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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
96.1 | $C_3:C_{32}$ | $2^{5} \cdot 3$ | $2^{5} \cdot 3$ | $48$ | $C_{16}$ | Solvable - 2 |
96.3 | $C_2^3.A_4$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $12$ | $C_2$ | Solvable - 3 |
96.4 | $S_3\times C_{16}$ | $2^{5} \cdot 3$ | $2^{4} \cdot 3$ | $48$ | $C_{16}$ | Solvable - 2 |
96.5 | $C_{48}:C_2$ | $2^{5} \cdot 3$ | $2^{4} \cdot 3$ | $36$ | $C_8$ | Solvable - 2 |
96.6 | $D_{48}$ | $2^{5} \cdot 3$ | $2^{4} \cdot 3$ | $27$ | $C_2$ | Solvable - 2 |
96.7 | $C_{48}:C_2$ | $2^{5} \cdot 3$ | $2^{4} \cdot 3$ | $27$ | $C_2$ | Solvable - 2 |
96.8 | $C_3:Q_{32}$ | $2^{5} \cdot 3$ | $2^{4} \cdot 3$ | $27$ | $C_2$ | Solvable - 2 |
96.9 | $C_{12}:C_8$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $48$ | $C_4^2$ | Solvable - 2 |
96.10 | $C_6.C_4^2$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $36$ | $C_2\times C_4$ | Solvable - 2 |
96.11 | $C_{12}:C_8$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $36$ | $C_2\times C_4$ | Solvable - 2 |
96.12 | $D_{12}:C_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $30$ | $C_4$ | Solvable - 2 |
96.13 | $C_2^2.D_{12}$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $21$ | $C_2$ | Solvable - 2 |
96.14 | $C_6.D_8$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $24$ | $C_2^2$ | Solvable - 2 |
96.15 | $C_{12}.Q_8$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $24$ | $C_2^2$ | Solvable - 2 |
96.16 | $D_{12}:C_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $24$ | $C_2^2$ | Solvable - 2 |
96.17 | $C_4.D_{12}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $24$ | $C_2^2$ | Solvable - 2 |
96.18 | $C_6:C_{16}$ | $2^{5} \cdot 3$ | $2^{4} \cdot 3$ | $48$ | $C_2\times C_8$ | Solvable - 2 |
96.19 | $C_3:\OD_{32}$ | $2^{5} \cdot 3$ | $2^{4} \cdot 3$ | $36$ | $C_8$ | Solvable - 2 |
96.20 | $C_{24}:C_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $48$ | $C_2\times C_8$ | Solvable - 2 |
96.21 | $C_{12}.D_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $36$ | $C_2\times C_4$ | Solvable - 2 |
96.22 | $C_{24}:C_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $36$ | $C_2\times C_4$ | Solvable - 2 |
96.23 | $C_6.Q_{16}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $30$ | $C_2^2$ | Solvable - 2 |
96.24 | $C_{24}:C_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $30$ | $C_2^2$ | Solvable - 2 |
96.25 | $C_{24}:C_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $30$ | $C_2^2$ | Solvable - 2 |
96.26 | $C_{24}.C_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $30$ | $C_4$ | Solvable - 2 |
96.27 | $D_6:C_8$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $36$ | $C_2\times C_4$ | Solvable - 2 |
96.28 | $D_{12}:C_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $30$ | $C_2^2$ | Solvable - 2 |
96.29 | $C_{12}.D_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $24$ | $C_4$ | Solvable - 2 |
96.30 | $C_4.D_{12}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $21$ | $C_2$ | Solvable - 2 |
96.31 | $C_4.D_{12}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $21$ | $C_2$ | Solvable - 2 |
96.32 | $D_{12}:C_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $24$ | $C_4$ | Solvable - 2 |
96.33 | $C_3:D_{16}$ | $2^{5} \cdot 3$ | $2^{4} \cdot 3$ | $18$ | $C_2$ | Solvable - 2 |
96.34 | $C_3:\SD_{32}$ | $2^{5} \cdot 3$ | $2^{4} \cdot 3$ | $18$ | $C_2$ | Solvable - 2 |
96.35 | $Q_{16}:S_3$ | $2^{5} \cdot 3$ | $2^{4} \cdot 3$ | $18$ | $C_2$ | Solvable - 2 |
96.36 | $C_3:Q_{32}$ | $2^{5} \cdot 3$ | $2^{4} \cdot 3$ | $18$ | $C_2$ | Solvable - 2 |
96.37 | $C_{12}.D_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $36$ | $C_2\times C_4$ | Solvable - 2 |
96.38 | $C_6.C_4^2$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $36$ | $C_2^3$ | Solvable - 2 |
96.39 | $C_6.D_8$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $24$ | $C_2^2$ | Solvable - 2 |
96.40 | $C_{12}.D_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $21$ | $C_2$ | Solvable - 2 |
96.41 | $C_2^3.D_6$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $21$ | $C_2$ | Solvable - 2 |
96.42 | $C_6.Q_{16}$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $24$ | $C_2^2$ | Solvable - 2 |
96.43 | $C_{12}.D_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $21$ | $C_2$ | Solvable - 2 |
96.44 | $C_{12}.D_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $24$ | $C_4$ | Solvable - 2 |
96.64 | $C_4^2:S_3$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $10$ | $C_1$ | Solvable - 3 |
96.65 | $A_4:C_8$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $20$ | $C_4$ | Solvable - 3 |
96.66 | $\SL(2,3):C_4$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $16$ | $C_2^2$ | Solvable - 4 |
96.67 | $\GU(2,3)$ | $2^{5} \cdot 3$ | $2^{3} \cdot 3$ | $16$ | $C_4$ | Solvable - 4 |
96.68 | $C_4^2:C_6$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $16$ | $C_2$ | Solvable - 2 |
96.69 | $C_4\times \SL(2,3)$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $28$ | $C_2\times C_4$ | Solvable - 3 |
96.70 | $C_2^3:A_4$ | $2^{5} \cdot 3$ | $2^{2} \cdot 3$ | $10$ | $C_1$ | Solvable - 2 |