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Note: Search results may be incomplete due to uncomputed quantities: Outer aut. group order (4830 objects)

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Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
134.1 $D_{67}$ $2 \cdot 67$ $2 \cdot 67$ $35$ $C_1$ $D_{67}$ $C_{67}$ $C_{2}$ Solvable - 2
142.1 $D_{71}$ $2 \cdot 71$ $2 \cdot 71$ $37$ $C_1$ $D_{71}$ $C_{71}$ $C_{2}$ Solvable - 2
146.1 $D_{73}$ $2 \cdot 73$ $2 \cdot 73$ $38$ $C_1$ $D_{73}$ $C_{73}$ $C_{2}$ Solvable - 2
158.1 $D_{79}$ $2 \cdot 79$ $2 \cdot 79$ $41$ $C_1$ $D_{79}$ $C_{79}$ $C_{2}$ Solvable - 2
166.1 $D_{83}$ $2 \cdot 83$ $2 \cdot 83$ $43$ $C_1$ $D_{83}$ $C_{83}$ $C_{2}$ Solvable - 2
178.1 $D_{89}$ $2 \cdot 89$ $2 \cdot 89$ $46$ $C_1$ $D_{89}$ $C_{89}$ $C_{2}$ Solvable - 2
182.1 $C_{13}\times D_7$ $2 \cdot 7 \cdot 13$ $2 \cdot 7 \cdot 13$ $65$ $C_{13}$ $D_7$ $C_7$ $C_{26}$ Solvable - 2
182.2 $C_7\times D_{13}$ $2 \cdot 7 \cdot 13$ $2 \cdot 7 \cdot 13$ $56$ $C_7$ $D_{13}$ $C_{13}$ $C_{14}$ Solvable - 2
182.3 $D_{91}$ $2 \cdot 7 \cdot 13$ $2 \cdot 7 \cdot 13$ $47$ $C_1$ $D_{91}$ $C_{91}$ $C_{2}$ Solvable - 2
190.1 $D_5\times C_{19}$ $2 \cdot 5 \cdot 19$ $2 \cdot 5 \cdot 19$ $76$ $C_{19}$ $D_5$ $C_5$ $C_{38}$ Solvable - 2
190.2 $C_5\times D_{19}$ $2 \cdot 5 \cdot 19$ $2 \cdot 5 \cdot 19$ $55$ $C_5$ $D_{19}$ $C_{19}$ $C_{10}$ Solvable - 2
190.3 $D_{95}$ $2 \cdot 5 \cdot 19$ $2 \cdot 5 \cdot 19$ $49$ $C_1$ $D_{95}$ $C_{95}$ $C_{2}$ Solvable - 2
194.1 $D_{97}$ $2 \cdot 97$ $2 \cdot 97$ $50$ $C_1$ $D_{97}$ $C_{97}$ $C_{2}$ Solvable - 2
202.1 $D_{101}$ $2 \cdot 101$ $2 \cdot 101$ $52$ $C_1$ $D_{101}$ $C_{101}$ $C_{2}$ Solvable - 2
206.1 $D_{103}$ $2 \cdot 103$ $2 \cdot 103$ $53$ $C_1$ $D_{103}$ $C_{103}$ $C_{2}$ Solvable - 2
214.1 $D_{107}$ $2 \cdot 107$ $2 \cdot 107$ $55$ $C_1$ $D_{107}$ $C_{107}$ $C_{2}$ Solvable - 2
218.1 $D_{109}$ $2 \cdot 109$ $2 \cdot 109$ $56$ $C_1$ $D_{109}$ $C_{109}$ $C_{2}$ Solvable - 2
222.3 $S_3\times C_{37}$ $2 \cdot 3 \cdot 37$ $2 \cdot 3 \cdot 37$ $111$ $C_{37}$ $S_3$ $C_3$ $C_{74}$ Solvable - 2
222.4 $C_3\times D_{37}$ $2 \cdot 3 \cdot 37$ $2 \cdot 3 \cdot 37$ $60$ $C_3$ $D_{37}$ $C_{37}$ $C_{6}$ Solvable - 2
222.5 $D_{111}$ $2 \cdot 3 \cdot 37$ $2 \cdot 3 \cdot 37$ $57$ $C_1$ $D_{111}$ $C_{111}$ $C_{2}$ Solvable - 2
226.1 $D_{113}$ $2 \cdot 113$ $2 \cdot 113$ $58$ $C_1$ $D_{113}$ $C_{113}$ $C_{2}$ Solvable - 2
230.1 $D_5\times C_{23}$ $2 \cdot 5 \cdot 23$ $2 \cdot 5 \cdot 23$ $92$ $C_{23}$ $D_5$ $C_5$ $C_{46}$ Solvable - 2
230.2 $C_5\times D_{23}$ $2 \cdot 5 \cdot 23$ $2 \cdot 5 \cdot 23$ $65$ $C_5$ $D_{23}$ $C_{23}$ $C_{10}$ Solvable - 2
230.3 $D_{115}$ $2 \cdot 5 \cdot 23$ $2 \cdot 5 \cdot 23$ $59$ $C_1$ $D_{115}$ $C_{115}$ $C_{2}$ Solvable - 2
238.1 $D_7\times C_{17}$ $2 \cdot 7 \cdot 17$ $2 \cdot 7 \cdot 17$ $85$ $C_{17}$ $D_7$ $C_7$ $C_{34}$ Solvable - 2
238.2 $C_7\times D_{17}$ $2 \cdot 7 \cdot 17$ $2 \cdot 7 \cdot 17$ $70$ $C_7$ $D_{17}$ $C_{17}$ $C_{14}$ Solvable - 2
238.3 $D_{119}$ $2 \cdot 7 \cdot 17$ $2 \cdot 7 \cdot 17$ $61$ $C_1$ $D_{119}$ $C_{119}$ $C_{2}$ Solvable - 2
246.1 $S_3\times C_{41}$ $2 \cdot 3 \cdot 41$ $2 \cdot 3 \cdot 41$ $123$ $C_{41}$ $S_3$ $C_3$ $C_{82}$ Solvable - 2
246.2 $C_3\times D_{41}$ $2 \cdot 3 \cdot 41$ $2 \cdot 3 \cdot 41$ $66$ $C_3$ $D_{41}$ $C_{41}$ $C_{6}$ Solvable - 2
246.3 $D_{123}$ $2 \cdot 3 \cdot 41$ $2 \cdot 3 \cdot 41$ $63$ $C_1$ $D_{123}$ $C_{123}$ $C_{2}$ Solvable - 2
254.1 $D_{127}$ $2 \cdot 127$ $2 \cdot 127$ $65$ $C_1$ $D_{127}$ $C_{127}$ $C_{2}$ 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
262.1 $D_{131}$ $2 \cdot 131$ $2 \cdot 131$ $67$ $C_1$ $D_{131}$ $C_{131}$ $C_{2}$ Solvable - 2
266.1 $D_7\times C_{19}$ $2 \cdot 7 \cdot 19$ $2 \cdot 7 \cdot 19$ $95$ $C_{19}$ $D_7$ $C_7$ $C_{38}$ Solvable - 2
266.2 $C_7\times D_{19}$ $2 \cdot 7 \cdot 19$ $2 \cdot 7 \cdot 19$ $77$ $C_7$ $D_{19}$ $C_{19}$ $C_{14}$ Solvable - 2
266.3 $D_{133}$ $2 \cdot 7 \cdot 19$ $2 \cdot 7 \cdot 19$ $68$ $C_1$ $D_{133}$ $C_{133}$ $C_{2}$ Solvable - 2
274.1 $D_{137}$ $2 \cdot 137$ $2 \cdot 137$ $70$ $C_1$ $D_{137}$ $C_{137}$ $C_{2}$ Solvable - 2
278.1 $D_{139}$ $2 \cdot 139$ $2 \cdot 139$ $71$ $C_1$ $D_{139}$ $C_{139}$ $C_{2}$ Solvable - 2
282.1 $S_3\times C_{47}$ $2 \cdot 3 \cdot 47$ $2 \cdot 3 \cdot 47$ $141$ $C_{47}$ $S_3$ $C_3$ $C_{94}$ Solvable - 2
282.2 $C_3\times D_{47}$ $2 \cdot 3 \cdot 47$ $2 \cdot 3 \cdot 47$ $75$ $C_3$ $D_{47}$ $C_{47}$ $C_{6}$ Solvable - 2
282.3 $D_{141}$ $2 \cdot 3 \cdot 47$ $2 \cdot 3 \cdot 47$ $72$ $C_1$ $D_{141}$ $C_{141}$ $C_{2}$ Solvable - 2
286.1 $C_{13}\times D_{11}$ $2 \cdot 11 \cdot 13$ $2 \cdot 11 \cdot 13$ $91$ $C_{13}$ $D_{11}$ $C_{11}$ $C_{26}$ Solvable - 2
286.2 $C_{11}\times D_{13}$ $2 \cdot 11 \cdot 13$ $2 \cdot 11 \cdot 13$ $88$ $C_{11}$ $D_{13}$ $C_{13}$ $C_{22}$ Solvable - 2
286.3 $D_{143}$ $2 \cdot 11 \cdot 13$ $2 \cdot 11 \cdot 13$ $73$ $C_1$ $D_{143}$ $C_{143}$ $C_{2}$ Solvable - 2
290.1 $D_5\times C_{29}$ $2 \cdot 5 \cdot 29$ $2 \cdot 5 \cdot 29$ $116$ $C_{29}$ $D_5$ $C_5$ $C_{58}$ Solvable - 2
290.2 $C_5\times D_{29}$ $2 \cdot 5 \cdot 29$ $2 \cdot 5 \cdot 29$ $80$ $C_5$ $D_{29}$ $C_{29}$ $C_{10}$ Solvable - 2
290.3 $D_{145}$ $2 \cdot 5 \cdot 29$ $2 \cdot 5 \cdot 29$ $74$ $C_1$ $D_{145}$ $C_{145}$ $C_{2}$ Solvable - 2
298.1 $D_{149}$ $2 \cdot 149$ $2 \cdot 149$ $76$ $C_1$ $D_{149}$ $C_{149}$ $C_{2}$ Solvable - 2
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