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Results (1-50 of at least 1000)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
24.12 $S_4$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ 5 $C_1$ $S_4$ $A_4$ $C_{2}$ Solvable - 3
48.30 $A_4:C_4$ $2^{4} \cdot 3$ $2^{2} \cdot 3$ 10 $C_2$ $S_4$ $A_4$ $C_{4}$ Solvable - 3
48.48 $C_2\times S_4$ $2^{4} \cdot 3$ $2^{2} \cdot 3$ 10 $C_2$ $S_4$ $A_4$ $C_{2}^{2}$ Solvable - 3
72.15 $C_2^2:D_9$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 9 $C_1$ $C_2^2:D_9$ $C_2^2:C_9$ $C_{2}$ Solvable - 3
72.40 $\SOPlus(4,2)$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 9 $C_1$ $\SOPlus(4,2)$ $C_3:S_3$ $C_{2}^{2}$ Solvable - 3
72.41 $\PSU(3,2)$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 6 $C_1$ $\PSU(3,2)$ $C_3:S_3$ $C_{2}^{2}$ Solvable - 3
72.42 $C_3\times S_4$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 15 $C_3$ $S_4$ $A_4$ $C_{6}$ Solvable - 3
72.43 $C_3:S_4$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 9 $C_1$ $C_3:S_4$ $C_3\times A_4$ $C_{2}$ Solvable - 3
96.64 $C_4^2:S_3$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ 10 $C_1$ $C_4^2:S_3$ $C_4^2:C_3$ $C_{2}$ Solvable - 3
96.65 $A_4:C_8$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ 20 $C_4$ $S_4$ $A_4$ $C_{8}$ Solvable - 3
96.185 $A_4:Q_8$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 14 $C_2$ $C_2\times S_4$ $C_2\times A_4$ $C_{2}^{2}$ Solvable - 3
96.186 $C_4\times S_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 20 $C_4$ $S_4$ $A_4$ $C_{2} \times C_{4}$ Solvable - 3
96.187 $C_4:S_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 14 $C_2$ $C_2\times S_4$ $C_2\times A_4$ $C_{2}^{2}$ Solvable - 3
96.194 $C_2^2.S_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 20 $C_2^2$ $S_4$ $A_4$ $C_{2} \times C_{4}$ Solvable - 3
96.195 $\GL(2,\mathbb{Z}/4)$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 14 $C_2$ $C_2\times S_4$ $C_2\times A_4$ $C_{2}^{2}$ Solvable - 3
96.204 $Q_8:A_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 11 $C_2$ $C_2^2:A_4$ $D_4:C_2^2$ $C_{3}$ Solvable - 3
96.226 $C_2^2\times S_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 20 $C_2^2$ $S_4$ $A_4$ $C_{2}^{3}$ Solvable - 3
96.227 $C_2^2:S_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 10 $C_1$ $C_2^2:S_4$ $C_2^2:A_4$ $C_{2}$ Solvable - 3
120.37 $C_5\times S_4$ $2^{3} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 25 $C_5$ $S_4$ $A_4$ $C_{10}$ Solvable - 3
120.38 $C_5:S_4$ $2^{3} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 13 $C_1$ $C_5:S_4$ $C_5\times A_4$ $C_{2}$ Solvable - 3
144.33 $C_6.S_4$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 18 $C_2$ $C_2^2:D_9$ $C_2^2:C_9$ $C_{4}$ Solvable - 3
144.109 $C_2^2:D_{18}$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 18 $C_2$ $C_2^2:D_9$ $C_2^2:C_9$ $C_{2}^{2}$ Solvable - 3
144.115 $S_3^2:C_4$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3$ 18 $C_2$ $\SOPlus(4,2)$ $C_3:S_3$ $C_{2} \times C_{4}$ Solvable - 3
144.116 $C_2.\SOPlus(4,2)$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3$ 18 $C_2$ $\SOPlus(4,2)$ $C_3:S_3$ $C_{2} \times C_{4}$ Solvable - 3
144.117 $C_3^2:D_8$ $2^{4} \cdot 3^{2}$ $2^{3} \cdot 3$ 15 $C_2$ $\SOPlus(4,2)$ $C_3^2:C_4$ $C_{2}^{2}$ Solvable - 3
144.118 $C_3^2:\SD_{16}$ $2^{4} \cdot 3^{2}$ $2^{3} \cdot 3$ 15 $C_2$ $\SOPlus(4,2)$ $C_3^2:C_4$ $C_{2}^{2}$ Solvable - 3
144.119 $C_3^2:Q_{16}$ $2^{4} \cdot 3^{2}$ $2^{3} \cdot 3$ 15 $C_2$ $\SOPlus(4,2)$ $C_3^2:C_4$ $C_{2}^{2}$ Solvable - 3
144.120 $C_2.\PSU(3,2)$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3$ 12 $C_2$ $\PSU(3,2)$ $C_3:S_3$ $C_{2} \times C_{4}$ Solvable - 3
144.123 $A_4:C_{12}$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3$ 30 $C_6$ $S_4$ $A_4$ $C_{12}$ Solvable - 3
144.126 $C_6.S_4$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3$ 18 $C_2$ $C_3:S_4$ $C_3\times A_4$ $C_{4}$ Solvable - 3
144.182 $F_9:C_2$ $2^{4} \cdot 3^{2}$ $2^{3} \cdot 3$ 9 $C_1$ $F_9:C_2$ $C_3^2:C_4$ $C_{2}^{2}$ Solvable - 3
144.183 $S_3\times S_4$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3$ 15 $C_1$ $S_3\times S_4$ $C_3\times A_4$ $C_{2}^{2}$ Solvable - 3
144.186 $S_3^2:C_2^2$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3$ 18 $C_2$ $\SOPlus(4,2)$ $C_3:S_3$ $C_{2}^{3}$ Solvable - 3
144.187 $C_2\times \PSU(3,2)$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3$ 12 $C_2$ $\PSU(3,2)$ $C_3:S_3$ $C_{2}^{3}$ Solvable - 3
144.188 $C_6\times S_4$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3$ 30 $C_6$ $S_4$ $A_4$ $C_{2} \times C_{6}$ Solvable - 3
144.189 $C_6:S_4$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3$ 18 $C_2$ $C_3:S_4$ $C_3\times A_4$ $C_{2}^{2}$ Solvable - 3
150.5 $C_5^2:S_3$ $2 \cdot 3 \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ 13 $C_1$ $C_5^2:S_3$ $C_5^2:C_3$ $C_{2}$ Solvable - 3
160.234 $C_2^4:D_5$ $2^{5} \cdot 5$ $2^{2} \cdot 5$ 10 $C_1$ $C_2^4:D_5$ $C_2^4:C_5$ $C_{2}$ Solvable - 3
168.43 $F_8:C_3$ $2^{3} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ 8 $C_1$ $F_8:C_3$ $F_8$ $C_{3}$ Solvable - 3
168.45 $C_7\times S_4$ $2^{3} \cdot 3 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ 35 $C_7$ $S_4$ $A_4$ $C_{14}$ Solvable - 3
168.46 $C_7:S_4$ $2^{3} \cdot 3 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ 17 $C_1$ $C_7:S_4$ $C_7\times A_4$ $C_{2}$ Solvable - 3
192.182 $C_2^3.S_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ 20 $C_2$ $C_4^2:S_3$ $C_4^2:C_3$ $C_{4}$ Solvable - 3
192.184 $C_2^3.S_4$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ 11 $C_1$ $C_2^3.S_4$ $C_2^2:A_4$ $C_{4}$ Solvable - 3
192.185 $C_2^3.S_4$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ 11 $C_1$ $C_2^3.S_4$ $C_4^2:C_3$ $C_{4}$ Solvable - 3
192.186 $A_4:C_{16}$ $2^{6} \cdot 3$ $2^{4} \cdot 3$ 40 $C_8$ $S_4$ $A_4$ $C_{16}$ Solvable - 3
192.201 $C_2\wr A_4$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ 16 $C_2$ $C_2^3:A_4$ $D_4:C_2^2$ $C_{6}$ Solvable - 3
192.202 $(C_2^2\times C_4):A_4$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ 16 $C_2$ $C_2^3:A_4$ $D_4:C_2^2$ $C_{6}$ Solvable - 3
192.944 $C_4^2:D_6$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ 20 $C_2$ $C_4^2:S_3$ $C_4^2:C_3$ $C_{2}^{2}$ Solvable - 3
192.955 $C_2^3:S_4$ $2^{6} \cdot 3$ $2^{2} \cdot 3$ 14 $C_1$ $C_2^3:S_4$ $C_2^2:A_4$ $C_{2}^{2}$ Solvable - 3
192.956 $C_4^2:D_6$ $2^{6} \cdot 3$ $2^{3} \cdot 3$ 14 $C_1$ $C_4^2:D_6$ $C_4^2:C_3$ $C_{2}^{2}$ Solvable - 3
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