We analyze three years of nearly-continuous Kepler spacecraft short cadence observations of the pulsating subdwarf B star KIC 3527751 .
We detect a total of 251 periodicities , most in the g -mode domain , but some where p -modes occur , confirming that KIC 3527751 is a hybrid pulsator .
We apply seismic tools to the periodicities to characterize the properties of KIC 3527751 .
Techniques to identify modes include asymptotic period spacing relationships , frequency multiplets , and the separation of multiplet splittings .
These techniques allow for 189 ( 75 % ) of the 251 periods to be associated with pulsation modes .
Included in these are three sets of \ell = 4 multiplets and possibly an \ell = 9 multiplet .
Period spacing sequences indicate \ell = 1 and 2 overtone spacings of 266.4 \pm 0.2 and 153.2 \pm 0.2 seconds , respectively .
We also calculate reduced periods , from which we find evidence of trapped pulsations .
Such mode trappings can be used to constrain the core/atmosphere transition layers .
Interestingly , frequency multiplets in the g -mode region , which sample deep into the star , indicate a rotation period of 42.6 \pm 3.4 days while p -mode multiplets , which sample the outer envelope , indicate a rotation period of 15.3 \pm 0.7 days .
We interpret this as differential rotation in the radial direction with the core rotating more slowly .
This is the first example of differential rotation for a subdwarf B star .