Word Game

Let G be the free group on the letters a, b, ..., z with relations u = v if u and v are both English words and are anagrams (same letters). Question: What is the center of G? The table below provides proofs that certain letters commute.

	a	c	d	e	g	i	l	n	o	p	s
a
b	x
c	x
d	x
e
f	x
g
h
i
j
k
l	x			x
m	x				x
n
o			x		x		x	x
p	x			x			x		x
q
r	x	x				x			x	x
s	x
t	x			x							x
u				x	x			x			x
v
w				x			x
x
y							x
z