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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
384.1 | $C_3:C_{128}$ | $2^{7} \cdot 3$ | $2^{7} \cdot 3$ | $192$ | $C_{64}$ | Solvable - 2 |
384.2 | $C_{384}$ | $2^{7} \cdot 3$ | $2^{7} \cdot 3$ | $384$ | $C_{384}$ | Cyclic |
384.3 | $C_4^2.\SL(2,3)$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $32$ | $C_2$ | Solvable - 3 |
384.4 | $C_2^4.\SL(2,3)$ | $2^{7} \cdot 3$ | $2^{2} \cdot 3$ | $14$ | $C_1$ | Solvable - 3 |
384.5 | $C_4^2.\SL(2,3)$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $14$ | $C_1$ | Solvable - 3 |
384.6 | $C_4^2.\SL(2,3)$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $14$ | $C_1$ | Solvable - 3 |
384.7 | $S_3\times C_{64}$ | $2^{7} \cdot 3$ | $2^{6} \cdot 3$ | $192$ | $C_{64}$ | Solvable - 2 |
384.8 | $C_{192}:C_2$ | $2^{7} \cdot 3$ | $2^{6} \cdot 3$ | $144$ | $C_{32}$ | Solvable - 2 |
384.9 | $D_{192}$ | $2^{7} \cdot 3$ | $2^{6} \cdot 3$ | $99$ | $C_2$ | Solvable - 2 |
384.10 | $C_{192}:C_2$ | $2^{7} \cdot 3$ | $2^{6} \cdot 3$ | $99$ | $C_2$ | Solvable - 2 |
384.11 | $C_3:Q_{128}$ | $2^{7} \cdot 3$ | $2^{6} \cdot 3$ | $99$ | $C_2$ | Solvable - 2 |
384.12 | $C_{24}:C_{16}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $192$ | $C_8^2$ | Solvable - 2 |
384.13 | $C_6.C_8^2$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $144$ | $C_4\times C_8$ | Solvable - 2 |
384.14 | $C_{24}:C_{16}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $144$ | $C_4\times C_8$ | Solvable - 2 |
384.15 | $C_{24}:C_{16}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $120$ | $C_2\times C_8$ | Solvable - 2 |
384.16 | $C_{24}:C_{16}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $120$ | $C_2\times C_8$ | Solvable - 2 |
384.17 | $D_{24}:C_8$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $108$ | $C_8$ | Solvable - 2 |
384.18 | $C_{24}.\OD_{16}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $84$ | $C_2\times C_4$ | Solvable - 2 |
384.19 | $D_{24}:C_8$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $72$ | $C_4$ | Solvable - 2 |
384.20 | $(C_2^2\times D_6):C_8$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $48$ | $C_2^2$ | Solvable - 2 |
384.21 | $C_2^3.(S_3\times C_8)$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $48$ | $C_2^2$ | Solvable - 2 |
384.22 | $C_2^3.(S_3\times C_8)$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $48$ | $C_2^2$ | Solvable - 2 |
384.23 | $C_2^3.(S_3\times C_8)$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $48$ | $C_2^2$ | Solvable - 2 |
384.24 | $C_2^3.D_{24}$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $45$ | $C_2^2$ | Solvable - 2 |
384.25 | $C_2^4.D_{12}$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $45$ | $C_2^2$ | Solvable - 2 |
384.26 | $C_2^3.D_{24}$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $45$ | $C_2^2$ | Solvable - 2 |
384.27 | $C_2^4.D_{12}$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $45$ | $C_2^2$ | Solvable - 2 |
384.28 | $(C_2^2\times C_4).D_{12}$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $48$ | $C_2^2$ | Solvable - 2 |
384.29 | $(C_2^2\times C_4).D_{12}$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $48$ | $C_2^2$ | Solvable - 2 |
384.30 | $(C_2\times D_{12}):C_8$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $48$ | $C_2^2$ | Solvable - 2 |
384.31 | $(C_2^2\times C_4).D_{12}$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $48$ | $C_2^2$ | Solvable - 2 |
384.32 | $(C_2\times C_4).D_{24}$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $45$ | $C_2^2$ | Solvable - 2 |
384.33 | $(C_2\times C_{12}).Q_{16}$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $45$ | $C_2^2$ | Solvable - 2 |
384.34 | $(C_2\times C_4).D_{24}$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $45$ | $C_2^2$ | Solvable - 2 |
384.35 | $(C_2\times C_{12}).Q_{16}$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $45$ | $C_2^2$ | Solvable - 2 |
384.36 | $(C_4\times C_{12}).D_4$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $36$ | $C_2$ | Solvable - 3 |
384.37 | $(C_4\times C_{12}).D_4$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $36$ | $C_2$ | Solvable - 3 |
384.38 | $(C_4\times C_{12}).D_4$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $36$ | $C_2$ | Solvable - 3 |
384.39 | $(C_4\times C_{12}).D_4$ | $2^{7} \cdot 3$ | $2^{3} \cdot 3$ | $36$ | $C_2$ | Solvable - 3 |
384.40 | $C_{24}.\OD_{16}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $60$ | $C_2^2$ | Solvable - 2 |
384.41 | $D_{24}:C_8$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $60$ | $C_2^2$ | Solvable - 2 |
384.42 | $C_{24}.\OD_{16}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $60$ | $C_2^2$ | Solvable - 2 |
384.43 | $C_8.D_{24}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $57$ | $C_2^2$ | Solvable - 2 |
384.44 | $C_{24}.Q_{16}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $57$ | $C_2^2$ | Solvable - 2 |
384.45 | $C_{12}.D_{16}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $72$ | $C_2\times C_4$ | Solvable - 2 |
384.46 | $C_{12}.\SD_{32}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $72$ | $C_2\times C_4$ | Solvable - 2 |
384.47 | $D_{24}:C_8$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $72$ | $C_2\times C_4$ | Solvable - 2 |
384.48 | $C_{12}.Q_{32}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $72$ | $C_2\times C_4$ | Solvable - 2 |
384.49 | $C_8.D_{24}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $57$ | $C_2^2$ | Solvable - 2 |
384.50 | $C_8.D_{24}$ | $2^{7} \cdot 3$ | $2^{4} \cdot 3$ | $57$ | $C_2^2$ | Solvable - 2 |