C_{18}$ | Abelian - 5 |
864.4655 | $C_2\times C_6^2\times C_{12}$ | $2^{5} \cdot 3^{3}$ | $2^{2} \cdot 3$ | $864$ | $C_2\times C_6^2\times C_{12}$ | Abelian - 4 |
864.4725 | $C_2^2\times C_6^3$ | $2^{5} \cdot 3^{3}$ | $2 \cdot 3$ | $864$ | $C_2^2\times C_6^3$ | Abelian - 5 |
1000.14 | $C_2^2\times C_{250}$ | $2^{3} \cdot 5^{3}$ | $2 \cdot 5^{3}$ | $1000$ | $C_2^2\times C_{250}$ | Abelian - 3 |
1000.113 | $C_2\times C_{10}\times C_{50}$ | $2^{3} \cdot 5^{3}$ | $2 \cdot 5^{2}$ | $1000$ | $C_2\times C_{10}\times C_{50}$ | Abelian - 3 |
1000.119 | $C_5^2\times C_{40}$ | $2^{3} \cdot 5^{3}$ | $2^{3} \cdot 5$ | $1000$ | $C_5^2\times C_{40}$ | Abelian - 3 |
1000.159 | $C_5\times C_{10}\times C_{20}$ | $2^{3} \cdot 5^{3}$ | $2^{2} \cdot 5$ | $1000$ | $C_5\times C_{10}\times C_{20}$ | Abelian - 3 |
1000.199 | $C_{10}^3$ | $2^{3} \cdot 5^{3}$ | $2 \cdot 5$ | $1000$ | $C_{10}^3$ | Abelian - 3 |
1296.73 | $C_2^2\times C_{324}$ | $2^{4} \cdot 3^{4}$ | $2^{2} \cdot 3^{4}$ | $1296$ | $C_2^2\times C_{324}$ | Abelian - 3 |
1296.634 | $C_2^3\times C_{162}$ | $2^{4} \cdot 3^{4}$ | $2 \cdot 3^{4}$ | $1296$ | $C_2^3\times C_{162}$ | Abelian - 4 |
1296.650 | $C_3^2\times C_{144}$ | $2^{4} \cdot 3^{4}$ | $2^{4} \cdot 3^{2}$ | $1296$ | $C_3^2\times C_{144}$ | Abelian - 3 |
1296.1201 | $C_2\times C_{18}\times C_{36}$ | $2^{4} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $1296$ | $C_2\times C_{18}\times C_{36}$ | Abelian - 3 |
1296.1204 | $C_2\times C_6\times C_{108}$ | $2^{4} \cdot 3^{4}$ | $2^{2} \cdot 3^{3}$ | $1296$ | $C_2\times C_6\times C_{108}$ | Abelian - 3 |
1296.1747 | $C_3\times C_{12}\times C_{36}$ | $2^{4} \cdot 3^{4}$ | $2^{2} \cdot 3^{2}$ | $1296$ | $C_3\times C_{12}\times C_{36}$ | Abelian - 3 |
1296.1759 | $C_3\times C_6\times C_{72}$ | $2^{4} \cdot 3^{4}$ | $2^{3} \cdot 3^{2}$ | $1296$ | $C_3\times C_6\times C_{72}$ | Abelian - 3 |