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Results (1-50 of 2309 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
540.85 $C_3^3:C_{20}$ $2^{2} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 150 $C_{10}$ $C_3^2:S_3$ $C_3^3$ $C_{20}$ Solvable - 2
540.86 $(C_3^2\times C_{15}):C_4$ $2^{2} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 138 $C_2$ $C_3^2:D_{15}$ $C_3^2\times C_{15}$ $C_{4}$ Solvable - 2
540.92 $C_3^3:F_5$ $2^{2} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 57 $C_1$ $C_3^3:F_5$ $C_3^2\times C_{15}$ $C_{4}$ Solvable - 2
540.104 $C_3^3:D_{10}$ $2^{2} \cdot 3^{3} \cdot 5$ $2 \cdot 3 \cdot 5$ 60 $C_1$ $C_3^3:D_{10}$ $C_3^2\times C_{15}$ $C_{2}^{2}$ Solvable - 2
540.117 $C_3^2:S_3\times C_{10}$ $2^{2} \cdot 3^{3} \cdot 5$ $2 \cdot 3 \cdot 5$ 150 $C_{10}$ $C_3^2:S_3$ $C_3^3$ $C_{2} \times C_{10}$ Solvable - 2
540.118 $C_3^2:D_{30}$ $2^{2} \cdot 3^{3} \cdot 5$ $2 \cdot 3 \cdot 5$ 138 $C_2$ $C_3^2:D_{15}$ $C_3^2\times C_{15}$ $C_{2}^{2}$ Solvable - 2
720.402 $D_{10}\times D_{18}$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ 96 $C_2^2$ $D_5\times D_9$ $C_{45}$ $C_{2}^{4}$ Solvable - 2
720.405 $C_{90}:C_2^3$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ 288 $C_2^2\times C_{18}$ $D_5$ $C_5$ $C_{2}^{3} \times C_{18}$ Solvable - 2
720.406 $C_{90}:C_2^3$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ 240 $C_2^2\times C_{10}$ $D_9$ $C_9$ $C_{2}^{3} \times C_{10}$ Solvable - 2
720.407 $C_2^2\times D_{90}$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ 192 $C_2^3$ $D_{45}$ $C_{45}$ $C_{2}^{4}$ Solvable - 2
720.408 $C_2^3\times C_{90}$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ 720 $C_2^3\times C_{90}$ $C_1$ $C_1$ $C_{2}^{3} \times C_{90}$ Abelian - 4
720.813 $D_{10}\times S_3^2$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 72 $C_2$ $D_5\times S_3^2$ $C_3\times C_{15}$ $C_{2}^{4}$ Solvable - 2
720.828 $C_6^2:D_{10}$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 144 $C_2\times C_6$ $S_3\times D_5$ $C_{15}$ $C_{2}^{3} \times C_{6}$ Solvable - 2
720.829 $C_6^2:D_{10}$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 96 $C_2^2$ $C_{15}:D_6$ $C_3\times C_{15}$ $C_{2}^{4}$ Solvable - 2
720.830 $C_5\times D_6^2$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 180 $C_2\times C_{10}$ $S_3^2$ $C_3^2$ $C_{2}^{3} \times C_{10}$ Solvable - 2
720.831 $D_6\times D_{30}$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 108 $C_2^2$ $S_3\times D_{15}$ $C_3\times C_{15}$ $C_{2}^{4}$ Solvable - 2
720.832 $C_5:D_6^2$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 84 $C_2^2$ $C_{15}:D_6$ $C_3\times C_{15}$ $C_{2}^{4}$ Solvable - 2
720.835 $D_{10}\times C_6^2$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 288 $C_2\times C_6^2$ $D_5$ $C_5$ $C_{2}^{2} \times C_{6}^{2}$ Solvable - 2
720.836 $C_2\times D_6\times C_{30}$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 360 $C_2^2\times C_{30}$ $S_3$ $C_3$ $C_{2}^{3} \times C_{30}$ Solvable - 2
720.837 $C_6^2:D_{10}$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 216 $C_2^2\times C_6$ $D_{15}$ $C_{15}$ $C_{2}^{3} \times C_{6}$ Solvable - 2
720.838 $C_2\times C_{30}:D_6$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 240 $C_2^2\times C_{10}$ $C_3:S_3$ $C_3^2$ $C_{2}^{3} \times C_{10}$ Solvable - 2
720.839 $C_6^2:D_{10}$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 192 $C_2^3$ $C_3:D_{15}$ $C_3\times C_{15}$ $C_{2}^{4}$ Solvable - 2
720.840 $C_2^2\times C_6\times C_{30}$ $2^{4} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 720 $C_2^2\times C_6\times C_{30}$ $C_1$ $C_1$ $C_{2}^{2} \times C_{6} \times C_{30}$ Abelian - 4
756.147 $C_3^3:C_{28}$ $2^{2} \cdot 3^{3} \cdot 7$ $2^{2} \cdot 3 \cdot 7$ 210 $C_{14}$ $C_3^2:S_3$ $C_3^3$ $C_{28}$ Solvable - 2
756.148 $(C_3^2\times C_{21}):C_4$ $2^{2} \cdot 3^{3} \cdot 7$ $2^{2} \cdot 3 \cdot 7$ 192 $C_2$ $C_3^2:D_{21}$ $C_3^2\times C_{21}$ $C_{4}$ Solvable - 2
756.172 $C_3^3:D_{14}$ $2^{2} \cdot 3^{3} \cdot 7$ $2 \cdot 3 \cdot 7$ 75 $C_1$ $C_3^3:D_{14}$ $C_3^2\times C_{21}$ $C_{2}^{2}$ Solvable - 2
756.187 $C_3^2:S_3\times C_{14}$ $2^{2} \cdot 3^{3} \cdot 7$ $2 \cdot 3 \cdot 7$ 210 $C_{14}$ $C_3^2:S_3$ $C_3^3$ $C_{2} \times C_{14}$ Solvable - 2
756.188 $C_3^2:D_{42}$ $2^{2} \cdot 3^{3} \cdot 7$ $2 \cdot 3 \cdot 7$ 192 $C_2$ $C_3^2:D_{21}$ $C_3^2\times C_{21}$ $C_{2}^{2}$ Solvable - 2
1008.504 $C_2\times D_{14}:C_{18}$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 168 $C_2^2\times C_6$ $F_7$ $C_7$ $C_{2}^{3} \times C_{18}$ Solvable - 2
1008.507 $D_{14}\times D_{18}$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 120 $C_2^2$ $D_7\times D_9$ $C_{63}$ $C_{2}^{4}$ Solvable - 2
1008.508 $C_2^2\times C_{14}:C_{18}$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 240 $C_2^3\times C_6$ $C_7:C_3$ $C_7$ $C_{2}^{3} \times C_{18}$ Solvable - 2
1008.513 $C_{126}:C_2^3$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 360 $C_2^2\times C_{18}$ $D_7$ $C_7$ $C_{2}^{3} \times C_{18}$ Solvable - 2
1008.514 $C_{126}:C_2^3$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 336 $C_2^2\times C_{14}$ $D_9$ $C_9$ $C_{2}^{3} \times C_{14}$ Solvable - 2
1008.515 $C_2^2\times D_{126}$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 264 $C_2^3$ $D_{63}$ $C_{63}$ $C_{2}^{4}$ Solvable - 2
1008.516 $C_2^3\times C_{126}$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 1008 $C_2^3\times C_{126}$ $C_1$ $C_1$ $C_{2}^{3} \times C_{126}$ Abelian - 4
1008.906 $C_2\times D_6\times F_7$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 84 $C_2^2$ $S_3\times F_7$ $C_{21}$ $C_{2}^{3} \times C_{6}$ Solvable - 2
1008.922 $D_{14}\times S_3^2$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 90 $C_2$ $D_7\times S_3^2$ $C_3\times C_{21}$ $C_{2}^{4}$ Solvable - 2
1008.928 $D_{14}:C_6^2$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 168 $C_2^2\times C_6$ $F_7$ $C_7$ $C_{2}^{2} \times C_{6}^{2}$ Solvable - 2
1008.929 $C_{14}:C_6\times D_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 120 $C_2^3$ $C_{21}:C_6$ $C_{21}$ $C_{2}^{3} \times C_{6}$ Solvable - 2
1008.930 $C_2\times D_{42}:C_6$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 96 $C_2^3$ $C_{21}:C_6$ $C_{21}$ $C_{2}^{3} \times C_{6}$ Solvable - 2
1008.939 $C_6^2:D_{14}$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 180 $C_2\times C_6$ $S_3\times D_7$ $C_{21}$ $C_{2}^{3} \times C_{6}$ Solvable - 2
1008.940 $C_6^2:D_{14}$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 120 $C_2^2$ $C_{21}:D_6$ $C_3\times C_{21}$ $C_{2}^{4}$ Solvable - 2
1008.941 $C_7\times D_6^2$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 252 $C_2\times C_{14}$ $S_3^2$ $C_3^2$ $C_{2}^{3} \times C_{14}$ Solvable - 2
1008.942 $D_6\times D_{42}$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 144 $C_2^2$ $S_3\times D_{21}$ $C_3\times C_{21}$ $C_{2}^{4}$ Solvable - 2
1008.943 $C_7:D_6^2$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 108 $C_2^2$ $C_{21}:D_6$ $C_3\times C_{21}$ $C_{2}^{4}$ Solvable - 2
1008.944 $C_2\times C_{14}:C_6^2$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 240 $C_2^3\times C_6$ $C_7:C_3$ $C_7$ $C_{2}^{2} \times C_{6}^{2}$ Solvable - 2
1008.949 $D_{14}\times C_6^2$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 360 $C_2\times C_6^2$ $D_7$ $C_7$ $C_{2}^{2} \times C_{6}^{2}$ Solvable - 2
1008.950 $C_2\times D_6\times C_{42}$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 504 $C_2^2\times C_{42}$ $S_3$ $C_3$ $C_{2}^{3} \times C_{42}$ Solvable - 2
1008.951 $C_6^2:D_{14}$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 288 $C_2^2\times C_6$ $D_{21}$ $C_{21}$ $C_{2}^{3} \times C_{6}$ Solvable - 2
1008.952 $C_6:D_6\times C_{14}$ $2^{4} \cdot 3^{2} \cdot 7$ $2 \cdot 3 \cdot 7$ 336 $C_2^2\times C_{14}$ $C_3:S_3$ $C_3^2$ $C_{2}^{3} \times C_{14}$ Solvable - 2
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