Mike wrote:
"Group Velocity and Velocity factor - Can someone explain how these two
relate in a waveguide."

Group velocity differs from phase velocity (which is defined as the
velocity at which a point of constant phase is propagated in a
progressive sinusoidal wave). Group velocity implies several transmitted
sinusoidal waves for which the medium has a velocity factor that is a
function of frequency.

Waveguides are used over limited frequency ranges so that their
dimensions exclude propagation of any but the dominant mode, and so that
the operating frequency is sufficiently above the low-frequency cutoff
of the guide to avoid excessive attenuation. The limited tange of
frequencies transmitted through a waveguide assures a group velocity
ahich equals the phase velocity and thus assures low attenuation.

Terman explains the above in his treatment of "Rectangular Waveguides"
which begins on page 128 of his 1955 opus.

Best regards, Richard Harrison, KB5WZI