Note: Search results may be incomplete due to uncomputed quantities: Outer aut. group order (4830 objects)
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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
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 |
16.11 | $C_2\times D_4$ | $2^{4}$ | $2^{2}$ | $10$ | $C_2^2$ | Nilpotent - 2 |
16.13 | $D_4:C_2$ | $2^{4}$ | $2^{2}$ | $10$ | $C_4$ | Nilpotent - 2 |
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 |
32.7 | $\OD_{16}:C_2$ | $2^{5}$ | $2^{3}$ | $11$ | $C_2$ | 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 |
32.12 | $C_4:C_8$ | $2^{5}$ | $2^{3}$ | $20$ | $C_2\times C_4$ | 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 |
32.17 | $\OD_{32}$ | $2^{5}$ | $2^{4}$ | $20$ | $C_8$ | Nilpotent - 2 |
32.18 | $D_{16}$ | $2^{5}$ | $2^{4}$ | $11$ | $C_2$ | Nilpotent - 4 |
32.20 | $Q_{32}$ | $2^{5}$ | $2^{4}$ | $11$ | $C_2$ | Nilpotent - 4 |
32.25 | $C_4\times D_4$ | $2^{5}$ | $2^{2}$ | $20$ | $C_2\times C_4$ | 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 |
32.37 | $C_2\times \OD_{16}$ | $2^{5}$ | $2^{3}$ | $20$ | $C_2\times C_4$ | Nilpotent - 2 |
32.38 | $\OD_{16}:C_2$ | $2^{5}$ | $2^{3}$ | $20$ | $C_8$ | Nilpotent - 2 |
32.39 | $C_2\times D_8$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.40 | $C_2\times \SD_{16}$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.41 | $C_2\times Q_{16}$ | $2^{5}$ | $2^{3}$ | $14$ | $C_2^2$ | Nilpotent - 3 |
32.42 | $D_8:C_2$ | $2^{5}$ | $2^{3}$ | $14$ | $C_4$ | Nilpotent - 3 |
64.4 | $C_2^3:C_8$ | $2^{6}$ | $2^{3}$ | $22$ | $C_2^2$ | Nilpotent - 3 |
64.5 | $C_2^2.\OD_{16}$ | $2^{6}$ | $2^{3}$ | $22$ | $C_2^2$ | Nilpotent - 3 |
64.6 | $D_4:C_8$ | $2^{6}$ | $2^{3}$ | $28$ | $C_2\times C_4$ | Nilpotent - 3 |
64.7 | $Q_8:C_8$ | $2^{6}$ | $2^{3}$ | $28$ | $C_2\times C_4$ | Nilpotent - 3 |
64.8 | $C_2^2.D_8$ | $2^{6}$ | $2^{3}$ | $19$ | $C_2^2$ | Nilpotent - 3 |
64.9 | $C_2^2.Q_{16}$ | $2^{6}$ | $2^{3}$ | $19$ | $C_2^2$ | Nilpotent - 3 |
64.10 | $C_4^2.C_2^2$ | $2^{6}$ | $2^{3}$ | $19$ | $C_2^2$ | Nilpotent - 3 |
64.11 | $C_4^2.C_2^2$ | $2^{6}$ | $2^{3}$ | $19$ | $C_2^2$ | Nilpotent - 3 |
64.12 | $C_4.D_8$ | $2^{6}$ | $2^{3}$ | $19$ | $C_2^2$ | Nilpotent - 3 |
64.13 | $C_4.D_8$ | $2^{6}$ | $2^{3}$ | $19$ | $C_2^2$ | Nilpotent - 3 |
64.14 | $C_4.Q_{16}$ | $2^{6}$ | $2^{3}$ | $19$ | $C_2^2$ | Nilpotent - 3 |
64.15 | $C_8:C_8$ | $2^{6}$ | $2^{3}$ | $28$ | $C_2\times C_4$ | Nilpotent - 3 |
64.16 | $C_8:C_8$ | $2^{6}$ | $2^{3}$ | $28$ | $C_2\times C_4$ | Nilpotent - 3 |
64.18 | $C_4^2:C_4$ | $2^{6}$ | $2^{3}$ | $22$ | $C_4$ | Nilpotent - 2 |
64.20 | $C_4^2:C_4$ | $2^{6}$ | $2^{3}$ | $28$ | $C_2\times C_4$ | Nilpotent - 3 |
64.23 | $C_2^2.C_4^2$ | $2^{6}$ | $2^{2}$ | $22$ | $C_2^2$ | Nilpotent - 3 |
64.24 | $\OD_{16}:C_4$ | $2^{6}$ | $2^{3}$ | $22$ | $C_2^2$ | Nilpotent - 3 |
64.25 | $\OD_{16}:C_4$ | $2^{6}$ | $2^{3}$ | $22$ | $C_4$ | Nilpotent - 3 |
64.28 | $C_{16}:C_4$ | $2^{6}$ | $2^{4}$ | $22$ | $C_4$ | Nilpotent - 2 |
64.29 | $C_2^2:C_{16}$ | $2^{6}$ | $2^{4}$ | $40$ | $C_2\times C_8$ | Nilpotent - 2 |