Map of luminosity gap, ΔM₁₂, as a function of BGG luminosity offset, D_offset symbolized by the BGGs stellar kinematic. Red and blue bordered squares highlight the limits of the regions inhabited by the relaxed and unrelaxed groups, respectively. Pie chart shows the fraction of aligned (A: red), misaligned (MA: blue), and counter-rotating (CR: sky blue) BGGs, as well as BGGs where there is too much uncertainty in their misalignment PA to classify them, due to low signal-to-noise (LSN: black) in the H_α velocity maps, within the effective radius (Re). Besides the pie charts, we present a representative example of a member of the relaxed and unrelaxed group, as found in the semi-analytic model from Raouf et al. (2017). The location of the brightest group galaxies (BGGs) and the second-brightest group galaxies (SBGGs) are highlighted with a filled circle symbol for each group. In the upper right panels, we provide representative examples of the stellar kinematics (SK), gas kinematics (GK) velocity map, and a postage stamp in r-band from the GAMA Panchromatic Swarp Imager (PSI), for a BGG in the relaxed and unrelaxed group. The major axes of rotation are shown by red and blue dashed lines in the SK and GK kinematic maps, respectively, along with the median signal to noise (S/N) in Re with STD error. Each kinematic map inside the panels has a 15″ side length, and the SAMI bundle size is shown by the circle. In the r-band optical postage stamp (right panels), we also show the δPA, sSFR, ΔM₁₂, and D_offset.