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Label | Name | Order | Exponent | $\card{\mathrm{conj}(G)}$ | Center | Type - length |
---|---|---|---|---|---|---|
1001.1 | $C_{1001}$ | $7 \cdot 11 \cdot 13$ | $7 \cdot 11 \cdot 13$ | $1001$ | $C_{1001}$ | Cyclic |
1002.1 | $S_3\times C_{167}$ | $2 \cdot 3 \cdot 167$ | $2 \cdot 3 \cdot 167$ | $501$ | $C_{167}$ | Solvable - 2 |
1002.2 | $C_3\times D_{167}$ | $2 \cdot 3 \cdot 167$ | $2 \cdot 3 \cdot 167$ | $255$ | $C_3$ | Solvable - 2 |
1002.3 | $D_{501}$ | $2 \cdot 3 \cdot 167$ | $2 \cdot 3 \cdot 167$ | $252$ | $C_1$ | Solvable - 2 |
1002.4 | $C_{1002}$ | $2 \cdot 3 \cdot 167$ | $2 \cdot 3 \cdot 167$ | $1002$ | $C_{1002}$ | Cyclic |
1003.1 | $C_{1003}$ | $17 \cdot 59$ | $17 \cdot 59$ | $1003$ | $C_{1003}$ | Cyclic |
1004.1 | $C_{251}:C_4$ | $2^{2} \cdot 251$ | $2^{2} \cdot 251$ | $254$ | $C_2$ | Solvable - 2 |
1004.2 | $C_{1004}$ | $2^{2} \cdot 251$ | $2^{2} \cdot 251$ | $1004$ | $C_{1004}$ | Cyclic |
1004.3 | $D_{502}$ | $2^{2} \cdot 251$ | $2 \cdot 251$ | $254$ | $C_2$ | Solvable - 2 |
1004.4 | $C_2\times C_{502}$ | $2^{2} \cdot 251$ | $2 \cdot 251$ | $1004$ | $C_2\times C_{502}$ | Abelian - 2 |
1005.1 | $C_{335}:C_3$ | $3 \cdot 5 \cdot 67$ | $3 \cdot 5 \cdot 67$ | $125$ | $C_5$ | Solvable - 2 |
1005.2 | $C_{1005}$ | $3 \cdot 5 \cdot 67$ | $3 \cdot 5 \cdot 67$ | $1005$ | $C_{1005}$ | Cyclic |
1006.1 | $D_{503}$ | $2 \cdot 503$ | $2 \cdot 503$ | $253$ | $C_1$ | Solvable - 2 |
1006.2 | $C_{1006}$ | $2 \cdot 503$ | $2 \cdot 503$ | $1006$ | $C_{1006}$ | Cyclic |
1007.1 | $C_{1007}$ | $19 \cdot 53$ | $19 \cdot 53$ | $1007$ | $C_{1007}$ | Cyclic |
1008.1 | $C_7:C_{144}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{4} \cdot 3^{2} \cdot 7$ | $168$ | $C_{24}$ | Solvable - 2 |
1008.2 | $C_7:C_{144}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{4} \cdot 3^{2} \cdot 7$ | $240$ | $C_{48}$ | Solvable - 2 |
1008.3 | $C_9:C_{112}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{4} \cdot 3^{2} \cdot 7$ | $336$ | $C_{56}$ | Solvable - 2 |
1008.4 | $C_7:C_{144}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{4} \cdot 3^{2} \cdot 7$ | $360$ | $C_{72}$ | Solvable - 2 |
1008.5 | $C_{63}:C_{16}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{4} \cdot 3^{2} \cdot 7$ | $264$ | $C_8$ | Solvable - 2 |
1008.6 | $C_{1008}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{4} \cdot 3^{2} \cdot 7$ | $1008$ | $C_{1008}$ | Cyclic |
1008.7 | $C_{56}:C_{18}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $168$ | $C_{24}$ | Solvable - 2 |
1008.8 | $C_{56}:C_{18}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $114$ | $C_{12}$ | Solvable - 2 |
1008.9 | $C_{56}:C_{18}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $87$ | $C_6$ | Solvable - 2 |
1008.10 | $C_{56}:C_{18}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $87$ | $C_6$ | Solvable - 2 |
1008.11 | $C_{168}.C_6$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $87$ | $C_6$ | Solvable - 2 |
1008.12 | $C_{14}:C_{72}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $168$ | $C_2\times C_{12}$ | Solvable - 2 |
1008.13 | $C_{28}.C_{36}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $114$ | $C_{12}$ | Solvable - 2 |
1008.14 | $C_{28}:C_{36}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{2} \cdot 3^{2} \cdot 7$ | $168$ | $C_2\times C_{12}$ | Solvable - 2 |
1008.15 | $C_{14}.(C_2\times C_{36})$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{2} \cdot 3^{2} \cdot 7$ | $114$ | $C_2\times C_6$ | Solvable - 2 |
1008.16 | $C_{28}:C_{36}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{2} \cdot 3^{2} \cdot 7$ | $114$ | $C_2\times C_6$ | Solvable - 2 |
1008.17 | $D_{14}:C_{36}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{2} \cdot 3^{2} \cdot 7$ | $114$ | $C_2\times C_6$ | Solvable - 2 |
1008.18 | $D_{28}:C_{18}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $78$ | $C_6$ | Solvable - 2 |
1008.19 | $C_7:(C_9\times \SD_{16})$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $78$ | $C_6$ | Solvable - 2 |
1008.20 | $D_{28}.C_{18}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $78$ | $C_6$ | Solvable - 2 |
1008.21 | $C_7:(C_9\times Q_{16})$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $78$ | $C_6$ | Solvable - 2 |
1008.22 | $(C_2\times C_{14}):C_{36}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{2} \cdot 3^{2} \cdot 7$ | $114$ | $C_2\times C_6$ | Solvable - 2 |
1008.23 | $C_{28}.D_{18}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $120$ | $C_4$ | Solvable - 2 |
1008.24 | $D_{63}:C_8$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $120$ | $C_4$ | Solvable - 2 |
1008.25 | $C_{63}:\OD_{16}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $114$ | $C_4$ | Solvable - 2 |
1008.26 | $C_{63}:\OD_{16}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $114$ | $C_4$ | Solvable - 2 |
1008.27 | $C_{63}:\SD_{16}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $102$ | $C_2$ | Solvable - 2 |
1008.28 | $C_{63}:\SD_{16}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $102$ | $C_2$ | Solvable - 2 |
1008.29 | $C_7:D_{72}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $102$ | $C_2$ | Solvable - 2 |
1008.30 | $C_{63}:Q_{16}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $102$ | $C_2$ | Solvable - 2 |
1008.31 | $C_{28}.D_{18}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $120$ | $C_4$ | Solvable - 2 |
1008.32 | $C_{63}:\OD_{16}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $114$ | $C_4$ | Solvable - 2 |
1008.33 | $C_{63}:D_8$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $90$ | $C_2$ | Solvable - 2 |
1008.34 | $C_9:D_{56}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $99$ | $C_2$ | Solvable - 2 |
1008.35 | $C_{63}:\SD_{16}$ | $2^{4} \cdot 3^{2} \cdot 7$ | $2^{3} \cdot 3^{2} \cdot 7$ | $90$ | $C_2$ | Solvable - 2 |