These are words for the maximal subgroup of Fi23 with shape 
[3^10].(L_3(3) x 2) .  'a' and 'b' are standard generators for 
any representation which can be called from the atlasrep package.  
Simply copy-and-paste the following into GAP to get the generators of 
this maximal subgroup.  If anyone has the desire, it would be much 
appreciated to get these words in shorter form.  I ignored the letters 
'f' and 'g' since those are often used for other variables in GAP, at 
least by me.


c:=a*b;
d:=b*c;
e:=c*d;
h:=d*e;
i:=c*e;
words:=[c^2*i^2*d*c*i*c^5*i*d*i^2*h^2*e*h^3*d*i*c^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*
h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*
d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*
c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^3*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i*h*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*
h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i*h*d
^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*
d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*
h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^
2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*
d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3
*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*
c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*
i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2
*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h
*d^2*i*h*c^2*i*e*d*h^3*d^2*h*c*i*h*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c
*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i
*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^
2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^3*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2
*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^3*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2
*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^
2*i*h*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c
*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^3*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i*h*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h
*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i*h*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d
*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2
*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d
*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*
d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c
*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*
i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i
^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*
c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2
*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h
*d^2*i*h*c^2*i*e*d*h^3*d^2*h*c*i*h*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i
*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^3*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2
*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^3*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2
*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^
2*i*h*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c
*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^3*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*
i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i*h*d^4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h
*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i*h*d^
4*h*d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d
*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2
*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*
d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*
i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i
^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*
c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2
*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i

^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2
*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*
h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*b*a*b,b*d^3*c^5*i*d*c^6*i*c*i^2*h*d*c*i^2*h*d^3*i*e*d*i^2*e*d*i^4*e*d*i*e*d*c^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*
c*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*h*d^4*h*
d*c*i^2*h^2*i^3*e*d*i*e*h^2*d*i*d*h*c^2*i*e*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h
*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2
*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d
^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h
*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c
*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d
*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*
c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2
*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i
^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i*d*c^2*i^3*d*c*i*c*i*c*i*d*h^3*d*i*e*h*d*i^3*e*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2
*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d^2*i^2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^
2*h*d^2*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d*c*i^2*h*d^2*i^2*h*d*c*i^2*h*b*a];