We present a Chandra observation of the candidate BL Lac object EXO 0423.4 - 0840 .
The X-ray emission from EXO 0423.4 - 0840 is clearly extended , and is associated with an optical early-type galaxy , MCG-01-12-005 , at the centre of cluster ClG 0422-09 .
We do not detect a point source which can be associated with a BL Lac , but we found a small radio source in the centre of MCG-01-12-005 .
The cluster gas temperature mapped by the Chandra observation drops continuously from 80 kpc towards the centre , and is locally single phase .
We measure a metallicity profile which declines outwards with a value 0.8 Z _ { \odot } in the centre , dropping to 0.35 Z _ { \odot } at larger radius , which we interpret as a superposition of cluster gas and a dense interstellar medium ( ISM ) in the central galaxy .
Although the temperature profile suggests that conduction is not efficient , the ISM and intra-cluster medium seem not to have mixed .
The entropy profile declines continuously towards the centre , in agreement with recent results on groups and clusters .
The radio source appears to have had some effect in terms of gas heating , as seen in the small scale ( \sim 10 kpc ) entropy core , and the asymmetric hard emission on the same scale .