While it would be ideal to have an even number of each sex it's not always possible to end up that way. I've often had uneven numbers and an extra female usually gets bred. An extra male just tags along anyway. The fact that your extra hen is an 'outcast' isn't at all unusual. There is one in every flock even with even numbers. Just the nature of the birds..
I'm much better at remembering info than where I got it from. Somewhere, regarding behavior, I read that there are alpha & beta couples. The alpha of course, are dominant, beta serves alpha but 2nd in line. The others may or may not couple or mate, but they serve as guards, protectors.
Some find that hogwash, but I can only speak from what I watched last yr. When I think of "Alpha" I think dominant, ruling. So my "presumed alpha" is based on exactly that, who ruled the roost. Lucy ruled the roost and no one ruled her except PJ, the male.
There was no question who was the alpha male and female, but though they started off seeming "together", they swapped mates before nesting began.
Presumed Alpha female built her nest in the field behind us. I could walk out to where she had her nest in the field & see her on the nest, her mate beside her, & the other 4 formed a ring around them abt 4-5 ft away from the nest.
She stayed on the nest all day. They, including her mate, would take breaks to come back up in the yard to eat or "chat" before heading back out. But if they were away longer than she approved of, she wld call & all 5 wld rush back to the nest.
Then came the day the Beta went off on her own to make her own nest, leaving the others guarding the Alpha. (This is where it starts sounding fantastical, so if you'd like you can look up "week #3 under Sydney to read it as it happened.)
So presumed Beta went off to make her nest, Alpha was on her nest, & the remaining 4 came up into the yard for a break. I was sitting w/them, giving them millet. Alpha began to call, the 4 stopped, looked, & began running toward her nest in the field behind the house.
Before they cleared the yard, Beta began calling from the front. She had built her nest in the field next to our neighbor's front yard. The 4 froze, SEEMED to look back & forth at each other.
Then 1 "guard" went w/the mate to the back while the other went to the front.
Beta's guard stayed w/her, but the other guard wld come up to sit w/her @ times before returning to his station out back. As before, I was able to walk near enough to see all of this w/o upsetting them.
This was how it went during the day, but all wld return to the coop before dark. It was their first season, almost like little kids playing house. They were laying eggs, but leaving them overnight.
The guards had always stayed together and cont to do so when not "on duty". I thought they had a nest, but going back later to look, it was just a comfy spot, no eggs.
Anyway, this is all counter-intuitive to what my mentors say regarding flock behavior, and it may very well be the result of having such a small "flock", but this was how their first season started.
(And there went using the pandemic as an excuse for how much time I spend watching these birds!)