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Order Exponent Nilpotency class Nilpotent
Center Commutator Central quotient Abelianization
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Results (1-50 of 983 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
8.1 $C_8$ $2^{3}$ $2^{3}$ 8 $C_8$ $C_1$ $C_1$ $C_{8}$ Cyclic
8.2 $C_2\times C_4$ $2^{3}$ $2^{2}$ 8 $C_2\times C_4$ $C_1$ $C_1$ $C_{2} \times C_{4}$ Abelian - 2
8.3 $D_4$ $2^{3}$ $2^{2}$ 5 $C_2$ $C_2^2$ $C_2$ $C_{2}^{2}$ Nilpotent - 2
8.4 $Q_8$ $2^{3}$ $2^{2}$ 5 $C_2$ $C_2^2$ $C_2$ $C_{2}^{2}$ Nilpotent - 2
8.5 $C_2^3$ $2^{3}$ $2$ 8 $C_2^3$ $C_1$ $C_1$ $C_{2}^{3}$ Abelian - 3
16.1 $C_{16}$ $2^{4}$ $2^{4}$ 16 $C_{16}$ $C_1$ $C_1$ $C_{16}$ Cyclic
16.2 $C_4^2$ $2^{4}$ $2^{2}$ 16 $C_4^2$ $C_1$ $C_1$ $C_{4}^{2}$ Abelian - 2
16.3 $C_2^2:C_4$ $2^{4}$ $2^{2}$ 10 $C_2^2$ $C_2^2$ $C_2$ $C_{2} \times C_{4}$ Nilpotent - 2
16.4 $C_4:C_4$ $2^{4}$ $2^{2}$ 10 $C_2^2$ $C_2^2$ $C_2$ $C_{2} \times C_{4}$ Nilpotent - 2
16.5 $C_2\times C_8$ $2^{4}$ $2^{3}$ 16 $C_2\times C_8$ $C_1$ $C_1$ $C_{2} \times C_{8}$ Abelian - 2
16.6 $\OD_{16}$ $2^{4}$ $2^{3}$ 10 $C_4$ $C_2^2$ $C_2$ $C_{2} \times C_{4}$ Nilpotent - 2
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
16.10 $C_2^2\times C_4$ $2^{4}$ $2^{2}$ 16 $C_2^2\times C_4$ $C_1$ $C_1$ $C_{2}^{2} \times C_{4}$ Abelian - 3
16.11 $C_2\times D_4$ $2^{4}$ $2^{2}$ 10 $C_2^2$ $C_2^2$ $C_2$ $C_{2}^{3}$ Nilpotent - 2
16.12 $C_2\times Q_8$ $2^{4}$ $2^{2}$ 10 $C_2^2$ $C_2^2$ $C_2$ $C_{2}^{3}$ Nilpotent - 2
16.13 $D_4:C_2$ $2^{4}$ $2^{2}$ 10 $C_4$ $C_2^2$ $C_2$ $C_{2}^{3}$ Nilpotent - 2
16.14 $C_2^4$ $2^{4}$ $2$ 16 $C_2^4$ $C_1$ $C_1$ $C_{2}^{4}$ Abelian - 4
27.1 $C_{27}$ $3^{3}$ $3^{3}$ 27 $C_{27}$ $C_1$ $C_1$ $C_{27}$ Cyclic
27.2 $C_3\times C_9$ $3^{3}$ $3^{2}$ 27 $C_3\times C_9$ $C_1$ $C_1$ $C_{3} \times C_{9}$ Abelian - 2
27.3 $\He_3$ $3^{3}$ $3$ 11 $C_3$ $C_3^2$ $C_3$ $C_{3}^{2}$ Nilpotent - 2
27.4 $C_9:C_3$ $3^{3}$ $3^{2}$ 11 $C_3$ $C_3^2$ $C_3$ $C_{3}^{2}$ Nilpotent - 2
27.5 $C_3^3$ $3^{3}$ $3$ 27 $C_3^3$ $C_1$ $C_1$ $C_{3}^{3}$ Abelian - 3
32.1 $C_{32}$ $2^{5}$ $2^{5}$ 32 $C_{32}$ $C_1$ $C_1$ $C_{32}$ Cyclic
32.2 $C_2.C_4^2$ $2^{5}$ $2^{2}$ 20 $C_2^3$ $C_2^2$ $C_2$ $C_{4}^{2}$ Nilpotent - 2
32.3 $C_4\times C_8$ $2^{5}$ $2^{3}$ 32 $C_4\times C_8$ $C_1$ $C_1$ $C_{4} \times C_{8}$ Abelian - 2
32.4 $C_8:C_4$ $2^{5}$ $2^{3}$ 20 $C_2\times C_4$ $C_2^2$ $C_2$ $C_{4}^{2}$ Nilpotent - 2
32.5 $C_2^2:C_8$ $2^{5}$ $2^{3}$ 20 $C_2\times C_4$ $C_2^2$ $C_2$ $C_{2} \times C_{8}$ Nilpotent - 2
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
32.12 $C_4:C_8$ $2^{5}$ $2^{3}$ 20 $C_2\times C_4$ $C_2^2$ $C_2$ $C_{2} \times C_{8}$ Nilpotent - 2
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
32.16 $C_2\times C_{16}$ $2^{5}$ $2^{4}$ 32 $C_2\times C_{16}$ $C_1$ $C_1$ $C_{2} \times C_{16}$ Abelian - 2
32.17 $\OD_{32}$ $2^{5}$ $2^{4}$ 20 $C_8$ $C_2^2$ $C_2$ $C_{2} \times C_{8}$ Nilpotent - 2
32.18 $D_{16}$ $2^{5}$ $2^{4}$ 11 $C_2$ $D_8$ $C_8$ $C_{2}^{2}$ Nilpotent - 4
32.19 $\SD_{32}$ $2^{5}$ $2^{4}$ 11 $C_2$ $D_8$ $C_8$ $C_{2}^{2}$ Nilpotent - 4
32.20 $Q_{32}$ $2^{5}$ $2^{4}$ 11 $C_2$ $D_8$ $C_8$ $C_{2}^{2}$ Nilpotent - 4
32.21 $C_2\times C_4^2$ $2^{5}$ $2^{2}$ 32 $C_2\times C_4^2$ $C_1$ $C_1$ $C_{2} \times C_{4}^{2}$ Abelian - 3
32.22 $C_2^3:C_4$ $2^{5}$ $2^{2}$ 20 $C_2^3$ $C_2^2$ $C_2$ $C_{2}^{2} \times C_{4}$ Nilpotent - 2
32.23 $C_2^2.D_4$ $2^{5}$ $2^{2}$ 20 $C_2^3$ $C_2^2$ $C_2$ $C_{2}^{2} \times C_{4}$ Nilpotent - 2
32.24 $C_4^2:C_2$ $2^{5}$ $2^{2}$ 20 $C_2\times C_4$ $C_2^2$ $C_2$ $C_{2}^{2} \times C_{4}$ Nilpotent - 2
32.25 $C_4\times D_4$ $2^{5}$ $2^{2}$ 20 $C_2\times C_4$ $C_2^2$ $C_2$ $C_{2}^{2} \times C_{4}$ Nilpotent - 2
32.26 $C_4\times Q_8$ $2^{5}$ $2^{2}$ 20 $C_2\times C_4$ $C_2^2$ $C_2$ $C_{2}^{2} \times C_{4}$ Nilpotent - 2
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