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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
8.1 | $C_8$ | $2^{3}$ | $2^{3}$ | $8$ | $C_8$ | Cyclic |
8.2 | $C_2\times C_4$ | $2^{3}$ | $2^{2}$ | $8$ | $C_2\times C_4$ | Abelian - 2 |
8.3 | $D_4$ | $2^{3}$ | $2^{2}$ | $5$ | $C_2$ | Nilpotent - 2 |
8.4 | $Q_8$ | $2^{3}$ | $2^{2}$ | $5$ | $C_2$ | Nilpotent - 2 |
8.5 | $C_2^3$ | $2^{3}$ | $2$ | $8$ | $C_2^3$ | Abelian - 3 |
16.1 | $C_{16}$ | $2^{4}$ | $2^{4}$ | $16$ | $C_{16}$ | Cyclic |
16.2 | $C_4^2$ | $2^{4}$ | $2^{2}$ | $16$ | $C_4^2$ | Abelian - 2 |
16.3 | $C_2^2:C_4$ | $2^{4}$ | $2^{2}$ | $10$ | $C_2^2$ | Nilpotent - 2 |
16.4 | $C_4:C_4$ | $2^{4}$ | $2^{2}$ | $10$ | $C_2^2$ | Nilpotent - 2 |
16.5 | $C_2\times C_8$ | $2^{4}$ | $2^{3}$ | $16$ | $C_2\times C_8$ | Abelian - 2 |
16.6 | $\OD_{16}$ | $2^{4}$ | $2^{3}$ | $10$ | $C_4$ | Nilpotent - 2 |
16.7 | $D_8$ | $2^{4}$ | $2^{3}$ | $7$ | $C_2$ | Nilpotent - 3 |
16.8 | $\SD_{16}$ | $2^{4}$ | $2^{3}$ | $7$ | $C_2$ | Nilpotent - 3 |
16.9 | $Q_{16}$ | $2^{4}$ | $2^{3}$ | $7$ | $C_2$ | Nilpotent - 3 |
16.10 | $C_2^2\times C_4$ | $2^{4}$ | $2^{2}$ | $16$ | $C_2^2\times C_4$ | Abelian - 3 |
16.11 | $C_2\times D_4$ | $2^{4}$ | $2^{2}$ | $10$ | $C_2^2$ | Nilpotent - 2 |
16.12 | $C_2\times Q_8$ | $2^{4}$ | $2^{2}$ | $10$ | $C_2^2$ | Nilpotent - 2 |
16.13 | $D_4:C_2$ | $2^{4}$ | $2^{2}$ | $10$ | $C_4$ | Nilpotent - 2 |
16.14 | $C_2^4$ | $2^{4}$ | $2$ | $16$ | $C_2^4$ | Abelian - 4 |
27.1 | $C_{27}$ | $3^{3}$ | $3^{3}$ | $27$ | $C_{27}$ | Cyclic |
27.2 | $C_3\times C_9$ | $3^{3}$ | $3^{2}$ | $27$ | $C_3\times C_9$ | Abelian - 2 |
27.3 | $\He_3$ | $3^{3}$ | $3$ | $11$ | $C_3$ | Nilpotent - 2 |
27.4 | $C_9:C_3$ | $3^{3}$ | $3^{2}$ | $11$ | $C_3$ | Nilpotent - 2 |
27.5 | $C_3^3$ | $3^{3}$ | $3$ | $27$ | $C_3^3$ | Abelian - 3 |
32.1 | $C_{32}$ | $2^{5}$ | $2^{5}$ | $32$ | $C_{32}$ | Cyclic |
32.2 | $C_2.C_4^2$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 2 |
32.3 | $C_4\times C_8$ | $2^{5}$ | $2^{3}$ | $32$ | $C_4\times C_8$ | Abelian - 2 |
32.4 | $C_8:C_4$ | $2^{5}$ | $2^{3}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.5 | $C_2^2:C_8$ | $2^{5}$ | $2^{3}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.6 | $C_2^3:C_4$ | $2^{5}$ | $2^{2}$ | $11$ | $C_2$ | Nilpotent - 3 |
32.7 | $\OD_{16}:C_2$ | $2^{5}$ | $2^{3}$ | $11$ | $C_2$ | Nilpotent - 3 |
32.8 | $C_4.D_4$ | $2^{5}$ | $2^{3}$ | $11$ | $C_2$ | Nilpotent - 3 |
32.9 | $D_4:C_4$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.10 | $Q_8:C_4$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.11 | $C_4\wr C_2$ | $2^{5}$ | $2^{3}$ | $14$ | $C_4$ | Nilpotent - 3 |
32.12 | $C_4:C_8$ | $2^{5}$ | $2^{3}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.13 | $C_8:C_4$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.14 | $C_8:C_4$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.15 | $C_8.C_4$ | $2^{5}$ | $2^{3}$ | $14$ | $C_4$ | Nilpotent - 3 |
32.16 | $C_2\times C_{16}$ | $2^{5}$ | $2^{4}$ | $32$ | $C_2\times C_{16}$ | Abelian - 2 |
32.17 | $\OD_{32}$ | $2^{5}$ | $2^{4}$ | $20$ | $C_8$ | Nilpotent - 2 |
32.18 | $D_{16}$ | $2^{5}$ | $2^{4}$ | $11$ | $C_2$ | Nilpotent - 4 |
32.19 | $\SD_{32}$ | $2^{5}$ | $2^{4}$ | $11$ | $C_2$ | Nilpotent - 4 |
32.20 | $Q_{32}$ | $2^{5}$ | $2^{4}$ | $11$ | $C_2$ | Nilpotent - 4 |
32.21 | $C_2\times C_4^2$ | $2^{5}$ | $2^{2}$ | $32$ | $C_2\times C_4^2$ | Abelian - 3 |
32.22 | $C_2^3:C_4$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 2 |
32.23 | $C_2^2.D_4$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 2 |
32.24 | $C_4^2:C_2$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.25 | $C_4\times D_4$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.26 | $C_4\times Q_8$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |