The results below are complete, since the LMFDB contains all groups of order at most 2000 except orders larger than 500 that are multiples of 128

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Order Exponent Nilpotency class Nilpotent
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Results (1-50 of 4320 matches)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
257.1 $C_{257}$ $257$ $257$ 257 $C_{257}$ $C_1$ $C_1$ $C_{257}$ Cyclic
258.1 $C_{43}:C_6$ $2 \cdot 3 \cdot 43$ $2 \cdot 3 \cdot 43$ 13 $C_1$ $C_{43}:C_6$ $C_{43}$ $C_{6}$ Solvable - 2
258.2 $C_{43}:C_6$ $2 \cdot 3 \cdot 43$ $2 \cdot 3 \cdot 43$ 34 $C_2$ $C_{43}:C_3$ $C_{43}$ $C_{6}$ Solvable - 2
258.3 $S_3\times C_{43}$ $2 \cdot 3 \cdot 43$ $2 \cdot 3 \cdot 43$ 129 $C_{43}$ $S_3$ $C_3$ $C_{86}$ Solvable - 2
258.4 $C_3\times D_{43}$ $2 \cdot 3 \cdot 43$ $2 \cdot 3 \cdot 43$ 69 $C_3$ $D_{43}$ $C_{43}$ $C_{6}$ Solvable - 2
258.5 $D_{129}$ $2 \cdot 3 \cdot 43$ $2 \cdot 3 \cdot 43$ 66 $C_1$ $D_{129}$ $C_{129}$ $C_{2}$ Solvable - 2
258.6 $C_{258}$ $2 \cdot 3 \cdot 43$ $2 \cdot 3 \cdot 43$ 258 $C_{258}$ $C_1$ $C_1$ $C_{258}$ Cyclic
259.1 $C_{259}$ $7 \cdot 37$ $7 \cdot 37$ 259 $C_{259}$ $C_1$ $C_1$ $C_{259}$ Cyclic
260.1 $C_5:C_{52}$ $2^{2} \cdot 5 \cdot 13$ $2^{2} \cdot 5 \cdot 13$ 104 $C_{26}$ $D_5$ $C_5$ $C_{52}$ Solvable - 2
260.2 $C_{13}:C_{20}$ $2^{2} \cdot 5 \cdot 13$ $2^{2} \cdot 5 \cdot 13$ 80 $C_{10}$ $D_{13}$ $C_{13}$ $C_{20}$ Solvable - 2
260.3 $C_{65}:C_4$ $2^{2} \cdot 5 \cdot 13$ $2^{2} \cdot 5 \cdot 13$ 68 $C_2$ $D_{65}$ $C_{65}$ $C_{4}$ Solvable - 2
260.4 $C_{260}$ $2^{2} \cdot 5 \cdot 13$ $2^{2} \cdot 5 \cdot 13$ 260 $C_{260}$ $C_1$ $C_1$ $C_{260}$ Cyclic
260.5 $C_{13}:C_{20}$ $2^{2} \cdot 5 \cdot 13$ $2^{2} \cdot 5 \cdot 13$ 35 $C_5$ $C_{13}:C_4$ $C_{13}$ $C_{20}$ Solvable - 2
260.6 $C_{65}:C_4$ $2^{2} \cdot 5 \cdot 13$ $2^{2} \cdot 5 \cdot 13$ 23 $C_1$ $C_{65}:C_4$ $C_{65}$ $C_{4}$ Solvable - 2
260.7 $C_{13}\times F_5$ $2^{2} \cdot 5 \cdot 13$ $2^{2} \cdot 5 \cdot 13$ 65 $C_{13}$ $F_5$ $C_5$ $C_{52}$ Solvable - 2
260.8 $C_{65}:C_4$ $2^{2} \cdot 5 \cdot 13$ $2^{2} \cdot 5 \cdot 13$ 29 $C_1$ $C_{65}:C_4$ $C_{65}$ $C_{4}$ Solvable - 2
260.9 $C_{65}:C_4$ $2^{2} \cdot 5 \cdot 13$ $2^{2} \cdot 5 \cdot 13$ 20 $C_1$ $C_{65}:C_4$ $C_{65}$ $C_{4}$ Solvable - 2
260.10 $C_{65}:C_4$ $2^{2} \cdot 5 \cdot 13$ $2^{2} \cdot 5 \cdot 13$ 20 $C_1$ $C_{65}:C_4$ $C_{65}$ $C_{4}$ Solvable - 2
260.11 $D_5\times D_{13}$ $2^{2} \cdot 5 \cdot 13$ $2 \cdot 5 \cdot 13$ 32 $C_1$ $D_5\times D_{13}$ $C_{65}$ $C_{2}^{2}$ Solvable - 2
260.12 $C_5\times D_{26}$ $2^{2} \cdot 5 \cdot 13$ $2 \cdot 5 \cdot 13$ 80 $C_{10}$ $D_{13}$ $C_{13}$ $C_{2} \times C_{10}$ Solvable - 2
260.13 $C_{13}\times D_{10}$ $2^{2} \cdot 5 \cdot 13$ $2 \cdot 5 \cdot 13$ 104 $C_{26}$ $D_5$ $C_5$ $C_{2} \times C_{26}$ Solvable - 2
260.14 $D_{130}$ $2^{2} \cdot 5 \cdot 13$ $2 \cdot 5 \cdot 13$ 68 $C_2$ $D_{65}$ $C_{65}$ $C_{2}^{2}$ Solvable - 2
260.15 $C_2\times C_{130}$ $2^{2} \cdot 5 \cdot 13$ $2 \cdot 5 \cdot 13$ 260 $C_2\times C_{130}$ $C_1$ $C_1$ $C_{2} \times C_{130}$ Abelian - 2
261.1 $C_{261}$ $3^{2} \cdot 29$ $3^{2} \cdot 29$ 261 $C_{261}$ $C_1$ $C_1$ $C_{261}$ Cyclic
261.2 $C_3\times C_{87}$ $3^{2} \cdot 29$ $3 \cdot 29$ 261 $C_3\times C_{87}$ $C_1$ $C_1$ $C_{3} \times C_{87}$ Abelian - 2
262.1 $D_{131}$ $2 \cdot 131$ $2 \cdot 131$ 67 $C_1$ $D_{131}$ $C_{131}$ $C_{2}$ Solvable - 2
262.2 $C_{262}$ $2 \cdot 131$ $2 \cdot 131$ 262 $C_{262}$ $C_1$ $C_1$ $C_{262}$ Cyclic
263.1 $C_{263}$ $263$ $263$ 263 $C_{263}$ $C_1$ $C_1$ $C_{263}$ Cyclic
264.1 $C_3:C_{88}$ $2^{3} \cdot 3 \cdot 11$ $2^{3} \cdot 3 \cdot 11$ 132 $C_{44}$ $S_3$ $C_3$ $C_{88}$ Solvable - 2
264.2 $C_{11}:C_{24}$ $2^{3} \cdot 3 \cdot 11$ $2^{3} \cdot 3 \cdot 11$ 84 $C_{12}$ $D_{11}$ $C_{11}$ $C_{24}$ Solvable - 2
264.3 $C_{33}:C_8$ $2^{3} \cdot 3 \cdot 11$ $2^{3} \cdot 3 \cdot 11$ 72 $C_4$ $D_{33}$ $C_{33}$ $C_{8}$ Solvable - 2
264.4 $C_{264}$ $2^{3} \cdot 3 \cdot 11$ $2^{3} \cdot 3 \cdot 11$ 264 $C_{264}$ $C_1$ $C_1$ $C_{264}$ Cyclic
264.5 $C_6.D_{22}$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 42 $C_2$ $S_3\times D_{11}$ $C_{33}$ $C_{2} \times C_{4}$ Solvable - 2
264.6 $C_6.D_{22}$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 42 $C_2$ $S_3\times D_{11}$ $C_{33}$ $C_{2} \times C_{4}$ Solvable - 2
264.7 $D_{33}:C_4$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 42 $C_2$ $S_3\times D_{11}$ $C_{33}$ $C_{2} \times C_{4}$ Solvable - 2
264.8 $C_{33}:D_4$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 39 $C_2$ $S_3\times D_{11}$ $C_{66}$ $C_{2}^{2}$ Solvable - 2
264.9 $C_3:D_{44}$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 39 $C_2$ $S_3\times D_{11}$ $C_{66}$ $C_{2}^{2}$ Solvable - 2
264.10 $C_{11}:D_{12}$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 39 $C_2$ $S_3\times D_{11}$ $C_{66}$ $C_{2}^{2}$ Solvable - 2
264.11 $C_{33}:Q_8$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 39 $C_2$ $S_3\times D_{11}$ $C_{66}$ $C_{2}^{2}$ Solvable - 2
264.12 $C_{11}\times \SL(2,3)$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 77 $C_{22}$ $A_4$ $Q_8$ $C_{33}$ Solvable - 3
264.13 $C_{33}:Q_8$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 75 $C_6$ $D_{22}$ $C_{22}$ $C_{2} \times C_{6}$ Solvable - 2
264.14 $C_{12}\times D_{11}$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 84 $C_{12}$ $D_{11}$ $C_{11}$ $C_{2} \times C_{12}$ Solvable - 2
264.15 $C_3\times D_{44}$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 75 $C_6$ $D_{22}$ $C_{22}$ $C_{2} \times C_{6}$ Solvable - 2
264.16 $C_{22}:C_{12}$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 84 $C_2\times C_6$ $D_{11}$ $C_{11}$ $C_{2} \times C_{12}$ Solvable - 2
264.17 $C_{33}:D_4$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 75 $C_6$ $D_{22}$ $C_{22}$ $C_{2} \times C_{6}$ Solvable - 2
264.18 $C_{33}:Q_8$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 99 $C_{22}$ $D_6$ $C_6$ $C_{2} \times C_{22}$ Solvable - 2
264.19 $S_3\times C_{44}$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 132 $C_{44}$ $S_3$ $C_3$ $C_{2} \times C_{44}$ Solvable - 2
264.20 $C_{11}\times D_{12}$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 99 $C_{22}$ $D_6$ $C_6$ $C_{2} \times C_{22}$ Solvable - 2
264.21 $C_6:C_{44}$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 132 $C_2\times C_{22}$ $S_3$ $C_3$ $C_{2} \times C_{44}$ Solvable - 2
264.22 $D_6:C_{22}$ $2^{3} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 99 $C_{22}$ $D_6$ $C_6$ $C_{2} \times C_{22}$ Solvable - 2
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