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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
256.1 | $C_{256}$ | $2^{8}$ | $2^{8}$ | $256$ | $C_{256}$ | Cyclic |
256.2 | $C_4.C_8^2$ | $2^{8}$ | $2^{3}$ | $88$ | $C_2^2\times C_4$ | Nilpotent - 2 |
256.3 | $C_4.C_8^2$ | $2^{8}$ | $2^{3}$ | $112$ | $C_2\times C_4^2$ | Nilpotent - 3 |
256.4 | $C_2^2.C_8^2$ | $2^{8}$ | $2^{3}$ | $88$ | $C_2^2\times C_4$ | Nilpotent - 3 |
256.5 | $(C_2\times C_4^2):C_8$ | $2^{8}$ | $2^{3}$ | $64$ | $C_2^3$ | Nilpotent - 3 |
256.6 | $C_4^2.D_8$ | $2^{8}$ | $2^{3}$ | $64$ | $C_2^3$ | Nilpotent - 3 |
256.7 | $C_4^3.C_2^2$ | $2^{8}$ | $2^{3}$ | $64$ | $C_2^3$ | Nilpotent - 3 |
256.8 | $(C_2^2\times C_8):C_8$ | $2^{8}$ | $2^{3}$ | $64$ | $C_2^3$ | Nilpotent - 3 |
256.9 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $64$ | $C_2^3$ | Nilpotent - 3 |
256.10 | $C_4^2.D_8$ | $2^{8}$ | $2^{3}$ | $64$ | $C_2^3$ | Nilpotent - 3 |
256.11 | $C_4^3.C_2^2$ | $2^{8}$ | $2^{3}$ | $64$ | $C_2^3$ | Nilpotent - 3 |
256.12 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $64$ | $C_2^3$ | Nilpotent - 3 |
256.13 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $76$ | $C_2^4$ | Nilpotent - 3 |
256.14 | $(C_2\times \OD_{16}):C_8$ | $2^{8}$ | $2^{3}$ | $76$ | $C_2^2\times C_4$ | Nilpotent - 3 |
256.15 | $C_4^2.D_8$ | $2^{8}$ | $2^{3}$ | $76$ | $C_2^2\times C_4$ | Nilpotent - 3 |
256.16 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $76$ | $C_2^2\times C_4$ | Nilpotent - 3 |
256.17 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $76$ | $C_2^2\times C_4$ | Nilpotent - 3 |
256.18 | $C_4^3.C_2^2$ | $2^{8}$ | $2^{3}$ | $76$ | $C_2^2\times C_4$ | Nilpotent - 3 |
256.19 | $C_4^2.D_8$ | $2^{8}$ | $2^{3}$ | $76$ | $C_2^2\times C_4$ | Nilpotent - 3 |
256.20 | $C_2^4.C_4^2$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.21 | $C_2^4.C_4^2$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.22 | $C_2^4.C_4^2$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.23 | $C_2^4.D_8$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.24 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.25 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.26 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.27 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.28 | $C_4^2.D_8$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.29 | $C_4^2.D_8$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.30 | $C_4^3.C_2^2$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.31 | $C_4^3.C_2^2$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.32 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.33 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.34 | $(C_2\times C_4^2).D_4$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.35 | $C_2^5.Q_8$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.36 | $C_4^3.C_2^2$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.37 | $C_4^2.D_8$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.38 | $C_4^2.D_8$ | $2^{8}$ | $2^{3}$ | $52$ | $C_2^3$ | Nilpotent - 3 |
256.39 | $C_{16}^2$ | $2^{8}$ | $2^{4}$ | $256$ | $C_{16}^2$ | Abelian - 2 |
256.40 | $C_{16}:C_{16}$ | $2^{8}$ | $2^{4}$ | $160$ | $C_8^2$ | Nilpotent - 2 |
256.41 | $C_{16}:C_{16}$ | $2^{8}$ | $2^{4}$ | $88$ | $C_4^2$ | Nilpotent - 2 |
256.42 | $C_2^4:C_{16}$ | $2^{8}$ | $2^{4}$ | $52$ | $C_2\times C_4$ | Nilpotent - 4 |
256.43 | $C_2^3.\OD_{32}$ | $2^{8}$ | $2^{4}$ | $52$ | $C_2\times C_4$ | Nilpotent - 4 |
256.44 | $(C_2\times D_4):C_{16}$ | $2^{8}$ | $2^{4}$ | $52$ | $C_2\times C_4$ | Nilpotent - 4 |
256.45 | $(C_2\times Q_8):C_{16}$ | $2^{8}$ | $2^{4}$ | $52$ | $C_2\times C_4$ | Nilpotent - 4 |
256.46 | $C_2^4.\OD_{16}$ | $2^{8}$ | $2^{4}$ | $46$ | $C_2\times C_4$ | Nilpotent - 4 |
256.47 | $C_2^4.\OD_{16}$ | $2^{8}$ | $2^{4}$ | $46$ | $C_2\times C_4$ | Nilpotent - 4 |
256.48 | $(C_2^2\times C_8).D_4$ | $2^{8}$ | $2^{4}$ | $46$ | $C_2\times C_4$ | Nilpotent - 4 |
256.49 | $(C_2^2\times C_8).D_4$ | $2^{8}$ | $2^{4}$ | $46$ | $C_2\times C_4$ | Nilpotent - 4 |
256.50 | $C_4^2:C_{16}$ | $2^{8}$ | $2^{4}$ | $52$ | $C_2\times C_4$ | Nilpotent - 4 |