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Results (1-50 of 9328 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
12.3 $A_4$ $2^{2} \cdot 3$ $2 \cdot 3$ 4 $C_1$ $A_4$ $C_2^2$ $C_{3}$ Solvable - 2
24.13 $C_2\times A_4$ $2^{3} \cdot 3$ $2 \cdot 3$ 8 $C_2$ $A_4$ $C_2^2$ $C_{6}$ Solvable - 2
36.3 $C_2^2:C_9$ $2^{2} \cdot 3^{2}$ $2 \cdot 3^{2}$ 12 $C_3$ $A_4$ $C_2^2$ $C_{9}$ Solvable - 2
36.9 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ $2^{2} \cdot 3$ 6 $C_1$ $C_3^2:C_4$ $C_3^2$ $C_{4}$ Solvable - 2
36.11 $C_3\times A_4$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ 12 $C_3$ $A_4$ $C_2^2$ $C_{3}^{2}$ Solvable - 2
48.3 $C_4^2:C_3$ $2^{4} \cdot 3$ $2^{2} \cdot 3$ 8 $C_1$ $C_4^2:C_3$ $C_4^2$ $C_{3}$ Solvable - 2
48.31 $C_4\times A_4$ $2^{4} \cdot 3$ $2^{2} \cdot 3$ 16 $C_4$ $A_4$ $C_2^2$ $C_{12}$ Solvable - 2
48.49 $C_2^2\times A_4$ $2^{4} \cdot 3$ $2 \cdot 3$ 16 $C_2^2$ $A_4$ $C_2^2$ $C_{2} \times C_{6}$ Solvable - 2
48.50 $C_2^2:A_4$ $2^{4} \cdot 3$ $2 \cdot 3$ 8 $C_1$ $C_2^2:A_4$ $C_2^4$ $C_{3}$ Solvable - 2
56.11 $F_8$ $2^{3} \cdot 7$ $2 \cdot 7$ 8 $C_1$ $F_8$ $C_2^3$ $C_{7}$ Solvable - 2
60.9 $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ 20 $C_5$ $A_4$ $C_2^2$ $C_{15}$ Solvable - 2
72.16 $C_2^2:C_{18}$ $2^{3} \cdot 3^{2}$ $2 \cdot 3^{2}$ 24 $C_6$ $A_4$ $C_2^2$ $C_{18}$ Solvable - 2
72.19 $C_3^2:C_8$ $2^{3} \cdot 3^{2}$ $2^{3} \cdot 3$ 12 $C_2$ $C_3^2:C_4$ $C_3^2$ $C_{8}$ Solvable - 2
72.39 $F_9$ $2^{3} \cdot 3^{2}$ $2^{3} \cdot 3$ 9 $C_1$ $F_9$ $C_3^2$ $C_{8}$ Solvable - 2
72.44 $S_3\times A_4$ $2^{3} \cdot 3^{2}$ $2 \cdot 3$ 12 $C_1$ $S_3\times A_4$ $C_2\times C_6$ $C_{6}$ Solvable - 2
72.45 $C_2\times C_3^2:C_4$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 12 $C_2$ $C_3^2:C_4$ $C_3^2$ $C_{2} \times C_{4}$ Solvable - 2
72.47 $C_6\times A_4$ $2^{3} \cdot 3^{2}$ $2 \cdot 3$ 24 $C_6$ $A_4$ $C_2^2$ $C_{3} \times C_{6}$ Solvable - 2
75.2 $C_5^2:C_3$ $3 \cdot 5^{2}$ $3 \cdot 5$ 11 $C_1$ $C_5^2:C_3$ $C_5^2$ $C_{3}$ Solvable - 2
80.49 $C_2^4:C_5$ $2^{4} \cdot 5$ $2 \cdot 5$ 8 $C_1$ $C_2^4:C_5$ $C_2^4$ $C_{5}$ Solvable - 2
84.10 $C_7\times A_4$ $2^{2} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ 28 $C_7$ $A_4$ $C_2^2$ $C_{21}$ Solvable - 2
84.11 $C_7:A_4$ $2^{2} \cdot 3 \cdot 7$ $2 \cdot 3 \cdot 7$ 12 $C_1$ $C_7:A_4$ $C_2\times C_{14}$ $C_{3}$ Solvable - 2
96.68 $C_4^2:C_6$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 16 $C_2$ $C_4^2:C_3$ $C_4^2$ $C_{6}$ Solvable - 2
96.70 $C_2^3:A_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 10 $C_1$ $C_2^3:A_4$ $C_2^4$ $C_{6}$ Solvable - 2
96.71 $C_4^2:C_6$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 10 $C_1$ $C_4^2:C_6$ $C_4^2$ $C_{6}$ Solvable - 2
96.72 $C_4^2:C_6$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 10 $C_1$ $C_4^2:C_6$ $C_4^2$ $C_{6}$ Solvable - 2
96.73 $C_8\times A_4$ $2^{5} \cdot 3$ $2^{3} \cdot 3$ 32 $C_8$ $A_4$ $C_2^2$ $C_{24}$ Solvable - 2
96.196 $C_2^3:C_{12}$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 32 $C_2\times C_4$ $A_4$ $C_2^2$ $C_{2} \times C_{12}$ Solvable - 2
96.197 $D_4\times A_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 20 $C_2$ $C_2^2\times A_4$ $C_2^3$ $C_{2} \times C_{6}$ Solvable - 2
96.199 $Q_8\times A_4$ $2^{5} \cdot 3$ $2^{2} \cdot 3$ 20 $C_2$ $C_2^2\times A_4$ $C_2^3$ $C_{2} \times C_{6}$ Solvable - 2
96.228 $C_2^3\times A_4$ $2^{5} \cdot 3$ $2 \cdot 3$ 32 $C_2^3$ $A_4$ $C_2^2$ $C_{2}^{2} \times C_{6}$ Solvable - 2
96.229 $C_2^3:A_4$ $2^{5} \cdot 3$ $2 \cdot 3$ 16 $C_2$ $C_2^2:A_4$ $C_2^4$ $C_{6}$ Solvable - 2
108.3 $C_2^2:C_{27}$ $2^{2} \cdot 3^{3}$ $2 \cdot 3^{3}$ 36 $C_9$ $A_4$ $C_2^2$ $C_{27}$ Solvable - 2
108.18 $C_9\times A_4$ $2^{2} \cdot 3^{3}$ $2 \cdot 3^{2}$ 36 $C_9$ $A_4$ $C_2^2$ $C_{3} \times C_{9}$ Solvable - 2
108.19 $C_9:A_4$ $2^{2} \cdot 3^{3}$ $2 \cdot 3^{2}$ 20 $C_3$ $C_3\times A_4$ $C_2\times C_6$ $C_{3}^{2}$ Solvable - 2
108.20 $C_3^2.A_4$ $2^{2} \cdot 3^{3}$ $2 \cdot 3^{2}$ 36 $C_3^2$ $A_4$ $C_2^2$ $C_{3} \times C_{9}$ Solvable - 2
108.21 $C_3^2.A_4$ $2^{2} \cdot 3^{3}$ $2 \cdot 3^{2}$ 20 $C_3$ $C_3\times A_4$ $C_2\times C_6$ $C_{3}^{2}$ Solvable - 2
108.22 $C_3^2:A_4$ $2^{2} \cdot 3^{3}$ $2 \cdot 3$ 20 $C_3$ $C_3\times A_4$ $C_2\times C_6$ $C_{3}^{2}$ Solvable - 2
108.36 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ $2^{2} \cdot 3$ 18 $C_3$ $C_3^2:C_4$ $C_3^2$ $C_{12}$ Solvable - 2
108.37 $C_3^3:C_4$ $2^{2} \cdot 3^{3}$ $2^{2} \cdot 3$ 12 $C_1$ $C_3^3:C_4$ $C_3^3$ $C_{4}$ Solvable - 2
108.41 $C_3^2\times A_4$ $2^{2} \cdot 3^{3}$ $2 \cdot 3$ 36 $C_3^2$ $A_4$ $C_2^2$ $C_{3}^{3}$ Solvable - 2
112.41 $C_2\times F_8$ $2^{4} \cdot 7$ $2 \cdot 7$ 16 $C_2$ $F_8$ $C_2^3$ $C_{14}$ Solvable - 2
120.39 $D_5\times A_4$ $2^{3} \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ 16 $C_1$ $D_5\times A_4$ $C_2\times C_{10}$ $C_{6}$ Solvable - 2
120.43 $C_{10}\times A_4$ $2^{3} \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ 40 $C_{10}$ $A_4$ $C_2^2$ $C_{30}$ Solvable - 2
132.6 $C_{11}\times A_4$ $2^{2} \cdot 3 \cdot 11$ $2 \cdot 3 \cdot 11$ 44 $C_{11}$ $A_4$ $C_2^2$ $C_{33}$ Solvable - 2
144.3 $C_4^2:C_9$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 24 $C_3$ $C_4^2:C_3$ $C_4^2$ $C_{9}$ Solvable - 2
144.34 $C_2^2:C_{36}$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 48 $C_{12}$ $A_4$ $C_2^2$ $C_{36}$ Solvable - 2
144.51 $C_3^2:C_{16}$ $2^{4} \cdot 3^{2}$ $2^{4} \cdot 3$ 24 $C_4$ $C_3^2:C_4$ $C_3^2$ $C_{16}$ Solvable - 2
144.68 $C_4^2:C_3^2$ $2^{4} \cdot 3^{2}$ $2^{2} \cdot 3$ 24 $C_3$ $C_4^2:C_3$ $C_4^2$ $C_{3}^{2}$ Solvable - 2
144.110 $C_2^3:C_{18}$ $2^{4} \cdot 3^{2}$ $2 \cdot 3^{2}$ 48 $C_2\times C_6$ $A_4$ $C_2^2$ $C_{2} \times C_{18}$ Solvable - 2
144.111 $C_2^4:C_9$ $2^{4} \cdot 3^{2}$ $2 \cdot 3^{2}$ 24 $C_3$ $C_2^2:A_4$ $C_2^4$ $C_{9}$ Solvable - 2
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