Methanol (CH3OH) is one of the most abundant interstellar molecules, offering a vast number of transitions to be studied, including many maser lines. While the strongest Galactic CH3OH lines, the so-called class II masers, show no indications for the presence of superluminous counterparts in external galaxies, the less luminous Galactic class I sources appear to be different. Here we report class I 36GHz CH3OH 4(-1) - 3(0) E line emission from the nearby galaxies Maffei2 and IC342, measured with the 100-m telescope at Effelsberg at three different epochs within a time span of about five weeks. The 36GHz methanol line of Maffei2 is the second most luminous among the sources detected with certainty outside the Local Group of galaxies. This is not matched by the moderate infrared luminosity of Maffei2. Higher resolution data are required to check whether this is related to its prominent bar and associated shocks. Upper limits for M82, NGC4388, NGC5728 and Arp220 are also presented. The previously reported detection of 36GHz maser emission in Arp220 is not confirmed. Non-detections are reported from the related class I 44GHz methanol transition towards Maffei2 and IC342, indicating that this line is not stronger than its 36GHz counterpart. In contrast to the previously detected 36GHz CH3OH emission in NGC253 and NGC4945, our 36GHz profiles towards Maffei2 and IC342 are similar to those of previously detected non-masing lines from other molecular species. However, by analogy to our Galactic center region, it may well be possible that the 36GHz methanol lines in Maffei~2 and IC~342 are composed of a large number of faint and narrow maser features that remain spatially unresolved. In view of this, a search for a weak broad 36GHz line component would also be desirable in NGC253 and NGC4945.
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