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Group delay of waveguide components is a function of the frequency you are applying. Near the lower cutoff, the group delay gets longer and longer, as the EM wave ping-pongs down the guide, and can easily be 10X the free-space group delay. But at the upper end of a waveguide's band, the group delay approaches the free-space group delay.
Let's start by presenting the equation the lower cutoff wavelength of the dominant TE10 mode in waveguide:
Now the equation for guide wavelength (the wavelength of a signal in the guide) which is smaller than the free-space wavelength:
Group velocity in a waveguide is speed at which EM energy travels in the guide (which is slower than free space). Equation is... and plotted below, we see it varies tremendously across the band for WR-90 (X-band) waveguide.