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Order Exponent Nilpotency class Nilpotent
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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
16.7 $D_8$ $2^{4}$ $2^{3}$ 7 $C_2$ $D_4$ $C_4$ $C_{2}^{2}$ Nilpotent - 3
16.8 $\SD_{16}$ $2^{4}$ $2^{3}$ 7 $C_2$ $D_4$ $C_4$ $C_{2}^{2}$ Nilpotent - 3
16.9 $Q_{16}$ $2^{4}$ $2^{3}$ 7 $C_2$ $D_4$ $C_4$ $C_{2}^{2}$ Nilpotent - 3
32.6 $C_2^3:C_4$ $2^{5}$ $2^{2}$ 11 $C_2$ $C_2^2:C_4$ $C_2^2$ $C_{2} \times C_{4}$ Nilpotent - 3
32.7 $\OD_{16}:C_2$ $2^{5}$ $2^{3}$ 11 $C_2$ $C_2^2:C_4$ $C_2^2$ $C_{2} \times C_{4}$ Nilpotent - 3
32.8 $C_4.D_4$ $2^{5}$ $2^{3}$ 11 $C_2$ $C_2^2:C_4$ $C_2^2$ $C_{2} \times C_{4}$ Nilpotent - 3
32.9 $D_4:C_4$ $2^{5}$ $2^{3}$ 14 $C_2^2$ $D_4$ $C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
32.10 $Q_8:C_4$ $2^{5}$ $2^{3}$ 14 $C_2^2$ $D_4$ $C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
32.11 $C_4\wr C_2$ $2^{5}$ $2^{3}$ 14 $C_4$ $D_4$ $C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
32.13 $C_8:C_4$ $2^{5}$ $2^{3}$ 14 $C_2^2$ $D_4$ $C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
32.14 $C_8:C_4$ $2^{5}$ $2^{3}$ 14 $C_2^2$ $D_4$ $C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
32.15 $C_8.C_4$ $2^{5}$ $2^{3}$ 14 $C_4$ $D_4$ $C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
32.39 $C_2\times D_8$ $2^{5}$ $2^{3}$ 14 $C_2^2$ $D_4$ $C_4$ $C_{2}^{3}$ Nilpotent - 3
32.40 $C_2\times \SD_{16}$ $2^{5}$ $2^{3}$ 14 $C_2^2$ $D_4$ $C_4$ $C_{2}^{3}$ Nilpotent - 3
32.41 $C_2\times Q_{16}$ $2^{5}$ $2^{3}$ 14 $C_2^2$ $D_4$ $C_4$ $C_{2}^{3}$ Nilpotent - 3
32.42 $D_8:C_2$ $2^{5}$ $2^{3}$ 14 $C_4$ $D_4$ $C_4$ $C_{2}^{3}$ Nilpotent - 3
32.43 $D_8:C_2$ $2^{5}$ $2^{3}$ 11 $C_2$ $C_2\times D_4$ $C_4$ $C_{2}^{3}$ Nilpotent - 3
32.44 $Q_{16}:C_2$ $2^{5}$ $2^{3}$ 11 $C_2$ $C_2\times D_4$ $C_4$ $C_{2}^{3}$ Nilpotent - 3
48.25 $C_3\times D_8$ $2^{4} \cdot 3$ $2^{3} \cdot 3$ 21 $C_6$ $D_4$ $C_4$ $C_{2} \times C_{6}$ Nilpotent - 3
48.26 $C_3\times \SD_{16}$ $2^{4} \cdot 3$ $2^{3} \cdot 3$ 21 $C_6$ $D_4$ $C_4$ $C_{2} \times C_{6}$ Nilpotent - 3
48.27 $C_3\times Q_{16}$ $2^{4} \cdot 3$ $2^{3} \cdot 3$ 21 $C_6$ $D_4$ $C_4$ $C_{2} \times C_{6}$ Nilpotent - 3
64.4 $C_2^3:C_8$ $2^{6}$ $2^{3}$ 22 $C_2^2$ $C_2^2:C_4$ $C_2^2$ $C_{2} \times C_{8}$ Nilpotent - 3
64.5 $C_2^2.\OD_{16}$ $2^{6}$ $2^{3}$ 22 $C_2^2$ $C_2^2:C_4$ $C_2^2$ $C_{2} \times C_{8}$ Nilpotent - 3
64.6 $D_4:C_8$ $2^{6}$ $2^{3}$ 28 $C_2\times C_4$ $D_4$ $C_4$ $C_{2} \times C_{8}$ Nilpotent - 3
64.7 $Q_8:C_8$ $2^{6}$ $2^{3}$ 28 $C_2\times C_4$ $D_4$ $C_4$ $C_{2} \times C_{8}$ Nilpotent - 3
64.8 $C_2^2.D_8$ $2^{6}$ $2^{3}$ 19 $C_2^2$ $C_2^2:C_4$ $C_2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
64.9 $C_2^2.Q_{16}$ $2^{6}$ $2^{3}$ 19 $C_2^2$ $C_2^2:C_4$ $C_2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
64.10 $C_4^2.C_2^2$ $2^{6}$ $2^{3}$ 19 $C_2^2$ $C_2^2:C_4$ $C_2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
64.11 $C_4^2.C_2^2$ $2^{6}$ $2^{3}$ 19 $C_2^2$ $C_2^2:C_4$ $C_2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
64.12 $C_4.D_8$ $2^{6}$ $2^{3}$ 19 $C_2^2$ $C_2^2:C_4$ $C_2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
64.13 $C_4.D_8$ $2^{6}$ $2^{3}$ 19 $C_2^2$ $C_2^2:C_4$ $C_2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
64.14 $C_4.Q_{16}$ $2^{6}$ $2^{3}$ 19 $C_2^2$ $C_2^2:C_4$ $C_2\times C_4$ $C_{2} \times C_{4}$ Nilpotent - 3
64.15 $C_8:C_8$ $2^{6}$ $2^{3}$ 28 $C_2\times C_4$ $D_4$ $C_4$ $C_{2} \times C_{8}$ Nilpotent - 3
64.16 $C_8:C_8$ $2^{6}$ $2^{3}$ 28 $C_2\times C_4$ $D_4$ $C_4$ $C_{2} \times C_{8}$ Nilpotent - 3
64.20 $C_4^2:C_4$ $2^{6}$ $2^{3}$ 28 $C_2\times C_4$ $D_4$ $C_4$ $C_{4}^{2}$ Nilpotent - 3
64.21 $C_4.C_4^2$ $2^{6}$ $2^{3}$ 28 $C_2^3$ $D_4$ $C_4$ $C_{4}^{2}$ Nilpotent - 3
64.22 $C_4.C_4^2$ $2^{6}$ $2^{3}$ 28 $C_2\times C_4$ $D_4$ $C_4$ $C_{4}^{2}$ Nilpotent - 3
64.23 $C_2^2.C_4^2$ $2^{6}$ $2^{2}$ 22 $C_2^2$ $C_2^2:C_4$ $C_2^2$ $C_{4}^{2}$ Nilpotent - 3
64.24 $\OD_{16}:C_4$ $2^{6}$ $2^{3}$ 22 $C_2^2$ $C_2^2:C_4$ $C_2^2$ $C_{4}^{2}$ Nilpotent - 3
64.25 $\OD_{16}:C_4$ $2^{6}$ $2^{3}$ 22 $C_4$ $C_2^2:C_4$ $C_2^2$ $C_{4}^{2}$ Nilpotent - 3
64.30 $\OD_{32}:C_2$ $2^{6}$ $2^{4}$ 22 $C_4$ $C_2^2:C_4$ $C_2^2$ $C_{2} \times C_{8}$ Nilpotent - 3
64.31 $\OD_{32}:C_2$ $2^{6}$ $2^{4}$ 28 $C_8$ $D_4$ $C_4$ $C_{2} \times C_{8}$ Nilpotent - 3
64.45 $C_8.C_8$ $2^{6}$ $2^{4}$ 28 $C_8$ $D_4$ $C_4$ $C_{2} \times C_{8}$ Nilpotent - 3
64.90 $C_2^4:C_4$ $2^{6}$ $2^{2}$ 22 $C_2^2$ $C_2^2:C_4$ $C_2^2$ $C_{2}^{2} \times C_{4}$ Nilpotent - 3
64.91 $C_2^3.C_2^3$ $2^{6}$ $2^{2}$ 22 $C_4$ $C_2^2:C_4$ $C_2^2$ $C_{2}^{2} \times C_{4}$ Nilpotent - 3
64.92 $\OD_{16}:C_2^2$ $2^{6}$ $2^{3}$ 22 $C_2^2$ $C_2^2:C_4$ $C_2^2$ $C_{2}^{2} \times C_{4}$ Nilpotent - 3
64.93 $\OD_{16}.C_2^2$ $2^{6}$ $2^{3}$ 22 $C_2^2$ $C_2^2:C_4$ $C_2^2$ $C_{2}^{2} \times C_{4}$ Nilpotent - 3
64.94 $\OD_{16}.C_2^2$ $2^{6}$ $2^{3}$ 22 $C_4$ $C_2^2:C_4$ $C_2^2$ $C_{2}^{2} \times C_{4}$ Nilpotent - 3
64.95 $C_2^2.D_8$ $2^{6}$ $2^{3}$ 28 $C_2^3$ $D_4$ $C_4$ $C_{2}^{2} \times C_{4}$ Nilpotent - 3
64.96 $C_2^2.Q_{16}$ $2^{6}$ $2^{3}$ 28 $C_2^3$ $D_4$ $C_4$ $C_{2}^{2} \times C_{4}$ Nilpotent - 3
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