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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
128.1 | $C_{128}$ | $2^{7}$ | $2^{7}$ | $128$ | $C_{128}$ | Cyclic |
128.2 | $(C_2\times D_4):C_8$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2^3$ | Nilpotent - 3 |
128.3 | $(C_2\times C_4).D_8$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2^3$ | Nilpotent - 3 |
128.4 | $(C_2\times Q_8):C_8$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2^3$ | Nilpotent - 3 |
128.5 | $C_2.C_8^2$ | $2^{7}$ | $2^{3}$ | $80$ | $C_2\times C_4^2$ | Nilpotent - 2 |
128.6 | $C_4^2:C_8$ | $2^{7}$ | $2^{3}$ | $44$ | $C_2\times C_4$ | Nilpotent - 2 |
128.7 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $44$ | $C_2\times C_4$ | Nilpotent - 2 |
128.8 | $C_4^2:C_8$ | $2^{7}$ | $2^{3}$ | $56$ | $C_4^2$ | Nilpotent - 3 |
128.9 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $56$ | $C_2^2\times C_4$ | Nilpotent - 3 |
128.10 | $\OD_{16}:C_8$ | $2^{7}$ | $2^{3}$ | $56$ | $C_4^2$ | Nilpotent - 3 |
128.11 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $56$ | $C_2^2\times C_4$ | Nilpotent - 3 |
128.12 | $C_2^3.C_4^2$ | $2^{7}$ | $2^{3}$ | $44$ | $C_2^3$ | Nilpotent - 3 |
128.13 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $44$ | $C_2\times C_4$ | Nilpotent - 3 |
128.14 | $C_2^3.C_4^2$ | $2^{7}$ | $2^{3}$ | $44$ | $C_2\times C_4$ | Nilpotent - 3 |
128.15 | $\OD_{16}:C_8$ | $2^{7}$ | $2^{3}$ | $44$ | $C_2\times C_4$ | Nilpotent - 3 |
128.16 | $C_2^4.D_4$ | $2^{7}$ | $2^{3}$ | $32$ | $C_2^2$ | Nilpotent - 3 |
128.17 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $32$ | $C_2^2$ | Nilpotent - 3 |
128.18 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $32$ | $C_2^2$ | Nilpotent - 3 |
128.19 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $32$ | $C_2^2$ | Nilpotent - 3 |
128.20 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $32$ | $C_2^2$ | Nilpotent - 3 |
128.21 | $C_2^3.D_8$ | $2^{7}$ | $2^{3}$ | $32$ | $C_2^2$ | Nilpotent - 3 |
128.22 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $32$ | $C_2^2$ | Nilpotent - 3 |
128.23 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $32$ | $C_2^2$ | Nilpotent - 3 |
128.24 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $32$ | $C_2^2$ | Nilpotent - 3 |
128.25 | $C_2^4.Q_8$ | $2^{7}$ | $2^{3}$ | $32$ | $C_2^2$ | Nilpotent - 3 |
128.26 | $C_2^3.D_8$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2^3$ | Nilpotent - 3 |
128.27 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2^3$ | Nilpotent - 3 |
128.28 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2^3$ | Nilpotent - 3 |
128.29 | $C_2^4.D_4$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2\times C_4$ | Nilpotent - 3 |
128.30 | $C_2^4.Q_8$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2\times C_4$ | Nilpotent - 3 |
128.31 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2\times C_4$ | Nilpotent - 3 |
128.32 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2\times C_4$ | Nilpotent - 3 |
128.33 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2\times C_4$ | Nilpotent - 3 |
128.34 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2\times C_4$ | Nilpotent - 3 |
128.35 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $38$ | $C_2\times C_4$ | Nilpotent - 3 |
128.36 | $C_2^3.C_4^2$ | $2^{7}$ | $2^{2}$ | $26$ | $C_2^2$ | Nilpotent - 3 |
128.37 | $C_2^3.C_4^2$ | $2^{7}$ | $2^{3}$ | $26$ | $C_2^2$ | Nilpotent - 3 |
128.38 | $C_2^3.C_4^2$ | $2^{7}$ | $2^{3}$ | $26$ | $C_2^2$ | Nilpotent - 3 |
128.39 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $26$ | $C_2^2$ | Nilpotent - 3 |
128.40 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $26$ | $C_2^2$ | Nilpotent - 3 |
128.41 | $C_4^2.D_4$ | $2^{7}$ | $2^{3}$ | $26$ | $C_2^2$ | Nilpotent - 3 |
128.42 | $C_8\times C_{16}$ | $2^{7}$ | $2^{4}$ | $128$ | $C_8\times C_{16}$ | Abelian - 2 |
128.43 | $C_{16}:C_8$ | $2^{7}$ | $2^{4}$ | $80$ | $C_4\times C_8$ | Nilpotent - 2 |
128.44 | $C_8:C_{16}$ | $2^{7}$ | $2^{4}$ | $80$ | $C_4\times C_8$ | Nilpotent - 2 |
128.45 | $C_{16}:C_8$ | $2^{7}$ | $2^{4}$ | $44$ | $C_2\times C_4$ | Nilpotent - 2 |
128.46 | $C_2^3:C_{16}$ | $2^{7}$ | $2^{4}$ | $44$ | $C_2\times C_4$ | Nilpotent - 3 |
128.47 | $C_2^3.\OD_{16}$ | $2^{7}$ | $2^{4}$ | $38$ | $C_2\times C_4$ | Nilpotent - 3 |
128.48 | $C_2^4:C_8$ | $2^{7}$ | $2^{3}$ | $26$ | $C_2^2$ | Nilpotent - 4 |
128.49 | $C_2^3.\OD_{16}$ | $2^{7}$ | $2^{3}$ | $26$ | $C_2^2$ | Nilpotent - 4 |
128.50 | $(C_2\times D_4):C_8$ | $2^{7}$ | $2^{3}$ | $26$ | $C_2^2$ | Nilpotent - 4 |