  We study in detail the little-Higgs model proposed by Low, Skiba and Smith
with an SU(6)/Sp(6) group structure. The effective theory at the TeV scale is a
two-Higgs doublet model (2HDM) with additional heavy vector-like fermions and
vector-bosons. We identify a set of independent input parameters and develop
expressions for masses and couplings in terms of these. We perform a random
scan of the parameter space and find points that satisfy constraints, including
the recent 8 TeV LHC Higgs measurements, namely, the Higgs mass, Higgs
couplings to the top, bottom, $\tau$, $W^\pm$ and $Z$, top-quark mass, and
collider bounds on colored vector-like fermions ($t'$ and $b'$), and also
precision electroweak constraints. The LHC constraints on the $hWW$ and $hZZ$
couplings are satisfied by being close to the "alignment limit". We find how
fine-tuned the model is after including these constraints. For the points that
satisfy the constraints, we present the 1-loop effective couplings of the
CP-even and CP-odd neutral scalars to two gluons including contributions of
standard model and heavy vector-like quarks. We also present the branching
ratios of the heavy neutral scalars into the $\gamma\gamma,\, \tau\bar\tau,\,
b\bar b,\, t\bar t, WW, ZZ, Zh, hh$ modes, and the heavy charged scalar into
$tb,\, \tau\nu, cs, W h$ modes. These will aid searches of the heavy scalars at
the LHC and other future colliders.
