Context. Class I methanol masers are known to be associated with shocked outflow regions around massive protostars, indicating a possible link between the maser properties and those of their host clumps. Aims. The main goals of this study are (1) to search for new class I methanol masers, (2) to statistically study the relationship between class I masers and shock tracers, (3) to compare the properties between class I masers and their host clumps, also as a function of their evolutionary stage, and (4) to constrain the physical conditions that excite multiple class I masers simultaneously. Methods. We analysed the 3 mm wavelength spectral line survey of 408 clumps identified by the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL), which were observed with the IRAM 30-meter telescope, focusing on the class I methanol masers with frequencies near 84, 95, and 104.3 GHz. Results. We detect narrow maser-like features towards 54, 100, and 4 sources in the maser lines near 84, 95, and 104.3 GHz, respectively. Among them, 50 masers at 84 GHz, 29 masers at 95 GHz, and 4 rare masers at 104.3 GHz are new discoveries. The new detections increase the number of known 104.3 GHz masers from five to nine. The 95 GHz class I methanol maser is generally stronger than the 84 GHz maser counterpart. We find nine sources showing class I methanol masers, but no SiO emission, indicating that class I methanol masers might be the only signpost of protostellar outflow activity in extremely embedded objects at the earliest evolutionary stage. Class I methanol masers that are associated with sources that show SiO line wings are more numerous and stronger than those without such wings. The total integrated intensity of class I methanol masers is well correlated with the integrated intensity and velocity coverage of the SiO (2−1) emission. The properties of class I methanol masers are positively correlated with the bolometric luminosity, clump mass, and peak H2 column density of their associated clumps, but are uncorrelated with the luminosity-to-mass ratio, dust temperature, and mean H2 volume density. Conclusions. We suggest that the properties of class I masers are related to shocks traced by SiO. Based on our observations, we conclude that class I methanol masers at 84 and 95 GHz can trace a similar evolutionary stage to the H2O maser, and appear prior to 6.7 and 12.2 GHz methanol and OH masers. Despite their small number, the 104.3 GHz class I masers appear to trace a shorter and more evolved stage compared to the other class I masers.
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