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Results (1-50 of 25008 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
4.2 $C_2^2$ $2^{2}$ $2$ $4$ $C_2^2$ $C_1$ $C_1$ $C_{2}^{2}$ Abelian - 2
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
9.2 $C_3^2$ $3^{2}$ $3$ $9$ $C_3^2$ $C_1$ $C_1$ $C_{3}^{2}$ Abelian - 2
12.4 $D_6$ $2^{2} \cdot 3$ $2 \cdot 3$ $6$ $C_2$ $S_3$ $C_3$ $C_{2}^{2}$ Solvable - 2
12.5 $C_2\times C_6$ $2^{2} \cdot 3$ $2 \cdot 3$ $12$ $C_2\times C_6$ $C_1$ $C_1$ $C_{2} \times C_{6}$ Abelian - 2
16.2 $C_4^2$ $2^{4}$ $2^{2}$ $16$ $C_4^2$ $C_1$ $C_1$ $C_{4}^{2}$ Abelian - 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
18.3 $C_3\times S_3$ $2 \cdot 3^{2}$ $2 \cdot 3$ $9$ $C_3$ $S_3$ $C_3$ $C_{6}$ Solvable - 2
18.5 $C_3\times C_6$ $2 \cdot 3^{2}$ $2 \cdot 3$ $18$ $C_3\times C_6$ $C_1$ $C_1$ $C_{3} \times C_{6}$ Abelian - 2
20.4 $D_{10}$ $2^{2} \cdot 5$ $2 \cdot 5$ $8$ $C_2$ $D_5$ $C_5$ $C_{2}^{2}$ Solvable - 2
20.5 $C_2\times C_{10}$ $2^{2} \cdot 5$ $2 \cdot 5$ $20$ $C_2\times C_{10}$ $C_1$ $C_1$ $C_{2} \times C_{10}$ Abelian - 2
24.4 $C_3:Q_8$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ $9$ $C_2$ $D_6$ $C_6$ $C_{2}^{2}$ Solvable - 2
24.5 $C_4\times S_3$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ $12$ $C_4$ $S_3$ $C_3$ $C_{2} \times C_{4}$ Solvable - 2
24.6 $D_{12}$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ $9$ $C_2$ $D_6$ $C_6$ $C_{2}^{2}$ Solvable - 2
24.7 $C_6:C_4$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ $12$ $C_2^2$ $S_3$ $C_3$ $C_{2} \times C_{4}$ Solvable - 2
24.9 $C_2\times C_{12}$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ $24$ $C_2\times C_{12}$ $C_1$ $C_1$ $C_{2} \times C_{12}$ Abelian - 2
24.10 $C_3\times D_4$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ $15$ $C_6$ $C_2^2$ $C_2$ $C_{2} \times C_{6}$ Nilpotent - 2
24.11 $C_3\times Q_8$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ $15$ $C_6$ $C_2^2$ $C_2$ $C_{2} \times C_{6}$ Nilpotent - 2
25.2 $C_5^2$ $5^{2}$ $5$ $25$ $C_5^2$ $C_1$ $C_1$ $C_{5}^{2}$ Abelian - 2
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
27.4 $C_9:C_3$ $3^{3}$ $3^{2}$ $11$ $C_3$ $C_3^2$ $C_3$ $C_{3}^{2}$ Nilpotent - 2
28.3 $D_{14}$ $2^{2} \cdot 7$ $2 \cdot 7$ $10$ $C_2$ $D_7$ $C_7$ $C_{2}^{2}$ Solvable - 2
28.4 $C_2\times C_{14}$ $2^{2} \cdot 7$ $2 \cdot 7$ $28$ $C_2\times C_{14}$ $C_1$ $C_1$ $C_{2} \times C_{14}$ Abelian - 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
32.12 $C_4:C_8$ $2^{5}$ $2^{3}$ $20$ $C_2\times C_4$ $C_2^2$ $C_2$ $C_{2} \times C_{8}$ 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
36.4 $D_{18}$ $2^{2} \cdot 3^{2}$ $2 \cdot 3^{2}$ $12$ $C_2$ $D_9$ $C_9$ $C_{2}^{2}$ Solvable - 2
36.5 $C_2\times C_{18}$ $2^{2} \cdot 3^{2}$ $2 \cdot 3^{2}$ $36$ $C_2\times C_{18}$ $C_1$ $C_1$ $C_{2} \times C_{18}$ Abelian - 2
36.6 $C_3:C_{12}$ $2^{2} \cdot 3^{2}$ $2^{2} \cdot 3$ $18$ $C_6$ $S_3$ $C_3$ $C_{12}$ Solvable - 2
36.8 $C_3\times C_{12}$ $2^{2} \cdot 3^{2}$ $2^{2} \cdot 3$ $36$ $C_3\times C_{12}$ $C_1$ $C_1$ $C_{3} \times C_{12}$ Abelian - 2
36.12 $C_6\times S_3$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ $18$ $C_6$ $S_3$ $C_3$ $C_{2} \times C_{6}$ Solvable - 2
36.14 $C_6^2$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ $36$ $C_6^2$ $C_1$ $C_1$ $C_{6}^{2}$ Abelian - 2
40.4 $C_5:Q_8$ $2^{3} \cdot 5$ $2^{2} \cdot 5$ $13$ $C_2$ $D_{10}$ $C_{10}$ $C_{2}^{2}$ Solvable - 2
40.5 $C_4\times D_5$ $2^{3} \cdot 5$ $2^{2} \cdot 5$ $16$ $C_4$ $D_5$ $C_5$ $C_{2} \times C_{4}$ Solvable - 2
40.6 $D_{20}$ $2^{3} \cdot 5$ $2^{2} \cdot 5$ $13$ $C_2$ $D_{10}$ $C_{10}$ $C_{2}^{2}$ Solvable - 2
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