Short answers, pulled from the story.
The word Dharmaguptaka combines Sanskrit terms meaning preserver of law or morality. Most scholars believe this school emerged from another group called the Mahīśāsakas in Northwest India during the first century CE.
Historical shifts saw them decline when the Kuşana Empire rose around the mid-first to third century AD. The Kuşana Empire favored a different sect called Sarvāstivāda instead of supporting the Dharmaguptakas.
Richard Salomon identified Gandhāran Buddhist texts as belonging to the Dharmaguptaka sect. These manuscripts represent the oldest extant Buddhist writings ever discovered and include scrolls held by the British Library from Nagarāha Afghanistan.
In the early fifth century CE, Dharmaguptaka Vinaya entered Chinese through translation efforts led by monk Buddhayaśas. By the eighth century, an imperial edict issued by Emperor Zhongzong mandated that all Sangha in China use this specific vinaya for ordination.
Textual evidence suggests members of the Dharmaguptaka school began accepting Mahāyāna sūtras at some unknown point. Paramārtha, a sixth-century monk from Ujjain, unequivocally associated the school with Mahāyāna traditions and portrayed them as perhaps closest to straightforward Mahāyāna practice among all groups.