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Results (1-50 of 38563 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
72.1 $C_9:C_8$ $2^{3} \cdot 3^{2}$ $2^{3} \cdot 3^{2}$ 24 $C_4$ $D_9$ $C_9$ $C_{8}$ Solvable - 2
72.3 $Q_8:C_9$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 21 $C_6$ $A_4$ $Q_8$ $C_{9}$ Solvable - 3
72.4 $C_9:Q_8$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 21 $C_2$ $D_{18}$ $C_{18}$ $C_{2}^{2}$ Solvable - 2
72.5 $C_4\times D_9$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 24 $C_4$ $D_9$ $C_9$ $C_{2} \times C_{4}$ Solvable - 2
72.6 $D_{36}$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 21 $C_2$ $D_{18}$ $C_{18}$ $C_{2}^{2}$ Solvable - 2
72.7 $C_{18}:C_4$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 24 $C_2^2$ $D_9$ $C_9$ $C_{2} \times C_{4}$ Solvable - 2
72.8 $C_9:D_4$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 21 $C_2$ $D_{18}$ $C_{18}$ $C_{2}^{2}$ Solvable - 2
72.12 $C_3:C_{24}$ $2^{3} \cdot 3^{2}$ $2^{3} \cdot 3$ 36 $C_{12}$ $S_3$ $C_3$ $C_{24}$ Solvable - 2
72.13 $C_3^2:C_8$ $2^{3} \cdot 3^{2}$ $2^{3} \cdot 3$ 24 $C_4$ $C_3:S_3$ $C_3^2$ $C_{8}$ Solvable - 2
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
72.16 $C_2^2:C_{18}$ $2^{3} \cdot 3^{2}$ $2 \cdot 3^{2}$ 24 $C_6$ $A_4$ $C_2^2$ $C_{18}$ Solvable - 2
72.17 $C_2\times D_{18}$ $2^{3} \cdot 3^{2}$ $2 \cdot 3^{2}$ 24 $C_2^2$ $D_9$ $C_9$ $C_{2}^{3}$ 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
72.20 $C_6.D_6$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 18 $C_2$ $S_3^2$ $C_3^2$ $C_{2} \times C_{4}$ Solvable - 2
72.21 $C_6.D_6$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 18 $C_2$ $S_3^2$ $C_3^2$ $C_{2} \times C_{4}$ Solvable - 2
72.22 $D_6:S_3$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 15 $C_2$ $S_3^2$ $C_3\times C_6$ $C_{2}^{2}$ Solvable - 2
72.23 $C_3:D_{12}$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 15 $C_2$ $S_3^2$ $C_3\times C_6$ $C_{2}^{2}$ Solvable - 2
72.24 $C_3^2:Q_8$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 15 $C_2$ $S_3^2$ $C_3\times C_6$ $C_{2}^{2}$ Solvable - 2
72.25 $C_3\times \SL(2,3)$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 21 $C_6$ $A_4$ $Q_8$ $C_{3}^{2}$ Solvable - 3
72.26 $C_3^2:Q_8$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 27 $C_6$ $D_6$ $C_6$ $C_{2} \times C_{6}$ Solvable - 2
72.27 $S_3\times C_{12}$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 36 $C_{12}$ $S_3$ $C_3$ $C_{2} \times C_{12}$ Solvable - 2
72.28 $C_3\times D_{12}$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 27 $C_6$ $D_6$ $C_6$ $C_{2} \times C_{6}$ Solvable - 2
72.29 $C_6:C_{12}$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 36 $C_2\times C_6$ $S_3$ $C_3$ $C_{2} \times C_{12}$ Solvable - 2
72.30 $C_6\wr C_2$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 27 $C_6$ $D_6$ $C_6$ $C_{2} \times C_{6}$ Solvable - 2
72.31 $C_3^2:Q_8$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 21 $C_2$ $C_6:S_3$ $C_3\times C_6$ $C_{2}^{2}$ Solvable - 2
72.32 $C_{12}:S_3$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 24 $C_4$ $C_3:S_3$ $C_3^2$ $C_{2} \times C_{4}$ Solvable - 2
72.33 $C_3:D_{12}$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 21 $C_2$ $C_6:S_3$ $C_3\times C_6$ $C_{2}^{2}$ Solvable - 2
72.34 $C_6.D_6$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 24 $C_2^2$ $C_3:S_3$ $C_3^2$ $C_{2} \times C_{4}$ Solvable - 2
72.35 $C_6^2:C_2$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 21 $C_2$ $C_6:S_3$ $C_3\times C_6$ $C_{2}^{2}$ 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
72.40 $\SOPlus(4,2)$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 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
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
72.46 $S_3\times D_6$ $2^{3} \cdot 3^{2}$ $2 \cdot 3$ 18 $C_2$ $S_3^2$ $C_3^2$ $C_{2}^{3}$ 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
72.48 $C_6\times D_6$ $2^{3} \cdot 3^{2}$ $2 \cdot 3$ 36 $C_2\times C_6$ $S_3$ $C_3$ $C_{2}^{2} \times C_{6}$ Solvable - 2
72.49 $C_6:D_6$ $2^{3} \cdot 3^{2}$ $2 \cdot 3$ 24 $C_2^2$ $C_3:S_3$ $C_3^2$ $C_{2}^{3}$ Solvable - 2
108.1 $C_{27}:C_4$ $2^{2} \cdot 3^{3}$ $2^{2} \cdot 3^{3}$ 30 $C_2$ $D_{27}$ $C_{27}$ $C_{4}$ 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
108.4 $D_{54}$ $2^{2} \cdot 3^{3}$ $2 \cdot 3^{3}$ 30 $C_2$ $D_{27}$ $C_{27}$ $C_{2}^{2}$ Solvable - 2
108.6 $C_9:C_{12}$ $2^{2} \cdot 3^{3}$ $2^{2} \cdot 3^{2}$ 36 $C_6$ $D_9$ $C_9$ $C_{12}$ Solvable - 2
108.7 $C_3:C_{36}$ $2^{2} \cdot 3^{3}$ $2^{2} \cdot 3^{2}$ 54 $C_{18}$ $S_3$ $C_3$ $C_{36}$ Solvable - 2
108.8 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ $2^{2} \cdot 3$ 20 $C_2$ $C_3^2:C_6$ $C_3^2$ $C_{12}$ Solvable - 2
108.9 $C_9:C_{12}$ $2^{2} \cdot 3^{3}$ $2^{2} \cdot 3^{2}$ 20 $C_2$ $C_9:C_6$ $C_9$ $C_{12}$ Solvable - 2
108.10 $C_6.D_9$ $2^{2} \cdot 3^{3}$ $2^{2} \cdot 3^{2}$ 30 $C_2$ $C_3:D_9$ $C_3\times C_9$ $C_{4}$ Solvable - 2
108.11 $\He_3:C_4$ $2^{2} \cdot 3^{3}$ $2^{2} \cdot 3$ 20 $C_6$ $C_3:S_3$ $\He_3$ $C_{4}$ Solvable - 3
108.15 $\He_3:C_4$ $2^{2} \cdot 3^{3}$ $2^{2} \cdot 3$ 14 $C_3$ $C_3^2:C_4$ $\He_3$ $C_{4}$ Solvable - 3
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