Determine group delay from the frequency response of FIR filter
The group delay is the negative derivative of the phase response as the OP has stated, and specifically for the delay of one clock sample, the phase will go linearly negative to $2\pi$ radians as the frequency goes from 0 to $f_s$
From the picture we see the phase is going approximately 800 degrees at a frequency of  $.17\pi$ rad/sample  (where $2\pi$ rad/sample is the sampling rate). So this would be equivalent to
$800/360*(2\pi)$ rad /$(.17\pi)$ rad/sample = $26$ sample delay
For linear phase filters, the group delay is half the order which would be 25.5 in this case (we can't resolve that from the graphic alone). The OP wrote that the order of the filter was 51 which implies 52 taps.