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In photometry of $γ$ Cas (B0.5 IVe) from the SMEI and BRITE-Constellation satellites, indications of low-order non-radial pulsation have recently been found, which would establish an important commonality with the class of classical Be stars at large. New photometry with the TESS satellite has detected three frequency groups near 1.0 ($g1$), 2.4 ($g2$), and 5.1 ($g3$) d$^{-1}$, respectively. Some individual frequencies are nearly harmonics or combination frequencies but not exactly so. Frequency groups are known from roughly three quarters of all classical Be stars and also from pulsations of $β$ Cep, SPB, and $γ$ Dor stars and, therefore, firmly establish $γ$ Cas as a non-radial pulsator. The total power in each frequency group is variable. An isolated feature exists at 7.57 d$^{-1}$ and, together with the strongest peaks in the second and third groups ordered by increasing frequency ($g2$ and $g3$), is the only one detected in all three TESS sectors. The former long-term 0.82 d$^{-1}$ variability would fall into $g1$ and has not returned at a significant level, questioning its attribution to rotational modulation. Low-frequency stochastic variability is a dominant feature of the TESS light curve, possibly caused by internal gravity waves excited at the core-envelope interface. These are known to be efficient at transporting angular momentum outward, and may also drive the oscillations that constitute $g1$ and $g2$. The hard X-ray flux of $γ$ Cas is the only remaining major property that distinguishes this star from the class of classical Be stars.