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We have performed a statistical analysis of a sample of 28 nearby galaxy groups derived primarily from the Two‐Dimensional  XMM–Newton  Group Survey, in order to ascertain what factors drive the observed differences in group properties. We specifically focus on entropy and the role of feedback, and divide the sample into cool core (CC) and non‐cool core (NCC) systems. This is the first time the latter have been studied in detail in the group regime. We find the coolest groups to have steeper entropy profiles than the warmest systems, and find NCC groups to have higher central entropy and to exhibit more scatter than their CC counterparts. We investigate the entropy distribution of the gas in each system, and compare this to the expected theoretical distribution under the condition that non‐gravitational processes are ignored. In all cases, the observed maximum entropy far exceeds that expected theoretically, and simple models for modifications of the theoretical entropy distribution perform poorly. A model which applies initial pre‐heating through an entropy shift to match the high entropy behaviour of the observed profile, followed by radiative cooling, generally fails to match the low entropy behaviour, and only performs well when the difference between the maximum entropy of the observed and theoretical distributions is small. Successful feedback models need to work differentially to increase the entropy range in the gas, and we suggest two basic possibilities.  We analyse the effects of feedback on the entropy distribution, finding systems with a high measure of ‘feedback impact’ to typically reach higher entropy than their low feedback counterparts. The abundance profiles of high and low feedback systems are comparable over the majority of the radial range, but the high feedback systems show significantly lower central metallicities compared to the low feedback systems. If low entropy, metal‐rich gas has been boosted to large entropy in the high feedback systems, it must now reside outside  0.5  r  500  , to remain undetected in our study. Considering gas as a function of scaled entropy, we find similar levels of enrichment in both high and low feedback systems, and argue that the lack of extra metals in the highest feedback systems points to an active galactic nucleus origin for the bulk of the feedback, probably acting within precursor structures.

A statistical analysis of the Two‐Dimensional XMM – Newton Group Survey: the impact of feedback on group properties