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Results (1-50 of 68413 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
128.1 $C_{128}$ $2^{7}$ $2^{7}$ 128 $C_{128}$ $C_1$ $C_1$ $C_{128}$ Cyclic
128.2 $(C_2\times D_4):C_8$ $2^{7}$ $2^{3}$ 38 $C_2^3$ $C_2^2:C_4$ $C_2\times C_4$ $C_{2} \times C_{8}$ Nilpotent - 3
128.3 $(C_2\times C_4).D_8$ $2^{7}$ $2^{3}$ 38 $C_2^3$ $C_2^2:C_4$ $C_2\times C_4$ $C_{2} \times C_{8}$ Nilpotent - 3
128.4 $(C_2\times Q_8):C_8$ $2^{7}$ $2^{3}$ 38 $C_2^3$ $C_2^2:C_4$ $C_2\times C_4$ $C_{2} \times C_{8}$ Nilpotent - 3
128.5 $C_2.C_8^2$ $2^{7}$ $2^{3}$ 80 $C_2\times C_4^2$ $C_2^2$ $C_2$ $C_{8}^{2}$ Nilpotent - 2
128.6 $C_4^2:C_8$ $2^{7}$ $2^{3}$ 44 $C_2\times C_4$ $C_4^2$ $C_4$ $C_{4} \times C_{8}$ Nilpotent - 2
128.7 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 44 $C_2\times C_4$ $C_4^2$ $C_4$ $C_{4} \times C_{8}$ Nilpotent - 2
128.8 $C_4^2:C_8$ $2^{7}$ $2^{3}$ 56 $C_4^2$ $D_4$ $C_4$ $C_{4} \times C_{8}$ Nilpotent - 3
128.9 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 56 $C_2^2\times C_4$ $D_4$ $C_4$ $C_{4} \times C_{8}$ Nilpotent - 3
128.10 $\OD_{16}:C_8$ $2^{7}$ $2^{3}$ 56 $C_4^2$ $D_4$ $C_4$ $C_{4} \times C_{8}$ Nilpotent - 3
128.11 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 56 $C_2^2\times C_4$ $D_4$ $C_4$ $C_{4} \times C_{8}$ Nilpotent - 3
128.12 $C_2^3.C_4^2$ $2^{7}$ $2^{3}$ 44 $C_2^3$ $C_2^2:C_4$ $C_2^2$ $C_{4} \times C_{8}$ Nilpotent - 3
128.13 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 44 $C_2\times C_4$ $C_2^2:C_4$ $C_2^2$ $C_{4} \times C_{8}$ Nilpotent - 3
128.14 $C_2^3.C_4^2$ $2^{7}$ $2^{3}$ 44 $C_2\times C_4$ $C_2^2:C_4$ $C_2^2$ $C_{4} \times C_{8}$ Nilpotent - 3
128.15 $\OD_{16}:C_8$ $2^{7}$ $2^{3}$ 44 $C_2\times C_4$ $C_2^2:C_4$ $C_2^2$ $C_{4} \times C_{8}$ Nilpotent - 3
128.16 $C_2^4.D_4$ $2^{7}$ $2^{3}$ 32 $C_2^2$ $C_2.C_4^2$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.17 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 32 $C_2^2$ $C_2.C_4^2$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.18 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 32 $C_2^2$ $C_2.C_4^2$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.19 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 32 $C_2^2$ $C_2.C_4^2$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.20 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 32 $C_2^2$ $C_2.C_4^2$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.21 $C_2^3.D_8$ $2^{7}$ $2^{3}$ 32 $C_2^2$ $C_2.C_4^2$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.22 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 32 $C_2^2$ $C_2.C_4^2$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.23 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 32 $C_2^2$ $C_2.C_4^2$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.24 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 32 $C_2^2$ $C_2.C_4^2$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.25 $C_2^4.Q_8$ $2^{7}$ $2^{3}$ 32 $C_2^2$ $C_2.C_4^2$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.26 $C_2^3.D_8$ $2^{7}$ $2^{3}$ 38 $C_2^3$ $C_2^2:C_4$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.27 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 38 $C_2^3$ $C_2^2:C_4$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.28 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 38 $C_2^3$ $C_2^2:C_4$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.29 $C_2^4.D_4$ $2^{7}$ $2^{3}$ 38 $C_2\times C_4$ $C_2^2:C_4$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.30 $C_2^4.Q_8$ $2^{7}$ $2^{3}$ 38 $C_2\times C_4$ $C_2^2:C_4$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.31 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 38 $C_2\times C_4$ $C_2^2:C_4$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.32 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 38 $C_2\times C_4$ $C_2^2:C_4$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.33 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 38 $C_2\times C_4$ $C_2^2:C_4$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.34 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 38 $C_2\times C_4$ $C_2^2:C_4$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.35 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 38 $C_2\times C_4$ $C_2^2:C_4$ $C_2\times C_4$ $C_{4}^{2}$ Nilpotent - 3
128.36 $C_2^3.C_4^2$ $2^{7}$ $2^{2}$ 26 $C_2^2$ $C_2.C_4^2$ $C_2^3$ $C_{4}^{2}$ Nilpotent - 3
128.37 $C_2^3.C_4^2$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2.C_4^2$ $C_2^3$ $C_{4}^{2}$ Nilpotent - 3
128.38 $C_2^3.C_4^2$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2.C_4^2$ $C_2^3$ $C_{4}^{2}$ Nilpotent - 3
128.39 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2.C_4^2$ $C_2^3$ $C_{4}^{2}$ Nilpotent - 3
128.40 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2.C_4^2$ $C_2^3$ $C_{4}^{2}$ Nilpotent - 3
128.41 $C_4^2.D_4$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2.C_4^2$ $C_2^3$ $C_{4}^{2}$ Nilpotent - 3
128.42 $C_8\times C_{16}$ $2^{7}$ $2^{4}$ 128 $C_8\times C_{16}$ $C_1$ $C_1$ $C_{8} \times C_{16}$ Abelian - 2
128.43 $C_{16}:C_8$ $2^{7}$ $2^{4}$ 80 $C_4\times C_8$ $C_2^2$ $C_2$ $C_{8}^{2}$ Nilpotent - 2
128.44 $C_8:C_{16}$ $2^{7}$ $2^{4}$ 80 $C_4\times C_8$ $C_2^2$ $C_2$ $C_{4} \times C_{16}$ Nilpotent - 2
128.45 $C_{16}:C_8$ $2^{7}$ $2^{4}$ 44 $C_2\times C_4$ $C_4^2$ $C_4$ $C_{4} \times C_{8}$ Nilpotent - 2
128.46 $C_2^3:C_{16}$ $2^{7}$ $2^{4}$ 44 $C_2\times C_4$ $C_2^2:C_4$ $C_2^2$ $C_{2} \times C_{16}$ Nilpotent - 3
128.47 $C_2^3.\OD_{16}$ $2^{7}$ $2^{4}$ 38 $C_2\times C_4$ $C_2^2:C_4$ $C_2\times C_4$ $C_{2} \times C_{8}$ Nilpotent - 3
128.48 $C_2^4:C_8$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2^3:C_4$ $C_2^3$ $C_{2} \times C_{8}$ Nilpotent - 4
128.49 $C_2^3.\OD_{16}$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2^3:C_4$ $C_2^3$ $C_{2} \times C_{8}$ Nilpotent - 4
128.50 $(C_2\times D_4):C_8$ $2^{7}$ $2^{3}$ 26 $C_2^2$ $C_2^3:C_4$ $C_2\times C_4$ $C_{2} \times C_{8}$ Nilpotent - 4
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