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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
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 |
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 |
16.6 | $\OD_{16}$ | $2^{4}$ | $2^{3}$ | $10$ | $C_4$ | Nilpotent - 2 |
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 |
24.10 | $C_3\times D_4$ | $2^{3} \cdot 3$ | $2^{2} \cdot 3$ | $15$ | $C_6$ | Nilpotent - 2 |
24.11 | $C_3\times Q_8$ | $2^{3} \cdot 3$ | $2^{2} \cdot 3$ | $15$ | $C_6$ | Nilpotent - 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 |
32.2 | $C_2.C_4^2$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 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 |
32.12 | $C_4:C_8$ | $2^{5}$ | $2^{3}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.17 | $\OD_{32}$ | $2^{5}$ | $2^{4}$ | $20$ | $C_8$ | Nilpotent - 2 |
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 |
32.27 | $C_2^2\wr C_2$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.28 | $C_4:D_4$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.29 | $C_2^2:Q_8$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.30 | $C_2^2.D_4$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.31 | $C_4^2:C_2$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.32 | $C_4.Q_8$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.33 | $C_4^2:C_2$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.34 | $C_4:D_4$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.35 | $C_4:Q_8$ | $2^{5}$ | $2^{2}$ | $14$ | $C_2^2$ | Nilpotent - 2 |
32.37 | $C_2\times \OD_{16}$ | $2^{5}$ | $2^{3}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.38 | $\OD_{16}:C_2$ | $2^{5}$ | $2^{3}$ | $20$ | $C_8$ | Nilpotent - 2 |
32.46 | $C_2^2\times D_4$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 2 |
32.47 | $C_2^2\times Q_8$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2^3$ | Nilpotent - 2 |
32.48 | $D_4:C_2^2$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.49 | $D_4:C_2^2$ | $2^{5}$ | $2^{2}$ | $17$ | $C_2$ | Nilpotent - 2 |
32.50 | $C_4.C_2^3$ | $2^{5}$ | $2^{2}$ | $17$ | $C_2$ | Nilpotent - 2 |
40.10 | $C_5\times D_4$ | $2^{3} \cdot 5$ | $2^{2} \cdot 5$ | $25$ | $C_{10}$ | Nilpotent - 2 |
40.11 | $C_5\times Q_8$ | $2^{3} \cdot 5$ | $2^{2} \cdot 5$ | $25$ | $C_{10}$ | Nilpotent - 2 |
48.21 | $C_2^2:C_{12}$ | $2^{4} \cdot 3$ | $2^{2} \cdot 3$ | $30$ | $C_2\times C_6$ | Nilpotent - 2 |
48.22 | $C_4:C_{12}$ | $2^{4} \cdot 3$ | $2^{2} \cdot 3$ | $30$ | $C_2\times C_6$ | Nilpotent - 2 |
48.24 | $C_3\times \OD_{16}$ | $2^{4} \cdot 3$ | $2^{3} \cdot 3$ | $30$ | $C_{12}$ | Nilpotent - 2 |
48.45 | $C_6\times D_4$ | $2^{4} \cdot 3$ | $2^{2} \cdot 3$ | $30$ | $C_2\times C_6$ | Nilpotent - 2 |
48.46 | $C_6\times Q_8$ | $2^{4} \cdot 3$ | $2^{2} \cdot 3$ | $30$ | $C_2\times C_6$ | Nilpotent - 2 |
48.47 | $D_4:C_6$ | $2^{4} \cdot 3$ | $2^{2} \cdot 3$ | $30$ | $C_{12}$ | Nilpotent - 2 |
54.10 | $C_2\times \He_3$ | $2 \cdot 3^{3}$ | $2 \cdot 3$ | $22$ | $C_6$ | Nilpotent - 2 |
54.11 | $C_9:C_6$ | $2 \cdot 3^{3}$ | $2 \cdot 3^{2}$ | $22$ | $C_6$ | Nilpotent - 2 |
56.9 | $C_7\times D_4$ | $2^{3} \cdot 7$ | $2^{2} \cdot 7$ | $35$ | $C_{14}$ | Nilpotent - 2 |
56.10 | $C_7\times Q_8$ | $2^{3} \cdot 7$ | $2^{2} \cdot 7$ | $35$ | $C_{14}$ | Nilpotent - 2 |