  This paper reports a systematic search of X-ray cavities, density jumps and
shocks in the inter-galactic environment of the galaxy group IC~1262 using {\it
Chandra}, GMRT and VLA archival observations. The X-ray imaging analysis
reveals a pair of X-ray cavities on the north and south of the X-ray peak, at
projected distances of 6.48\,kpc and 6.30\,kpc respectively. Total mechanical
power contained in both these cavities is found to be $\sim$12.37$\times
10^{42}$ erg~s$^{-1}$, and compares well with the X-ray luminosity, within the
cooling radius, measured to be $\sim 3.29 \times 10^{42}$ erg~s$^{-1}$,
suggesting that the mechanical power injected by the central AGN efficiently
balances the radiative loss. We detect a previously unknown X-ray cavity at the
position of southern radio lobe in the intra-group medium and find a loop of
excess X-ray emission extending $\sim$100 kpc southwest from the central
galaxy. The X-ray cavity at the position of southern radio lobe probably
represents a first generation X-ray cavity. Two surface brightness edges are
evident to the west and east$-$north of the center of this group. The radio
galaxy at the core of the IC~1262 group is a rare low-redshift ultra-steep
radio galaxy, its spectral index being $\alpha\! \sim\! -1.73$ (including the
central AGN) and $\alpha\! \sim\! -2.08$ (excluding the central AGN). We detect
a radio phoenix embedded within the southern radio lobe, for the first time in
a poor group, with a spectral index ($\alpha \!\leq\! -1.92$). The spectral
index distribution across the phoenix steepens with increasing distance from
its intensity peak.
