Sorting table of strings into alphabetical order?

Hi everyone. I have a table with names of players and I want to order them in alphabetical order so they show up in alphabetical order on my custom playerlist GUI.

However, when testing the below script, if the names are very similar (E.G: Player1 and Player2), they are sorted by the time each value was added to the table for each player.

game.StarterGui:SetCoreGuiEnabled("PlayerList",false)

local main = script.Parent
local player = game.Players.LocalPlayer

local curPlayer = main:WaitForChild("CurrentPlayer")
local list = main:WaitForChild("Players")

local bc = "rbxassetid://93338133"
local tbc = "rbxassetid://93338428"
local obc = "rbxassetid://93338264"

local tempFrame = script:WaitForChild("PlayerTempFrame")

game:GetService("ContentProvider"):Preload(bc)
game:GetService("ContentProvider"):Preload(tbc)
game:GetService("ContentProvider"):Preload(obc)

players = {}

function updateScrollLength()
	wait()
	local y = 0
	for _,v in pairs(list:GetChildren()) do
		y = y + v.AbsoluteSize.Y
	end
	local height = (y/list.AbsoluteSize.Y)*.69
	list.CanvasSize = UDim2.new(0,0,height,0)
end

list.ChildAdded:connect(updateScrollLength)
list.ChildRemoved:connect(updateScrollLength)

function doRefresh()
	curPlayer.Text = player.Name
	for i,v in pairs(list:GetChildren()) do
		v:Destroy()
	end
	players = {}
	for i,v in pairs(game.Players:GetPlayers()) do
		table.insert(players,v.Name)
		table.sort(players, function(a, b) return a:byte() < b:byte() end)
		local frame = tempFrame:Clone()
		frame.Position = UDim2.new(0,0,0,20 * (#players - 1))
		frame.Name = "Player"
		frame.PlayerName.Text = players[i]
		if game.Players[players[i]].MembershipType == Enum.MembershipType.BuildersClub then
			frame.BC.Image = bc
		elseif game.Players[players[i]].MembershipType == Enum.MembershipType.TurboBuildersClub then
			frame.BC.Image = tbc
		elseif game.Players[players[i]].MembershipType == Enum.MembershipType.OutrageousBuildersClub then
			frame.BC.Image = obc
		else
			frame.BC.Image = ""
		end
		frame.Parent = list
	end
end

doRefresh()
game.Players.ChildAdded:connect(doRefresh)
game.Players.ChildRemoved:connect(doRefresh)

Is there anyway I can sort the table so Player1 always shows first before Player2 if that situation occurs? I've looked at ROBLOX's playerlist script but that gives me no answers.

Any help is appreciated, thanks!