# Interpreting semidirect product in GAP in terms of underlying groups

I obtained the group $$G$$ which is the semidirect product $$(\mathbb{Z}_5 \times \mathbb{Z}_5) \rtimes \mathbb{Z}_3$$ in GAP as below.

gap> m:=[[4,0],[0,2]]*One(GF(5));
[ [ Z(5)^2, 0*Z(5) ], [ 0*Z(5), Z(5) ] ]
gap> s1:=SemidirectProduct(Group(m),GF(5)^2);
<matrix group of size 100 with 3 generators>


And when I obtained the elements of $$G$$ I get a list which continues as follows.

gap> Elements(s1);
[ [ [ 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) ], [ 0*Z(5), Z(5)^0, 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), 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)^2, Z(5)^0 ] ],...


I want to write the elements as $$(\bar0,(\bar0,\bar0)),(\bar0,(\bar0,\bar1)),(\bar0,(\bar0,\bar2))$$,....

Can someone please tell how to interpret the elements in the above list which are present as [ Z(5)^0, 0*Z(5), 0*Z(5) ], [ 0*Z(5), Z(5)^0, 0*Z(5) ] ... to obtain the form I want.

What does Z(5)^0, 0*Z(5) mean?

The notation Z(5) stands for a generator of the unit group of the finite field with five elements. So Z(5)^0 is $$1$$, and 0*Z(5) is $$0$$ is the finite field. The command IntFFE will convert these numbers for you.
gap> IntFFE(Z(5));