We investigate the charge transport in triphenylene core based homologous series of discotic mesogens (HATn) by the time-of-flight method. HAT5, HAT6 and HAT8 exhibit Colh phase whereas HAT4 shows Colhp phase. For the investigated homologous series, we have observed a single transit in the transient photocurrent curves corresponding to positive charge carriers having the mobility in order of 10-2 to 10-4 cm2/vs. The hole mobility decreases with increasing the number of carbon atoms (n) in the alkyl chain attached to the triphenylene core, which follows the empirical exponential relationship: u=a.exp(-b/n). Furthermore, the dielectric measurement has been done on these compounds to bring a correlation between the molecular ordering by varying the alkyl chain of the HATn compounds. In the light of structure-property correlation, we have noticed that the hole mobility and permittivity vary according to the length of alkyl chain attached to the triphenylene core. The molecular ordering is also discussed via phase behaviour of compounds and confirmed by polarized optical textures. The change in entropy also decreases with increasing alkyl chain length of the HATn compounds rendering an agreement with that of the mobility and dielectric measurements. The HATn compounds show their potential applications in opto-electronics and could serve as organic semiconductors; however, the poor conductivity remains as a futuristic challenge.