Stacking cosmic microwave background (CMB) maps around known galaxy clusters and groups provides a powerful probe of the distribution of hot gas in these systems via the Sunyaev-Zeldovich (SZ) effect. A stacking analysis allows one to detect the average SZ signal around low mass halos, and to extend measurements out to large scales, which are too faint to detect individually in the SZ or in X-ray emission. In addition, cross correlations between SZ maps and other tracers of large-scale structure (with known redshifts) can be used to extract the redshift-dependence of the SZ background. Motivated by these exciting prospects, we measure the two-point cross-correlation function between a catalog of $sim 380,000$ galaxy groups (with redshifts spanning $z=0.01-0.2$) from the Sloan Digital Sky Survey (SDSS) and Compton-y parameter maps constructed by the Planck collaboration. We find statistically significant correlations between the group catalog and Compton-y maps in each of six separate mass bins, with estimated halo masses in the range $10^{11.5-15.5} M_odot/h$. We compare these measurements with halo models of the SZ signal, which describe the stacked measurement in terms of one-halo and two-halo terms. The one-halo term quantifies the average pressure profile around the groups in a mass bin, while the two-halo term describes the contribution of correlated neighboring halos. For the more massive groups we find clear evidence for the one- and two-halo regimes, while groups with mass below $10^{13} M_odot/h$ are dominated by the two-halo term given the resolution of Planck data. We use the signal in the two-halo regime to determine the bias-weighted electron pressure of the universe: $langle b P_e rangle= 1.50 pm 0.226 times 10^{-7}$ keV cm$^{-3}$ (1-$sigma$) at $zapprox 0.15$.
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