# By Schwartz-Werner, this group is not even realizable
# because there is an element g of order at least 8
# such that C_G(g) = <g>.

G = gap.SmallGroup(64,32)

flag = False
for g in G.Elements():
    if g.Order() >= 8 and gap.Centralizer(G,g) == G.Subgroup([g]):
        flag = True
        break
if flag:
    print("There exists g in G with |g| >= 8 and such that C_G(g) = <g>.")
else:
    print("Failed")