  Rhenium based noncentrosymmetric superconductors crystallizing in $\alpha$-Mn
structure have become potential candidates to exhibit an unconventional
superconducting ground-state. Here we report a detailed investigation on the
superconducting and normal state properties of Re$_{5.5}$Ta, that also has the
$\alpha$-Mn structure. Magnetization, specific heat, and transport measurements
confirm the bulk superconducting transition \textit{T}$_{C}$ at 8.0 K. Upper
critical field value (H$_{C2}$(0)) calculated from magnetization, specific heat
and AC transport measurements exceed the Pauli paramagnetic limit (14.7 T),
indicating that the superconducting properties of Re$_{5.5}$Ta are probably
unconventional in nature. However, low-temperature specific heat and
transverse-field muon spin rotation measurements suggest a surprising nodeless
isotropic superconducting gap, although with strong electron-phonon coupling.
