I think I can clarify the misunderstandings regarding the "first female GLO" debate.

ADPi was formerly The Adelphian Society
(the earliest NPC sisterhood ever founded which is presently under a Greek Letter name)

Phi Mu was The Philomathean Society
Pi Beta Phi was I.C. Sorosis

I think I.C. Sorosis was the first ever to change its name to a Greek Letter name, so I suppose it could be said to be the first ever Greek letter society, by the taking on of Greek Letters.

However, The Adelphian Society existed before I.C. Sororis did, even though it changed its name after IC Sorosis.

Kappa Alpha Theta was the first ever sisterhood to be founded using Greek Letters; that is, it did not have a former name.