Identifying result from a Cayley graph in gap

Question

I constructed a group s which is the semidirect product $\mathbb{Z}_3 \ltimes (\mathbb{Z}_5 \times \mathbb{Z}_5)$ using GAP commands as below.

gap> m:=[[0,-1],[1,-1]]*One(GF(5));
[ [ 0*Z(5), Z(5)^2 ], [ Z(5)^0, Z(5)^2 ] ]

gap> s:=SemidirectProduct(Group(m),GF(5)^2);
Group([ [ [ 0*Z(5), Z(5)^2, 0*Z(5) ], [ Z(5)^0, Z(5)^2, 0*Z(5) ], [ 0*Z(5), 0*Z(5), Z(5)^0 ] ], 
  [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], [ Z(5)^0, 0*Z(5), Z(5)^0 ] ] ])

Then I have obtained an irredundant generating set for s as below and drew the Cayley graph.(There is a .gap program which enables the computation of irredundant generating set as I need).

gap> S:=IrredUndirGenSetsUpToAut(s);
[ [ [ [ 0*Z(5), Z(5)^2, 0*Z(5) ], [ Z(5)^0, Z(5)^2, 0*Z(5) ], [ 0*Z(5), 0*Z(5), Z(5)^0 ] ], 
      [ [ 0*Z(5), Z(5)^2, 0*Z(5) ], [ Z(5)^0, Z(5)^2, 0*Z(5) ], [ 0*Z(5), Z(5)^0, Z(5)^0 ] ] ], 
  [ [ [ 0*Z(5), Z(5)^2, 0*Z(5) ], [ Z(5)^0, Z(5)^2, 0*Z(5) ], [ 0*Z(5), 0*Z(5), Z(5)^0 ] ], 
      [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], [ 0*Z(5), Z(5)^0, Z(5)^0 ] ] ] ]

gap> S1:=S[1];
[ [ [ 0*Z(5), Z(5)^2, 0*Z(5) ], [ Z(5)^0, Z(5)^2, 0*Z(5) ], [ 0*Z(5), 0*Z(5), Z(5)^0 ] ], 
  [ [ 0*Z(5), Z(5)^2, 0*Z(5) ], [ Z(5)^0, Z(5)^2, 0*Z(5) ], [ 0*Z(5), Z(5)^0, Z(5)^0 ] ] ]

gap> CayleyGraph(s,S1);
rec( adjacencies := [ [ 17, 26, 51, 52 ] ], group := <permutation group of size 75 with 2 generators>, 
  isGraph := true, isSimple := true, 
  names := [ [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], [ 0*Z(5), 0*Z(5), Z(5)^0 ] ], 
      [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], [ Z(5)^0, 0*Z(5), Z(5)^0 ] ], 
      [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], [ Z(5)^2, 0*Z(5), Z(5)^0 ] ], 
      [ [ 0*Z(5), Z(5)^2, 0*Z(5) ], [ Z(5)^0, Z(5)^2, 0*Z(5) ], [ 0*Z(5), Z(5)^2, Z(5)^0 ] ], 
      [ [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ], [ Z(5), 0*Z(5), Z(5)^0 ] ], ...

In the Cayley graph is this list showing the vertices in the order they are connected?

Does the list above mean that the vertices are connected as $(\bar{1},\bar{0},\bar{0}) to (\bar{0},\bar{1},\bar{0}) to (\bar{0},\bar{0},\bar{1}) to (\bar{0},\bar{4},\bar{0})$ and so on?

And in the triplet [ Z(5)^0, 0*Z(5), 0*Z(5) ], is the first element from $\mathbb{Z}_3$ and the 2nd and 3rd elements from $(\mathbb{Z}_5 \times \mathbb{Z}_5)$?

Please help me with this question.

Thanks a lot in advance.