Wayne Madsen hit 93, but five wickets in the day for Adam Riley put Kent in control after Day Three of the Specsavers County Championship match at The 3aaa County Ground.
Madsen and Alex Hughes (66) shared a 130-run partnership for the third wicket, but after both fell just before lunch Derbyshire lost regular wickets to be dismissed for 400 – a first innings deficit of 161 runs.
Kent enforced the follow-on and Riley, who took three in the first innings earlier in the day, claimed two more wickets to leave Derbyshire 83-2 at stumps, still trailing by 78 runs.
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