The affix vuñ comes the sense is 'a collection thereof' after a word denoting a gotra (Patronymic) and after 1. ukṣa 2. uṣṭra 3. urabhra 4. rājana 5. rājanya 6. rājaputra 7. vatsa 8. manuṣya and 9. aja,
The word गोत्र is used here in its popular and not technical sense, meaning any descendant or offspring. Thus औपगवकम्, औक्षकम्, 6.4.144 औष्ट्रकम्, औरभ्रकम्, राजकम्, 6.4.144 राजन्यकम्, राजपुत्रकम्, वात्सकम्, मानुष्यकम्, आजकम् ॥ The final य of मनुष्य and राजन्य is not elided when the affix अक् is added 6.4.150
Vart:- Also after the word वृद्ध e.g. वार्द्धकम् 'a collection of old men'.,