  Half-maximal gauged supergravity in seven dimensions coupled to $n$ vector
multiplets contains $n+3$ vectors and $3n+1$ scalars parametrized by
$\mathbb{R}^+\times SO(3,n)/SO(3)\times SO(n)$ coset manifold. The two-form
field in the gravity multiplet can be dualized to a three-form field which
admits a topological mass term. Possible non-compact gauge groups take the form
of $G_0\times H\subset SO(3,n)$ with a compact group $H$. $G_0$ is one of the
five possibilities; $SO(3,1)$, $SL(3,\mathbb{R})$, $SO(2,2)$, $SO(2,1)$ and
$SO(2,2)\times SO(2,1)$. We investigate all of these possible non-compact gauge
groups and classify their vacua. Unlike the gauged supergravity without a
topological mass term, there are new supersymmetric $AdS_7$ vacua in the
$SO(3,1)$ and $SL(3,\mathbb{R})$ gaugings. These correspond to new $N=(1,0)$
superconformal field theories (SCFT) in six dimensions. Additionally, we find a
class of $AdS_5\times S^2$ and $AdS_5\times H^2$ backgrounds with $SO(2)$ and
$SO(2)\times SO(2)$ symmetries. These should correspond to $N=1$ SCFTs in four
dimensions obtained from twisted compactifications of six-dimensional field
theories on $S^2$ or $H^2$. We also study RG flows from six-dimensional
$N=(1,0)$ SCFT to $N=1$ SCFT in four dimensions and RG flows from a
four-dimensional $N=1$ SCFT to a six-dimensional SYM in the IR. The former are
driven by a vacuum expectation value of a dimension-four operator dual to the
supergravity dilaton while the latter are driven by vacuum expectation values
of marginal operators.
