Do maple have hashtable ?

i would like to use for premutation group

a := f(x,y) = f(y,x)

how to get x and y from left side f(x,y)

and get y and x from right side f(y,x)?

from (x+2)^4

sys:=[a[2]*b[2] = 1,a[1]*b[2]+a[2]*b[1] = 8,a[0]*b[2]+a[1]*b[1]+a[2]*b[0] = 24,a[0]*b[1]+a[1]*b[0] = 32,a[0]*b[0] = 16];

solve(sys, {a[0],a[1],a[2],b[0],b[1],b[2]});

1 1 2

1 2 2

for example, above

is there a function to represent it as a group

a,b ; a^2, b^2, a*b = b*a

is a presentation

a and b are permutation group

a*b = b*a is relation

i am not sure a^2 or b^2 are generator, i guess they are

so how to find a and b which are permutation group?

is it a,b ; a^2, b^2, a*b = b*a     or      a,b ; a^2=1, b^2=1, a*b = b*a  ?

if a^2, b^2, a*b = b*a , i do not know what is a^2 if a^2 = 1