CICs are NOT charities and don't fall under the same tax bracket.
As a limited company a CIC is liable to CT just like any other company. It will be chargeable on any trading profits (though it will be a question of fact whether or not a particular CIC is trading) and on its investment income and gains.
It is eligible for any reliefs which are available to all companies but there are no CIC specific tax exemptions/reliefs available.