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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
65.1 | $C_{65}$ | $5 \cdot 13$ | $5 \cdot 13$ | $65$ | $C_{65}$ | Cyclic |
66.1 | $S_3\times C_{11}$ | $2 \cdot 3 \cdot 11$ | $2 \cdot 3 \cdot 11$ | $33$ | $C_{11}$ | Solvable - 2 |
66.2 | $C_3\times D_{11}$ | $2 \cdot 3 \cdot 11$ | $2 \cdot 3 \cdot 11$ | $21$ | $C_3$ | Solvable - 2 |
66.3 | $D_{33}$ | $2 \cdot 3 \cdot 11$ | $2 \cdot 3 \cdot 11$ | $18$ | $C_1$ | Solvable - 2 |
66.4 | $C_{66}$ | $2 \cdot 3 \cdot 11$ | $2 \cdot 3 \cdot 11$ | $66$ | $C_{66}$ | Cyclic |
67.1 | $C_{67}$ | $67$ | $67$ | $67$ | $C_{67}$ | Cyclic |
68.1 | $C_{17}:C_4$ | $2^{2} \cdot 17$ | $2^{2} \cdot 17$ | $20$ | $C_2$ | Solvable - 2 |
68.2 | $C_{68}$ | $2^{2} \cdot 17$ | $2^{2} \cdot 17$ | $68$ | $C_{68}$ | Cyclic |
68.3 | $C_{17}:C_4$ | $2^{2} \cdot 17$ | $2^{2} \cdot 17$ | $8$ | $C_1$ | Solvable - 2 |
68.4 | $D_{34}$ | $2^{2} \cdot 17$ | $2 \cdot 17$ | $20$ | $C_2$ | Solvable - 2 |
68.5 | $C_2\times C_{34}$ | $2^{2} \cdot 17$ | $2 \cdot 17$ | $68$ | $C_2\times C_{34}$ | Abelian - 2 |
69.1 | $C_{69}$ | $3 \cdot 23$ | $3 \cdot 23$ | $69$ | $C_{69}$ | Cyclic |
70.1 | $C_7\times D_5$ | $2 \cdot 5 \cdot 7$ | $2 \cdot 5 \cdot 7$ | $28$ | $C_7$ | Solvable - 2 |
70.2 | $C_5\times D_7$ | $2 \cdot 5 \cdot 7$ | $2 \cdot 5 \cdot 7$ | $25$ | $C_5$ | Solvable - 2 |
70.3 | $D_{35}$ | $2 \cdot 5 \cdot 7$ | $2 \cdot 5 \cdot 7$ | $19$ | $C_1$ | Solvable - 2 |
70.4 | $C_{70}$ | $2 \cdot 5 \cdot 7$ | $2 \cdot 5 \cdot 7$ | $70$ | $C_{70}$ | Cyclic |
71.1 | $C_{71}$ | $71$ | $71$ | $71$ | $C_{71}$ | Cyclic |
72.1 | $C_9:C_8$ | $2^{3} \cdot 3^{2}$ | $2^{3} \cdot 3^{2}$ | $24$ | $C_4$ | Solvable - 2 |
72.2 | $C_{72}$ | $2^{3} \cdot 3^{2}$ | $2^{3} \cdot 3^{2}$ | $72$ | $C_{72}$ | Cyclic |
72.3 | $Q_8:C_9$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3^{2}$ | $21$ | $C_6$ | Solvable - 3 |
72.4 | $C_9:Q_8$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3^{2}$ | $21$ | $C_2$ | Solvable - 2 |
72.5 | $C_4\times D_9$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3^{2}$ | $24$ | $C_4$ | Solvable - 2 |
72.6 | $D_{36}$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3^{2}$ | $21$ | $C_2$ | Solvable - 2 |
72.7 | $C_{18}:C_4$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3^{2}$ | $24$ | $C_2^2$ | Solvable - 2 |
72.8 | $C_9:D_4$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3^{2}$ | $21$ | $C_2$ | Solvable - 2 |
72.9 | $C_2\times C_{36}$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3^{2}$ | $72$ | $C_2\times C_{36}$ | Abelian - 2 |
72.10 | $D_4\times C_9$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3^{2}$ | $45$ | $C_{18}$ | Nilpotent - 2 |
72.11 | $Q_8\times C_9$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3^{2}$ | $45$ | $C_{18}$ | Nilpotent - 2 |
72.12 | $C_3:C_{24}$ | $2^{3} \cdot 3^{2}$ | $2^{3} \cdot 3$ | $36$ | $C_{12}$ | Solvable - 2 |
72.13 | $C_3^2:C_8$ | $2^{3} \cdot 3^{2}$ | $2^{3} \cdot 3$ | $24$ | $C_4$ | Solvable - 2 |
72.14 | $C_3\times C_{24}$ | $2^{3} \cdot 3^{2}$ | $2^{3} \cdot 3$ | $72$ | $C_3\times C_{24}$ | Abelian - 2 |
72.15 | $C_2^2:D_9$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3^{2}$ | $9$ | $C_1$ | Solvable - 3 |
72.16 | $C_2^2:C_{18}$ | $2^{3} \cdot 3^{2}$ | $2 \cdot 3^{2}$ | $24$ | $C_6$ | Solvable - 2 |
72.17 | $C_2\times D_{18}$ | $2^{3} \cdot 3^{2}$ | $2 \cdot 3^{2}$ | $24$ | $C_2^2$ | Solvable - 2 |
72.18 | $C_2^2\times C_{18}$ | $2^{3} \cdot 3^{2}$ | $2 \cdot 3^{2}$ | $72$ | $C_2^2\times C_{18}$ | Abelian - 3 |
72.19 | $C_3^2:C_8$ | $2^{3} \cdot 3^{2}$ | $2^{3} \cdot 3$ | $12$ | $C_2$ | Solvable - 2 |
72.20 | $C_6.D_6$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $18$ | $C_2$ | Solvable - 2 |
72.21 | $C_6.D_6$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $18$ | $C_2$ | Solvable - 2 |
72.22 | $D_6:S_3$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $15$ | $C_2$ | Solvable - 2 |
72.23 | $C_3:D_{12}$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $15$ | $C_2$ | Solvable - 2 |
72.24 | $C_3^2:Q_8$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $15$ | $C_2$ | Solvable - 2 |
72.25 | $C_3\times \SL(2,3)$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $21$ | $C_6$ | Solvable - 3 |
72.26 | $C_3^2:Q_8$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $27$ | $C_6$ | Solvable - 2 |
72.27 | $S_3\times C_{12}$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $36$ | $C_{12}$ | Solvable - 2 |
72.28 | $C_3\times D_{12}$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $27$ | $C_6$ | Solvable - 2 |
72.29 | $C_6:C_{12}$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $36$ | $C_2\times C_6$ | Solvable - 2 |
72.30 | $C_6\wr C_2$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $27$ | $C_6$ | Solvable - 2 |
72.31 | $C_3^2:Q_8$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $21$ | $C_2$ | Solvable - 2 |
72.32 | $C_{12}:S_3$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $24$ | $C_4$ | Solvable - 2 |
72.33 | $C_3:D_{12}$ | $2^{3} \cdot 3^{2}$ | $2^{2} \cdot 3$ | $21$ | $C_2$ | Solvable - 2 |