  We analyse 829,481 stars from the Next Generation Transit Survey (NGTS) to
extract variability periods. We utilise a generalisation of the autocorrelation
function (the G-ACF), which applies to irregularly sampled time series data. We
extract variability periods for 16,880 stars from late-A through to mid-M
spectral types and periods between 0.1 and 130 days with no assumed variability
model. We find variable signals associated with a number of astrophysical
phenomena, including stellar rotation, pulsations and multiple-star systems.
The extracted variability periods are compared with stellar parameters taken
from Gaia DR2, which allows us to identify distinct regions of variability in
the Hertzsprung-Russell Diagram. We explore a sample of rotational
main-sequence objects in period-colour space, in which we observe a dearth of
rotation periods between 15 and 25 days. This 'bi-modality' was previously only
seen in space-based data. We demonstrate that stars in sub-samples above and
below the period gap appear to arise from a stellar population not
significantly contaminated by excess multiple systems. We also observe a small
population of long-period variable M-dwarfs, which highlight a departure from
the predictions made by rotational evolution models fitted to solar-type
main-sequence objects. The NGTS data spans a period and spectral type range
that links previous rotation studies such as those using data from Kepler, K2
and MEarth.

Solar and Stellar Astrophysics