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Results (1-50 of 18629 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
360.36 $C_3^2:C_{40}$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{3} \cdot 3 \cdot 5$ 120 $C_{20}$ $C_3:S_3$ $C_3^2$ $C_{40}$ Solvable - 2
360.37 $C_{12}.D_{15}$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{3} \cdot 3 \cdot 5$ 96 $C_4$ $C_3:D_{15}$ $C_3\times C_{15}$ $C_{8}$ Solvable - 2
360.45 $D_5\times D_{18}$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ 48 $C_2$ $D_5\times D_9$ $C_{45}$ $C_{2}^{3}$ Solvable - 2
360.47 $C_{18}\times D_{10}$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ 144 $C_2\times C_{18}$ $D_5$ $C_5$ $C_{2}^{2} \times C_{18}$ Solvable - 2
360.48 $C_{10}\times D_{18}$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ 120 $C_2\times C_{10}$ $D_9$ $C_9$ $C_{2}^{2} \times C_{10}$ Solvable - 2
360.49 $C_2\times D_{90}$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ 96 $C_2^2$ $D_{45}$ $C_{45}$ $C_{2}^{3}$ Solvable - 2
360.50 $C_2^2\times C_{90}$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ 360 $C_2^2\times C_{90}$ $C_1$ $C_1$ $C_{2}^{2} \times C_{90}$ Abelian - 3
360.54 $(C_3\times C_{15}):C_8$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{3} \cdot 3 \cdot 5$ 42 $C_2$ $C_3^2:F_5$ $C_3\times C_{15}$ $C_{8}$ Solvable - 2
360.65 $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 48 $C_2$ $C_{15}:D_6$ $C_3\times C_{15}$ $C_{2} \times C_{4}$ Solvable - 2
360.66 $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 48 $C_2$ $C_{15}:D_6$ $C_3\times C_{15}$ $C_{2} \times C_{4}$ Solvable - 2
360.67 $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 48 $C_2$ $C_{15}:D_6$ $C_3\times C_{15}$ $C_{2} \times C_{4}$ Solvable - 2
360.68 $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 45 $C_2$ $C_{15}:D_6$ $C_3\times C_{30}$ $C_{2}^{2}$ Solvable - 2
360.69 $C_3^2:D_{20}$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 45 $C_2$ $C_{15}:D_6$ $C_3\times C_{30}$ $C_{2}^{2}$ Solvable - 2
360.70 $C_{15}:D_{12}$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 45 $C_2$ $C_{15}:D_6$ $C_3\times C_{30}$ $C_{2}^{2}$ Solvable - 2
360.71 $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 45 $C_2$ $C_{15}:D_6$ $C_3\times C_{30}$ $C_{2}^{2}$ Solvable - 2
360.105 $C_{60}.S_3$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 105 $C_{10}$ $C_6:S_3$ $C_3\times C_6$ $C_{2} \times C_{10}$ Solvable - 2
360.106 $C_{60}:S_3$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 120 $C_{20}$ $C_3:S_3$ $C_3^2$ $C_{2} \times C_{20}$ Solvable - 2
360.107 $C_{15}:D_{12}$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 105 $C_{10}$ $C_6:S_3$ $C_3\times C_6$ $C_{2} \times C_{10}$ Solvable - 2
360.108 $C_{30}.D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 120 $C_2\times C_{10}$ $C_3:S_3$ $C_3^2$ $C_{2} \times C_{20}$ Solvable - 2
360.109 $C_6^2:C_{10}$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 105 $C_{10}$ $C_6:S_3$ $C_3\times C_6$ $C_{2} \times C_{10}$ Solvable - 2
360.110 $C_6.D_{30}$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 93 $C_2$ $C_3:D_{30}$ $C_3\times C_{30}$ $C_{2}^{2}$ Solvable - 2
360.111 $C_{12}:D_{15}$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 96 $C_4$ $C_3:D_{15}$ $C_3\times C_{15}$ $C_{2} \times C_{4}$ Solvable - 2
360.112 $C_3:D_{60}$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 93 $C_2$ $C_3:D_{30}$ $C_3\times C_{30}$ $C_{2}^{2}$ Solvable - 2
360.113 $C_6.D_{30}$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 96 $C_2^2$ $C_3:D_{15}$ $C_3\times C_{15}$ $C_{2} \times C_{4}$ Solvable - 2
360.114 $C_6^2:D_5$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 93 $C_2$ $C_3:D_{30}$ $C_3\times C_{30}$ $C_{2}^{2}$ Solvable - 2
360.127 $C_3:S_3\times F_5$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 30 $C_1$ $C_3:S_3\times F_5$ $C_3\times C_{15}$ $C_{2} \times C_{4}$ Solvable - 2
360.137 $D_5\times S_3^2$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 36 $C_1$ $D_5\times S_3^2$ $C_3\times C_{15}$ $C_{2}^{3}$ Solvable - 2
360.140 $C_{15}:S_4$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 45 $C_5$ $C_3:S_4$ $C_3\times A_4$ $C_{10}$ Solvable - 3
360.141 $C_{15}:S_4$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 33 $C_1$ $C_{15}:S_4$ $A_4\times C_{15}$ $C_{2}$ Solvable - 3
360.147 $C_2\times C_3^2:F_5$ $2^{3} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 42 $C_2$ $C_3^2:F_5$ $C_3\times C_{15}$ $C_{2} \times C_{4}$ Solvable - 2
360.151 $C_{30}:D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 72 $C_6$ $S_3\times D_5$ $C_{15}$ $C_{2}^{2} \times C_{6}$ Solvable - 2
360.152 $C_{30}:D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 48 $C_2$ $C_{15}:D_6$ $C_3\times C_{15}$ $C_{2}^{3}$ Solvable - 2
360.153 $C_{10}\times S_3^2$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 90 $C_{10}$ $S_3^2$ $C_3^2$ $C_{2}^{2} \times C_{10}$ Solvable - 2
360.154 $S_3\times D_{30}$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 54 $C_2$ $S_3\times D_{15}$ $C_3\times C_{15}$ $C_{2}^{3}$ Solvable - 2
360.155 $C_{30}:D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 42 $C_2$ $C_{15}:D_6$ $C_3\times C_{15}$ $C_{2}^{3}$ Solvable - 2
360.157 $D_5\times C_6^2$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 144 $C_6^2$ $D_5$ $C_5$ $C_{2} \times C_{6}^{2}$ Solvable - 2
360.158 $D_6\times C_{30}$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 180 $C_2\times C_{30}$ $S_3$ $C_3$ $C_{2}^{2} \times C_{30}$ Solvable - 2
360.159 $C_6\times D_{30}$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 108 $C_2\times C_6$ $D_{15}$ $C_{15}$ $C_{2}^{2} \times C_{6}$ Solvable - 2
360.160 $C_{30}:D_6$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 120 $C_2\times C_{10}$ $C_3:S_3$ $C_3^2$ $C_{2}^{2} \times C_{10}$ Solvable - 2
360.161 $C_6:D_{30}$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 96 $C_2^2$ $C_3:D_{15}$ $C_3\times C_{15}$ $C_{2}^{3}$ Solvable - 2
360.162 $C_2\times C_6\times C_{30}$ $2^{3} \cdot 3^{2} \cdot 5$ $2 \cdot 3 \cdot 5$ 360 $C_2\times C_6\times C_{30}$ $C_1$ $C_1$ $C_{2} \times C_{6} \times C_{30}$ Abelian - 3
504.49 $C_3^2:C_{56}$ $2^{3} \cdot 3^{2} \cdot 7$ $2^{3} \cdot 3 \cdot 7$ 168 $C_{28}$ $C_3:S_3$ $C_3^2$ $C_{56}$ Solvable - 2
504.50 $C_{12}.D_{21}$ $2^{3} \cdot 3^{2} \cdot 7$ $2^{3} \cdot 3 \cdot 7$ 132 $C_4$ $C_3:D_{21}$ $C_3\times C_{21}$ $C_{8}$ Solvable - 2
504.56 $D_{14}:C_{18}$ $2^{3} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 84 $C_2\times C_6$ $F_7$ $C_7$ $C_{2}^{2} \times C_{18}$ Solvable - 2
504.59 $D_7\times D_{18}$ $2^{3} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 60 $C_2$ $D_7\times D_9$ $C_{63}$ $C_{2}^{3}$ Solvable - 2
504.60 $C_2\times C_{14}:C_{18}$ $2^{3} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 120 $C_2^2\times C_6$ $C_7:C_3$ $C_7$ $C_{2}^{2} \times C_{18}$ Solvable - 2
504.63 $C_{18}\times D_{14}$ $2^{3} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 180 $C_2\times C_{18}$ $D_7$ $C_7$ $C_{2}^{2} \times C_{18}$ Solvable - 2
504.64 $C_{14}\times D_{18}$ $2^{3} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 168 $C_2\times C_{14}$ $D_9$ $C_9$ $C_{2}^{2} \times C_{14}$ Solvable - 2
504.65 $C_2\times D_{126}$ $2^{3} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 132 $C_2^2$ $D_{63}$ $C_{63}$ $C_{2}^{3}$ Solvable - 2
504.66 $C_2^2\times C_{126}$ $2^{3} \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 504 $C_2^2\times C_{126}$ $C_1$ $C_1$ $C_{2}^{2} \times C_{126}$ Abelian - 3
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