If I understand your question right, your group $G$ has order $5160960$,
and it has an elementary abelian normal subgroup $N$ of order $2^7$ such
that $G/N \cong {\rm S}_8$. This can be found with GAP as follows:

```
gap> A := PermutationMat((1,2),9);;
gap> B := PermutationMat((1,2,3,4,5,6,7,8),9);;
gap> C := [[1,-1,0,0,0,0,0,0,1]/2,
> [-1,1,0,0,0,0,0,0,1]/2,
> [1,1,2,0,0,0,0,0,-1]/2,
> [1,1,0,2,0,0,0,0,-1]/2,
> [1,1,0,0,2,0,0,0,-1]/2,
> [1,1,0,0,0,2,0,0,-1]/2,
> [1,1,0,0,0,0,2,0,-1]/2,
> [1,1,0,0,0,0,0,2,-1]/2,
> [1,1,0,0,0,0,0,0,0]];;
gap> G := Group(A,B,C);
<matrix group with 3 generators>
gap> Size(G);
5160960
gap> N := NormalSubgroups(G);
[ Group([ ]), <matrix group of size 2 with 1 generators>,
<matrix group of size 128 with 7 generators>,
<matrix group of size 2580480 with 9 generators>,
<matrix group of size 5160960 with 3 generators> ]
gap> StructureDescription(N[3]);
"C2 x C2 x C2 x C2 x C2 x C2 x C2"
gap> Q := G/N[3];
Group([ (16,24)(17,21)(18,22)(19,23)(20,25)(27,28), (1,6,19,21,12,20,24,13)
(2,16,23,11)(3,5,9,17,22,27,25,14)(4,7,8,10,18,26,28,15), (16,24)(17,21)
(18,22)(19,23)(20,25)(27,28) ])
gap> StructureDescription(Q);
"S8"
```