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Order Exponent Nilpotency class Nilpotent
Center Commutator Central quotient Abelianization
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Results (10 matches)

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Label Name Family name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
1.1 $C_1$ $\OD_{1}$ $1$ $1$ 1 $C_1$ $C_1$ $C_1$ $C_1$ Trivial
2.1 $C_2$ $\OD_{2}$ $2$ $2$ 2 $C_2$ $C_1$ $C_1$ $C_{2}$ Cyclic
4.2 $C_2^2$ $\OD_{4}$ $2^{2}$ $2$ 4 $C_2^2$ $C_1$ $C_1$ $C_{2}^{2}$ Abelian - 2
8.3 $D_4$ $\OD_{8}$ $2^{3}$ $2^{2}$ 5 $C_2$ $C_2^2$ $C_2$ $C_{2}^{2}$ Nilpotent - 2
16.6 $\OD_{16}$ $\OD_{16}$ $2^{4}$ $2^{3}$ 10 $C_4$ $C_2^2$ $C_2$ $C_{2} \times C_{4}$ Nilpotent - 2
32.17 $\OD_{32}$ $\OD_{32}$ $2^{5}$ $2^{4}$ 20 $C_8$ $C_2^2$ $C_2$ $C_{2} \times C_{8}$ Nilpotent - 2
64.51 $\OD_{64}$ $\OD_{64}$ $2^{6}$ $2^{5}$ 40 $C_{16}$ $C_2^2$ $C_2$ $C_{2} \times C_{16}$ Nilpotent - 2
128.160 $\OD_{128}$ $\OD_{128}$ $2^{7}$ $2^{6}$ 80 $C_{32}$ $C_2^2$ $C_2$ $C_{2} \times C_{32}$ Nilpotent - 2
256.538 $\OD_{256}$ $\OD_{256}$ $2^{8}$ $2^{7}$ 160 $C_{64}$ $C_2^2$ $C_2$ $C_{2} \times C_{64}$ Nilpotent - 2
512.2041 $\OD_{512}$ $\OD_{512}$ $2^{9}$ $2^{8}$ 320 $C_{128}$ $C_2^2$ $C_2$ $C_{2} \times C_{128}$ Nilpotent - 2
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