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Matriarchate

//ˈmeɪtɹiɑːkət// noun

Noun

1
A matriarchal system or community.
"The fact that in most lands the moon was originally a female deity has led many historians to dispute the superiority of the moon over the sun in ancient mythology. In putting forth this argument they overlook one important and significant factor: the existence of a matriarchate preceding the domination of woman by man. That such a condition was perfectly natural will be realized when it is remembered there was no recognition of the part played by the male in fecundation."
2
a form of social organization in which a female is the family head and title is traced through the female line wordnet
3
The position of a matriarch.

From matriarch + -ate (forms nouns denoting rank or office, a system ruled by people of such office), modeled after patriarchate.

Unscramble this word: matriarchate