Unfortunately, the "StructureDescription"
function in GAP doesn't always provide the easiest description of a
group as a split or non-split extension, so not all of the presentations
below can easily be seen in terms of what GAP calls the group.  However, 
to me, they are still easier to work with than the six-generator 
PC presentations that GAP uses.  Keep in mind that for some operations 
(especially finding automorphism groups), these shorter presentations 
are not as efficient as GAP's presentations.

I welcome any input.

GAP Group 1
Structure Description Z64
f:=FreeGroup("a"); 
a:=f.1;
g:=f/[a^64];

GAP Group 2
Structure Description Z8 x Z8
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^8,b^8,Comm(a,b)];

GAP Group 3
Structure Description Z8 : Z8
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^8,b^8,a^b*a^3];

GAP Group 4
Structure Description ((Z8 x Z2) : Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b),Comm(a,c)*a^4*b,Comm(a,d)*c,Comm(b,c),Comm(b,d),Comm(c,d)];

GAP Group 5
Structure Description (Z4 x Z2) : Z8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^2,c^8,Comm(a,b),Comm(a,c)*a^2*b,Comm(b,c)*a^2];

GAP Group 6
Structure Description (Z8 x Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c)*a^2*b,Comm(b,c)];

GAP Group 7
Structure Description Q8 : Z8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^8,a^2*b^2,a^b*a,Comm(a,c)*b,Comm(b,c)];

GAP Group 8
Structure Description ((Z8 x Z2) : Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b),a^c*a^(-1)*b,Comm(b,c),Comm(a,d)*a^2,Comm(b,d),Comm(c,d)];

GAP Group 9
Structure Description (Q8 x Z2) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^4,Comm(a,b)*c^2,Comm(a,c)*b^(-1)*a,Comm(b,c)*a^(-1)*b];

GAP Group 10
Structure Description (Z8 : Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^4,Comm(a,c),Comm(b,c)*a^2];

GAP Group 11
Structure Description (Z2 x Z2) . ((Z4 x Z2) : Z2) = (Z4 x Z2) . (Z4 x 
Z2)
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2*a^4,Comm(a,b)*a^4,Comm(a,c)*b,Comm(b,c)*b^2];

GAP Group 12
Structure Description (Z4 : Z8) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^8,c^2,Comm(a,b)*a^2,Comm(a,c)*a^(-2),Comm(b,c)*b^(-2)*a^(-1)];


GAP Group 13
Structure Description (Z2 x Z2) . ((Z4 x Z2) : Z2) = (Z4 x Z2) . (Z4 x 
Z2)
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2*a^4,Comm(a,b)*a^4*b^2,Comm(a,c)*b,Comm(b,c)*b^2];

GAP Group 14
Structure Description (Z2 x Z2) . ((Z4 x Z2) : Z2) = (Z4 x Z2) . (Z4 x 
Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2*d,c^2*d,d^2,Comm(a,b)*a^4*d,Comm(a,c)*b*d,Comm(b,c)*d,Comm(a,d),Comm(b,d),Comm(c,d)];


GAP Group 15
Structure Description Z8 : Z8
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^8,b^8,a^b*a^5];

GAP Group 16
Structure Description Z8 : Z8
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^8,b^8,a^b*a];

GAP Group 17
Structure Description (Z8 x Z2) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^2,c^4,Comm(a,b),a^c*b*a^(-1),Comm(b,c)];

GAP Group 18
Structure Description (Z8 x Z2) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^2,c^4,Comm(a,b),Comm(a,c)*b^(-1)*a^(-2),Comm(b,c)*a^(-4)];


GAP Group 19
Structure Description Z4 . (Z4 x Z4)
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4*c^2,b^4*c^2,c^4,Comm(a,b)*c,Comm(a,c),Comm(b,c)];


GAP Group 20
Structure Description (Z4 x Z4) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^4,Comm(a,b),a^c*b*a,Comm(b,c)];

GAP Group 21
Structure Description (Z8 x Z2) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^2,c^4,Comm(a,b),a^c*b*a,Comm(b,c)];

GAP Group 22
Structure Description (Z4 x Z2) . D8 = Z4 . (Z4 x Z4)
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4*c^2,b^4*c^2,c^4,Comm(a,b)*c,Comm(a,c)*a^4,Comm(b,c)];

GAP Group 23
Structure Description (Z4 x Z2 x Z2) : Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^2,d^4,Comm(a,b),Comm(a,c),Comm(b,c),Comm(a,d)*b,Comm(b,d)*c,Comm(c,d)];


GAP Group 24
Structure Description (Z8 : Z2) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^2,c^4,Comm(a,b)*a^(-4),Comm(a,c)*b^(-1),Comm(b,c)];

GAP Group 25
Structure Description (Z8 x Z2) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^2,c^4,Comm(a,b),Comm(a,c)*b^(-1),Comm(b,c)*a^(-4)];


GAP Group 26
Structure Description Z16 x Z4
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^16,b^4,Comm(a,b)];

GAP Group 27
Structure Description Z16 : Z4
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^16,b^4,Comm(a,b)*a^8];

GAP Group 28
Structure Description Z16 : Z4
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^16,b^4,a^b*a^(-5)];

GAP Group 29
Structure Description (Z16 x Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,Comm(a,b),Comm(b,c),a^c*b*a^(-1)];

GAP Group 30
Structure Description (Z16 : Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,a^b*a^(7),a^c*b*a^(-1),Comm(b,c)];

GAP Group 31
Structure Description (Z16 x Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,Comm(a,b),a^c*b*a^(-5),b^c*b*a^8];

GAP Group 32
Structure Description ((Z8 : Z2) : Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b)*a^4,Comm(a,c)*b,Comm(a,d)*b*c,Comm(b,c),Comm(b,d),Comm(c,d)];


GAP Group 33
Structure Description (Z4 x Z2 x Z2) : Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^2,d^4,Comm(a,b),Comm(a,c),Comm(b,c),Comm(a,d)*c,Comm(b,d),Comm(c,d)*b];

GAP Group 34
Structure Description (((Z4 x Z2) : Z2) : Z2) : Z2 or (D8 x Z2) : Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^2,d^4,Comm(a,b)*a^2,Comm(a,c),Comm(a,d)*c,Comm(b,c),Comm(b,d)*a,Comm(c,d)*a^2];

GAP Group 35
Structure Description (Z4 x Z4) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^4,Comm(a,b),Comm(a,c)*b,Comm(b,c)*a^2];


GAP Group 36
Structure Description (Z2 . ((Z4 x Z2) : Z2) = (Z2 x Z2) . (Z4 x Z2)) : 
Z2 or Z2 . (((Z4 x Z2) : Z2) : Z2) = (Z4 x Z2) . (Z4 x Z2)
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4*e,b^2,c^2*e,d^2,e^2,Comm(a,b)*e,Comm(a,c)*b,Comm(b,c),Comm(a,d)*c,Comm(b,d),Comm(c,d)*e,Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 37
Structure Description Z2 . (((Z4 x Z2) : Z2) : Z2) = (Z4 x Z2) . (Z4 x 
Z2)
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4*e,b^2,c^2*e,d^2*e,e^2,Comm(a,b)*e,Comm(a,c)*b,Comm(b,c),Comm(a,d)*c,Comm(b,d),Comm(c,d)*e,Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 38
Structure Description (Z16 x Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,Comm(a,b),a^c*b*a,Comm(b,c)];

GAP Group 39
Structure Description Q16 : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2*a^8,Comm(a,b),a^c*b*a,Comm(b,c)];

GAP Group 40
Structure Description (Z16 x Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,Comm(a,b),a^c*b*a^(-3),b^c*b*a^8];

GAP Group 41
Structure Description (Z16 : Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2*b,a^b*a^7,a^c*b*a];

GAP Group 42
Structure Description (Z16 : Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,a^b*a^7,a^c*b*a^(-3),Comm(b,c)];

GAP Group 43
Structure Description Z2 . ((Z8 x Z2) : Z2) = Z8 . (Z4 x Z2)
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2*a^8,a^b*a^7,a^c*b*a^(-3),Comm(b,c)];

GAP Group 44
Structure Description Z4 : Z16
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^4,b^16,Comm(a,b)*a^2];

GAP Group 45
Structure Description Z8 . D8 = Z4 . (Z8 x Z2)
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^8,b^16,a^4*b^8,Comm(a,b)*a^2];

GAP Group 46
Structure Description Z16 : Z4
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^16,b^4,a^b*a^(-3)];

GAP Group 47
Structure Description Z16 : Z4
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^16,b^4,a^b*a];

GAP Group 48
Structure Description Z16 : Z4
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^16,b^4,a^b*a^9];

GAP Group 49
Structure Description Z4 . D16 = Z8 . (Z4 x Z2)
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^16,b^4*a^8,a^b*a];

GAP Group 50
Structure Description Z32 x Z2
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^32,b^2,Comm(a,b)];

GAP Group 51
Structure Description Z32 : Z2
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^32,b^2,a^b*a^15];

GAP Group 52
Structure Description D64
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^32,b^2,a^b*a];

GAP Group 53
Structure Description QD64
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^32,b^2,a^b*a^17];

GAP Group 54
Structure Description Q64
f:=FreeGroup("a","b");
a:=f.1;
b:=f.2;
g:=f/[a^32,b^4,a^16*b^2,a^b*a];

GAP Group 55
Structure Description Z4 x Z4 x Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^4,Comm(a,b),Comm(a,c),Comm(b,c)];

GAP Group 56
Structure Description ((Z4 x Z2) : Z4) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b),a^c*a^(-1)*b,Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 57
Structure Description (Z4 x Z4) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^4,Comm(a,b)*c^2,Comm(a,c),Comm(b,c)];

GAP Group 58
Structure Description ((Z4 x Z2) : Z2) x Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=[a^4,b^2,c^2,d^4,Comm(a,b),a^c*a^(-1)*b,Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 59
Structure Description (Z4 : Z4) x Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^4,a^b*a,Comm(a,c),Comm(b,c)];

GAP Group 60
Structure Description (Z2 x ((Z4 x Z2) : Z2)) : Z2 or (Z2 x Z2 x Z2 x 
Z2) : Z4
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^2,b^2,c^2,d^2,e^4,Comm(a,b),Comm(a,c),Comm(a,d),Comm(a,e)*d,Comm(b,c),Comm(b,d),Comm(b,e)*c,Comm(c,d),Comm(c,e),Comm(d,e)];


GAP Group 61
Structure Description ((Z4 : Z4) x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*c,Comm(c,d)];

GAP Group 62
Structure Description ((Z4 x Z2) : Z4) : Z2 or (Z4 x Z2 x Z2) : Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^2,d^4,Comm(a,b),Comm(a,c),Comm(a,d)*c,Comm(b,c),Comm(b,d)*a^2,Comm(c,d)];

GAP Group 63
Structure Description (Z4 x Z4) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^4,Comm(a,b),Comm(a,c)*b^2,Comm(b,c)*a^2];

GAP Group 64
Structure Description (Z4 x Z4) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^4,Comm(a,b),Comm(a,c)*b^2,Comm(b,c)*a^2*b^2];

GAP Group 65
Structure Description (Z4 x Z4) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^4,Comm(a,b),Comm(a,c)*a^2,Comm(b,c)*b^2];


GAP Group 66
Structure Description ((Z4 : Z4) x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d)*c,Comm(b,c),Comm(b,d)*c,Comm(c,d)];


GAP Group 67
Structure Description (Z4 x Z2 x Z2 x Z2) : Z2 or (D8 x Z2) : Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^2,d^4,Comm(a,b)*a^2,Comm(a,c),Comm(a,d)*c,Comm(b,c),Comm(b,d)*c,Comm(c,d)];


GAP Group 68
Structure Description (Z4 : Z4) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^4,Comm(a,b)*a^2,Comm(a,c)*b^2,Comm(b,c)];


GAP Group 69
Structure Description (Z4 x Z4 x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b)*a^2,Comm(a,c)*d,Comm(a,d),Comm(b,c)*a^2,Comm(b,d),Comm(c,d)];

GAP Group 70
Structure Description (Z4 : Z4) : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^4,Comm(a,b)*a^2,Comm(a,c)*a^2,Comm(b,c)*a^2*b^2];


GAP Group 71
Structure Description (Z4 x Z4 x Z2) : Z2 or (D8 x Z2) : Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^2,d^4,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a^2*c,Comm(c,d)];

GAP Group 72
Structure Description (Q8 x Z2) : Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,a^2*b^2,a^b*a,c^2,Comm(a,c),Comm(b,c),d^4,Comm(a,d)*c,Comm(b,d),Comm(c,d)];

GAP Group 73
Structure Description (Z2 x Z2 x D8) : Z2 or (Z4 x Z2) : D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b),Comm(a,c)*b,Comm(a,d)*a^2,Comm(b,c),Comm(b,d),Comm(c,d)*c^2];


GAP Group 74
Structure Description (Z2 x Z2 x Q8) : Z2 or (Z2 x Z2 x Z2) : Q8
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^2,b^2,c^2,d^4,e^2*d^2,Comm(d,e)*d^2,Comm(a,b),Comm(a,c),Comm(a,d)*c,Comm(a,e)*b,Comm(b,c),Comm(b,d),Comm(b,e),Comm(c,d),Comm(c,e)];


GAP Group 75
Structure Description (Z2 x ((Z4 x Z2) : Z2)) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b),Comm(a,c)*a^2,Comm(a,d)*b,Comm(b,c),Comm(b,d),Comm(c,d)*c^2];

GAP Group 76
Structure Description (Z4 x Z2) : Q8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,c^2*d^2,Comm(a,b),Comm(a,c)*b,Comm(a,d)*a^2,Comm(b,c),Comm(b,d),Comm(c,d)*c^2];


GAP Group 77
Structure Description ((Z4 : Z4) x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,a^b*a,Comm(a,c),Comm(a,d)*c,Comm(b,c),Comm(b,d)*a^2*b^2,Comm(c,d)];

GAP Group 78
Structure Description ((Z4 : Z4) x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,a^b*a,Comm(a,c),Comm(a,d)*b^2,Comm(b,c),Comm(b,d)*c,Comm(c,d)];

GAP Group 79
Structure Description (Z2 x Z2 x Z2) . (Z2 x Z2 x Z2) or Z2 . ((Z2 x Z2) 
. (Z2 x Z2 x Z2))
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,Comm(a,b)*a^2,c^4,d^2,a^2*c^2,Comm(a,c)*b^2*d,Comm(b,c)*d,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 80
Structure Description ((Z4 : Z4) x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,a^b*a,Comm(a,c),Comm(a,d)*a^2*b^2,Comm(b,c),Comm(b,d)*c,Comm(c,d)];

GAP Group 81
Structure Description (Z2 x Z2 x Z2) . (Z2 x Z2 x Z2) or Z2 . ((Z2 x Z2) 
. (Z2 x Z2 x Z2))
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,a^b*a,c^4,d^2,a^2*c^2*d,Comm(a,c)*b^2,Comm(b,c)*d,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 82
Structure Description (Z2 x Z2 x Z2) . (Z2 x Z2 x Z2) or Z2 . ((Z4 x Z4) 
: Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2*d,d^2,Comm(a,b)*d,a^c*a^(-1)*b^2*d,b^c*b*a^2,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 83
Structure Description Z8 x Z4 x Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c),Comm(b,c)];

GAP Group 84
Structure Description (Z8 : Z4) x Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^4,Comm(a,c),Comm(b,c)];

GAP Group 85
Structure Description (Z8 : Z2) x Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^2,c^4,a^b*a^3,Comm(a,c),Comm(b,c)];

GAP Group 86
Structure Description (Z8 x Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c),Comm(b,c)*a^4];

GAP Group 87
Structure Description ((Z8 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b),a^c*a^(-1)*b,Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 88
Structure Description ((Z8 : Z2) x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b),Comm(a,c)*a^4*b,Comm(a,d)*b,Comm(b,c),Comm(b,d),Comm(c,d)];

GAP Group 89
Structure Description (Z8 x Z2 x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b),Comm(a,c),Comm(a,d)*b,Comm(b,c),Comm(b,d),Comm(c,d)*a^4];


GAP Group 90
Structure Description (((Z4 x Z2) : Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=[a^4,b^2,c^2,d^2,e^2,Comm(a,b),a^c*a^(-1)*b,Comm(b,c),a^d*a^(-1)*c,Comm(b,d),Comm(c,d),Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];


GAP Group 91
Structure Description (((Z4 x Z2) : Z2) : Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,a^2*b^2,Comm(a,b)*a^2,c^2,Comm(a,c),Comm(b,c),d^4,Comm(a,d)*c,Comm(b,d),Comm(c,d)*a^2];

GAP Group 92
Structure Description ((Z8 : Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,a^b*a^3,a^c*a^(-1)*b,Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 93
Structure Description (Z2 . ((Z4 x Z2) : Z2) = (Z2 x Z2) . (Z4 x Z2)) x 
Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2*a^4,d^2,a^b*a^3,a^c*b*a^(-1),Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 94
Structure Description ((Z8 : Z2) x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b)*a^4,Comm(a,c),Comm(a,d)*b,Comm(b,c),Comm(b,d),Comm(c,d)*a^4];

GAP Group 95
Structure Description ((Z8 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b),a^c*a*b,Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 96
Structure Description (Q8 : Z4) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^4,d^2,a^2*b^2,a^b*a,a^c*b^(-1),b^c*a^(-1),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 97
Structure Description (Z8 x Z2 x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b),Comm(a,c),Comm(a,d)*a^2*b,Comm(b,c),Comm(b,d),Comm(c,d)*a^4];

GAP Group 98
Structure Description (Z2 x (Z8 : Z2)) : Z2 or D8 : (Z4 x Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c)*a^2,Comm(a,d),Comm(b,c)*a^3,Comm(b,d)*a^2,Comm(c,d)];


GAP Group 99
Structure Description (Z2 x (Z8 : Z2)) : Z2 or (D8 x Z2): Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^2,d^4,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a*c,Comm(c,d)*a^2];

GAP Group 100
Structure Description (Q8 : Z4) : Z2 (Z2 probably acts trivially on Q8 
here)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^4,d^2,a^2*b^2,a^b*a,a^c*b^(-1),b^c*a^(-1),Comm(a,d),Comm(b,d),Comm(c,d)*a^2]; 
IdGroup(g);

GAP Group 101
Structure Description ((Z4 x Z4) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*b^(-1),b^c*a^(-1),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 102
Structure Description (Z2 x (Z8 : Z2)) : Z2 or (D8 x Z2): Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^2,d^4,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a,Comm(c,d)*a^2];

GAP Group 103
Structure Description (Z4 : Z8) x Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^8,c^2,Comm(a,b)*a^2,Comm(a,c),Comm(b,c)];

GAP Group 104
Structure Description (Z4 : Z8) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^8,c^2,Comm(a,b)*a^2,Comm(a,c),Comm(b,c)*b^4];

GAP Group 105
Structure Description (Z4 : Z8) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^8,c^2,Comm(a,b)*a^2,Comm(a,c)*b^4,Comm(b,c)*b^4];

GAP Group 106
Structure Description (Z8 : Z4) x Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^6,Comm(a,c),Comm(b,c)];

GAP Group 107
Structure Description (Z8 : Z4) x Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^2,Comm(a,c),Comm(b,c)];

GAP Group 108
Structure Description (Z8 : Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^2,Comm(a,c),Comm(b,c)*a^4];

GAP Group 109
Structure Description (Z8 : Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^2,Comm(a,c)*a^4,Comm(b,c)];

GAP Group 110
Structure Description Z2 x (Z4 . D8 = Z4 . (Z4 x Z2))
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^8,c^2,a^b*a,a^4*b^4,Comm(a,c),Comm(b,c)];

GAP Group 111
Structure Description (Z4 . D8 = Z4 . (Z4 x Z2)) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^8,c^2,a^b*a,a^4*b^4,Comm(a,c)*a^4,Comm(b,c)];

GAP Group 112
Structure Description (Z8 x Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c)*b^2,Comm(b,c)];

GAP Group 113
Structure Description (Z4 : Z8) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^8,c^2,Comm(a,b)*b^4,b^c*a^2*b^(-1),Comm(a,c)];

GAP Group 114
Structure Description (Z8 x Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c)*a^4*b^2,Comm(b,c)*a^4];

GAP Group 115
Structure Description D8 x Z8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^2,c^8,Comm(a,c),Comm(b,c),a^b*a];

GAP Group 116
Structure Description (Z8 x Z2 x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b),Comm(a,c),Comm(a,d)*a^4,Comm(b,c),Comm(b,d)*c,Comm(c,d)];


GAP Group 117
Structure Description (Z8 x Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c)*b^2,Comm(b,c)*a^4*b^2];

GAP Group 118
Structure Description D16 x Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,Comm(a,c),Comm(b,c),a^b*a];

GAP Group 119
Structure Description QD16 x Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,Comm(a,c),Comm(b,c),a^b*a^5];

GAP Group 120
Structure Description Q16 x Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^4,a^8*b^2,c^2,Comm(a,c),Comm(b,c),a^b*a];

GAP Group 121
Structure Description (Z4 x Q8) : Z2 or Z8 : (Z4 x Z2)
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^2,Comm(a,c)*a^6,Comm(b,c)];

GAP Group 122
Structure Description Q16 : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,a^4*b^(-2),c^4,Comm(a,b)*a^2,Comm(a,c)*a^4,Comm(b,c)];

GAP Group 123
Structure Description (Z4 x D8) : Z2 or Z8: (Z4 x Z2)
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^4,Comm(a,c)*a^2,Comm(b,c)];

GAP Group 124
Structure Description (Z8 x Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c)*a^6,Comm(b,c)*a^2];

GAP Group 125
Structure Description ((Z4 x Z4) : Z2) : Z2 or D16 : Z4
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^2,c^4,Comm(a,b)*a^2,Comm(a,c)*a^4,Comm(b,c)*a^2];

GAP Group 126
Structure Description Z8 x Q8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^4,c^8,a^2*b^2,Comm(a,c),Comm(b,c),a^b*a];

GAP Group 127
Structure Description Z8 : Q8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^4,b^2*c^2,b^c*b,Comm(a,b)*a^4,Comm(a,c)];

GAP Group 128
Structure Description (D8 x Z2 x Z2) : Z2 or D8 : D8 (a few more 
structures)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c)*a^2,Comm(a,d),Comm(b,c)*a,Comm(b,d),Comm(c,d)*c^2];


GAP Group 129
Structure Description (Z2 x Z2 x Q8) : Z2 or Q8 : D8 (a few more 
structures)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2*a^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c)*b,Comm(a,d),Comm(b,c)*a^2,Comm(b,d),Comm(c,d)*c^2];


GAP Group 130
Structure Description (Z2 x D16) : Z2 or D8 : D8 (a few more structures)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c)*a^2,Comm(a,d),Comm(b,c)*a,Comm(b,d)*a^2,Comm(c,d)*c^2];

GAP Group 131
Structure Description (Z2 x QD16) : Z2 or (Z2 x Z2) : QD16
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^2,b^2,c^8,d^2,Comm(a,b),Comm(a,c),Comm(a,d),Comm(b,c)*a,Comm(b,d),Comm(c,d)*c^6];


GAP Group 132
Structure Description (Z2 x Q16) : Z2 or (Z2 x Z2) : Q16
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^2,b^2,c^8,c^4*d^2,Comm(a,b),Comm(a,c),Comm(a,d),Comm(b,c)*a,Comm(b,d),Comm(c,d)*c^2];


GAP Group 133
Structure Description (Z2 x Q16) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,a^4*b^2,c^2,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d)*a^2*c,Comm(b,c),Comm(b,d),Comm(c,d)];

GAP Group 134
Structure Description ((Z4 x Z4) : Z2) : Z2 or D8 : D8 (a few more 
structures)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d)*a^2,Comm(b,c)*a,Comm(b,d),Comm(c,d)*c^2];

GAP Group 135
Structure Description ((Z4 x Z4) : Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*b^(-1),b^c*a^(-1),Comm(a,d)*b^2,Comm(b,d)*a^2,Comm(c,d)*a*b^3];

GAP Group 136
Structure Description ((Z4 x Z4) : Z2) : Z2 or (Z8 : Z2) : (Z2 x Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*b^(-1),b^c*a^(-1),Comm(a,d)*b^2,Comm(b,d)*a^2,Comm(c,d)*a^2*b^2];

GAP Group 137
Structure Description ((Z4 x Z4) : Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*b^(-1),b^c*a^(-1),Comm(a,d)*a*b,Comm(b,d)*a*b,Comm(c,d)*a^2*b^2];

GAP Group 138
Structure Description (((Z4 x Z2) : Z2) : Z2) : Z2 or a split extension 
of a central product of two D8s where the action swaps the D8s
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,e^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),a^e*c^(-1),Comm(b,c),Comm(b,d),b^e*d^(-1),Comm(c,d)*c^2,c^e*a^(-1),d^e*b^(-1),a^2*c^2];


GAP Group 139
Structure Description (((Z4 x Z2) : Z2) : Z2) : Z2 or (Z4 x Z2 x Z2) : 
(Z2 x Z2)
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^2,c^2,d^2,e^2,Comm(a,b),Comm(a,c),Comm(a,d)*b,Comm(a,e)*c,Comm(b,c),Comm(b,d),Comm(b,e)*a^2,Comm(c,d)*a^2,Comm(c,e),Comm(d,e)];

GAP Group 140
Structure Description (Z4 x D8) : Z2 or Z4 : D16
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^8,c^2,Comm(a,b)*a^2,Comm(a,c),Comm(b,c)*b^2];

GAP Group 141
Structure Description (Z2 x QD16) : Z2 or Z4 : QD16
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^8,c^2,Comm(a,b)*a^2,Comm(a,c)*a^2,Comm(b,c)*b^6];

GAP Group 142
Structure Description (Q8 : Z4) : Z2 or Z4 : QD16
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^8,c^2,Comm(a,b)*a^2,Comm(a,c),Comm(b,c)*b^6];


GAP Group 143
Structure Description Z4 : Q16
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^8,c^4,b^4*c^2,b^c*b,Comm(a,b)*a^2,Comm(a,c)];

GAP Group 144
Structure Description (Z4 x D8) : Z2 or (Q8 : Z4) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^4,d^2,a^2*b^2,a^b*a,a^c*b^(-1),b^c*a^(-1),Comm(a,d)*c^2,Comm(b,d)*a^2*c^2,Comm(c,d)*a*b];

GAP Group 145
Structure Description (Z2 x Q16) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,a^4*b^2,c^2,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d)*a^2*c,Comm(b,c),Comm(b,d)*c,Comm(c,d)];

GAP Group 146
Structure Description (Z8 x Z2 x Z2) : Z2 or Z8 : D8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^4,Comm(a,c)*a^2,Comm(b,c)*b^2];

GAP Group 147
Structure Description (Z8 x Z2 x Z2) : Z2 or Z8 : D8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^2,Comm(a,c),Comm(b,c)*b^2];

GAP Group 148
Structure Description (Z2 x Q16) : Z2 or (Z2 x Z2) : Q16
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^2,b^2,c^8,c^4*d^2,Comm(a,b),Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a,Comm(c,d)*c^2];

GAP Group 149
Structure Description (Z2 x (Z8 : Z2)) : Z2 or Z8 : D8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^2,Comm(a,c)*a^6,Comm(b,c)*b^2];

GAP Group 150
Structure Description (Z2 x (Z8 : Z2)) : Z2 or Z8 : D8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^6,Comm(a,c)*a^2,Comm(b,c)*b^2];

GAP Group 151
Structure Description (Z2 x Q16) : Z2 or (Q8 : Z4) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^4,d^2,a^2*b^2,a^b*a,a^c*b^(-1),b^c*a^(-1),Comm(a,d)*c^2,Comm(b,d)*c^2,Comm(c,d)*a^2*c^2];

GAP Group 152
Structure Description (QD16 x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b)*a^6,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a^2*c,Comm(c,d)*a^4];

GAP Group 153
Structure Description (D16 x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a^2*c,Comm(c,d)*a^4];

GAP Group 154
Structure Description (Z2 x Q16) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,a^4*b^2,c^2,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a^2*c,Comm(c,d)*a^4];

GAP Group 155
Structure Description (Z8 : Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^2,Comm(a,c)*a^2*b^2,Comm(b,c)];

GAP Group 156
Structure Description Q8 : Q8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,a^2*b^2,c^4,c^2*d^2,Comm(a,b)*a^2,Comm(a,c)*b^(-1)*a^(-1),Comm(a,d),Comm(b,c)*a^(-1)*b^(-1),Comm(b,d),Comm(c,d)*c^2];

GAP Group 157
Structure Description (Z8 : Z4) : Z2 or D8 : Q8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2*c^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d)*a^2,Comm(b,c)*a^2,Comm(b,d)*a,Comm(c,d)*c^2];

GAP Group 158
Structure Description Q8 : Q8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,a^2*b^2,c^4,c^2*d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d)*a^2,Comm(b,c)*a^2,Comm(b,d)*a,Comm(c,d)*c^2];


GAP Group 159
Structure Description (Z8 : Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^2,Comm(a,c)*a^6*b^2,Comm(b,c)];

GAP Group 160
Structure Description (Z2 x Z2) . (Z2 x D8) = (Z4 x Z2) . (Z2 x Z2 x Z2) 
or Z2 . ((Z8 x Z2) : Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2*d,c^2*d,d^2,Comm(a,b)*d,Comm(a,c)*a^2,Comm(b,c)*b^2*a^4,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 161
Structure Description ((Z4 : Z4) x Z2) : Z2 or (Z8 : Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^2,Comm(a,c)*b^2,Comm(b,c)];

GAP Group 162
Structure Description (Z2 x (Z4 : Z4)) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^6,Comm(a,c)*b^2,Comm(b,c)*b^2];

GAP Group 163
Structure Description ((Z8 x Z2) : Z2) : Z2 or (Z8 : Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^2,Comm(a,c)*a^4*b^2,Comm(b,c)*b^2];

GAP Group 164
Structure Description (Q8 : Z4) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^4,d^2,a^2*b^2,a^b*a,a^c*b^(-1),b^c*a^(-1),Comm(a,d)*c^2,Comm(b,d)*c^2,Comm(c,d)];

GAP Group 165
Structure Description (Q8 : Z4) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^4,d^2,a^2*b^2,a^b*a,a^c*b^(-1),b^c*a^(-1),Comm(a,d)*a^2*c^2,Comm(b,d)*a^2*c^2,Comm(c,d)];

GAP Group 166
Structure Description (Z8 : Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^2,Comm(a,c)*b^2,Comm(b,c)*a^4];


GAP Group 167
Structure Description (Z8 x Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c)*a^2*b^2,Comm(b,c)*b^2];


GAP Group 168
Structure Description (Z2 x Z2) . (Z2 x D8) = (Z4 x Z2) . (Z2 x Z2 x Z2) 
or Z2 . (QD16 x Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2*d,c^2*d,d^2,Comm(a,c),Comm(b,c)*d,a^b*a^5*d,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 169
Structure Description (Z8 x Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c)*a^2*b^2,Comm(b,c)*a^4*b^2];

GAP Group 170
Structure Description (Q8 : Z4) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^4,d^2,a^2*b^2,a^b*a,a^c*b^(-1),b^c*a^(-1),Comm(a,d)*c^2,Comm(b,d)*a^2*c^2,Comm(c,d)*a*b*c^2];

GAP Group 171
Structure Description ((Z8 x Z2) : Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^4,Comm(a,c)*a^2*b^2,Comm(b,c)*b^2];

GAP Group 172
Structure Description (Z2 x Z2) . (Z2 x D8) = (Z4 x Z2) . (Z2 x Z2 x Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4*d,b^4,c^2*d,d^2,Comm(a,b)*d,a^c*a*b^2,b^c*b,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 173
Structure Description (Z8 x Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c)*a^6,Comm(b,c)*b^2];

GAP Group 174
Structure Description (Z8 x Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c)*a^2,Comm(b,c)*b^2];

GAP Group 175
Structure Description Z4 : Q16
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^4,b^8,c^4,b^4*c^2,b^c*b,Comm(a,b),Comm(a,c)*a^2];

GAP Group 176
Structure Description (Z8 x Z4) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b),Comm(a,c)*a^6,Comm(b,c)*a^4*b^2];

GAP Group 177
Structure Description (Z2 x D16) : Z2 or Z8 : D8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^4,Comm(a,c)*a^2,Comm(b,c)*b^2];

GAP Group 178
Structure Description (Z2 x Q16) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^2,Comm(a,b)*a^4,Comm(a,c)*a^6,Comm(b,c)*a^4*b^2];

GAP Group 179
Structure Description Z8 : Q8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^4,b^2*c^2,b^c*b,Comm(a,b)*a^6,Comm(a,c)];

GAP Group 180
Structure Description (Z2 x Z2) . (Z2 x D8) = (Z4 x Z2) . (Z2 x Z2 x Z2) 
or Z2 . ((Z8 x Z2) : Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2*d,c^2*d,d^2,Comm(a,b),Comm(a,c)*a^2,Comm(b,c)*b^2*a^4,Comm(a,d),Comm(b,d),Comm(c,d)];


GAP Group 181
Structure Description Z8 : Q8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^4,b^2*c^2,b^c*b,Comm(a,b)*a^2,Comm(a,c)];

GAP Group 182
Structure Description Z8 : Q8
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^8,b^4,c^4,b^2*c^2,b^c*b,Comm(a,b)*a^6,Comm(a,c)*a^2];

GAP Group 183
Structure Description Z16 x Z2 x Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,Comm(a,b),Comm(a,c),Comm(b,c)];

GAP Group 184
Structure Description (Z16 : Z2) x Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,a^b*a^7,Comm(a,c),Comm(b,c)];

GAP Group 185
Structure Description (Z16 x Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,Comm(a,b),Comm(a,c),b^c*b*a^8];

GAP Group 186
Structure Description D32 x Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,Comm(a,c),Comm(b,c),a^b*a];

GAP Group 187
Structure Description QD32 x Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,Comm(a,c),Comm(b,c),a^b*a^9];


GAP Group 188
Structure Description Q32 x Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^4,a^8*b^2,c^2,Comm(a,c),Comm(b,c),a^b*a];

GAP Group 189
Structure Description (Z16 x Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,Comm(a,b),a^c*a,b^c*b*a^8];

GAP Group 190
Structure Description (D16 x Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,a^b*a^7,a^c*a^9,Comm(b,c)];


GAP Group 191
Structure Description (Q16 x Z2) : Z2
f:=FreeGroup("a","b","c");
a:=f.1;
b:=f.2;
c:=f.3;
g:=f/[a^16,b^2,c^2,a^b*a^(7),a^c*a^(9),b^c*b*a^8];

GAP Group 192
Structure Description Z4 x Z4 x Z2 x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),Comm(c,d)];

GAP Group 193
Structure Description ((Z4 x Z2) : Z2) x Z2 x Z2 
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=[a^4,b^2,c^2,d^2,e^2,Comm(a,b),a^c*a^(-1)*b,Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d),Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 194
Structure Description (Z4 : Z4) x Z2 x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,a^b*a,Comm(a,c),Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 195
Structure Description ((Z4 x Z4) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*a^(-1)*b^2,Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 196
Structure Description D8 x Z4 x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,c),Comm(b,c),a^b*a,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 197
Structure Description Q8 x Z4 x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^4,d^2,a^2*b^2,Comm(a,c),Comm(b,c),a^b*a,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 198
Structure Description ((Z4 x Z2) : Z2) x Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^2,d^4,Comm(a,b),Comm(a,d),Comm(b,d),a^c*a,Comm(b,c)*a^2,Comm(c,d)];

GAP Group 199
Structure Description (D8 x Z4) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),Comm(c,d)*a^2];


GAP Group 200
Structure Description (Q8 x Z4) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,a^2*b^2,a^b*a,c^2,Comm(a,c),Comm(b,c),d^4,Comm(a,d),Comm(b,d),Comm(c,d)*a^2];

GAP Group 201
Structure Description (Z4 x Q8) : Z2 or (Z4 x Z2) : D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c)*a^2,Comm(a,d),Comm(b,c),Comm(b,d)*a^2,Comm(c,d)];

GAP Group 202
Structure Description ((Z2 x Z2 x Z2 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d","e","h");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
h:=f.6;
g:=f/[a^2,b^2,c^2,d^2,e^2,h^2,Comm(a,b),Comm(a,c),Comm(a,d),a^e*a*b,Comm(b,c),Comm(b,d),Comm(b,e),Comm(c,d),c^e*c*d,Comm(d,e),Comm(a,h),Comm(b,h),Comm(c,h),Comm(d,h),Comm(e,h)];

GAP Group 203
Structure Description ((Z4 x Z2 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^2,c^2,d^2,e^2,Comm(a,b),Comm(a,c),Comm(b,c),a^d*a,b^d*b*c,Comm(c,d),Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 204
Structure Description ((Q8 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^4,a^2*b^2,a^b*a,c^2,e^2,Comm(a,c),Comm(b,c),d^2,Comm(a,d)*c,Comm(b,d),Comm(c,d),Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 205
Structure Description ((Z4 x Z2 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^2,c^2,d^2,e^2,Comm(a,b),Comm(a,c),Comm(b,c),a^d*b*a^(-1),Comm(b,d),Comm(c,d)*a^2,Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 206
Structure Description (Z4 x Z2 x Z2 x Z2) : Z2 or (Z4 x Z2) : D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b),Comm(a,c),Comm(a,d),Comm(b,c)*a^2,Comm(b,d),Comm(c,d)*c^2];

GAP Group 207
Structure Description ((Z4 x Z4) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*a*b^2,b^c*b,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 208
Structure Description ((Z2 x Z2) . (Z2 x Z2 x Z2)) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,d^2,a^b*a,c^4,a^2*c^2,Comm(a,c)*b^2,Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 209
Structure Description ((Z4 x Z4) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,Comm(a,b),a^c*a^(-1)*b^2,b^c*b*a^2,d^2,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 210
Structure Description (Z4 x Z4 x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*b^2,Comm(c,d)*a^2*b^2];

GAP Group 211
Structure Description ((Z4 x Z4) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,Comm(a,b),a^c*a,b^c*b,d^2,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 212
Structure Description (Z4 : Q8) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^4,d^2,b^2*c^2,b^c*b,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 213
Structure Description (Z4 x Z4 x Z2) : Z2 or (Z4 x Z2) : D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b),Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a^2,Comm(c,d)*c^2];


GAP Group 214
Structure Description (Q8 x Z4) : Z2 or (Z4 x Z2) : Q8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,c^2*d^2,Comm(a,b),Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a^2,Comm(c,d)*c^2];
	
GAP Group 215
Structure Description (Z2 x Z2 x D8) : Z2 or (Z2 x Z2 x Z2) : D8
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^2,b^2,c^2,d^4,e^2,Comm(a,b),Comm(a,c),Comm(a,d)*c,Comm(a,e),Comm(b,c),Comm(b,d),Comm(b,e)*c,Comm(c,d),Comm(c,e),Comm(d,e)*d^2];

GAP Group 216
Structure Description (Z2 x Z2 x D8) : Z2 or (Z4 x Z2) : D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b),Comm(a,c),Comm(a,d)*a^2,Comm(b,c)*a^2,Comm(b,d),Comm(c,d)*c^2];


GAP Group 217
Structure Description (Q8 x Z2 x Z2) : Z2 or ((Z4 x Z4): Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*a^(-1)*b^2,Comm(a,d)*a^2*b^2,Comm(b,c),Comm(b,d)*b^2,Comm(c,d)*b^2];

GAP Group 218
Structure Description (Z2 x ((Z4 x Z2) : Z2)) : Z2 or (Z4 x Z2) : D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b),Comm(a,c)*a^2,Comm(a,d),Comm(b,c),Comm(b,d)*a^2,Comm(c,d)*c^2];

GAP Group 219
Structure Description (Z4 x D8) : Z2 or (Z4 x Z4) : (Z2 x Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),Comm(a,c)*b^2,Comm(a,d),Comm(b,c)*a^2,Comm(b,d)*b^2,Comm(c,d)];

GAP Group 220
Structure Description (Z4 x D8) : Z2 or ((Z4 : Z4) x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d)*b^2,Comm(b,c),Comm(b,d),Comm(c,d)*a^2];

GAP Group 221
Structure Description (Z4 x D8) : Z2 or ((Z4 x Z4) : Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*a^(-1)*b^2,Comm(a,d),Comm(b,c),Comm(b,d)*b^2,Comm(c,d)*a^2*b^2];

GAP Group 222
Structure Description (Z4 x Q8) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,a^2*b^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a^2*c^2,Comm(c,d)*a^2];

GAP Group 223
Structure Description (Z4 x Q8) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*a^(-1)*b^2,Comm(a,d),Comm(b,c),Comm(b,d)*b^2,Comm(c,d)*a^2];

GAP Group 224
Structure Description ((Z2 x Q8) : Z2) : Z2 or (Z2 x Z2 x Z2) : Q8
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^2,b^2,c^2,d^4,e^2,Comm(a,b),Comm(a,c),Comm(a,d)*c,Comm(a,e),Comm(b,c),Comm(b,d),Comm(b,e)*c,Comm(c,d),Comm(c,e),Comm(d,e)*d^2];

GAP Group 225
Structure Description (Z4 : Q8) : Z2 or (Z4 x Z2) : Q8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,c^2*d^2,Comm(a,b),Comm(a,c),Comm(a,d)*a^2,Comm(b,c)*a^2,Comm(b,d),Comm(c,d)*c^2];

GAP Group 226
Structure Description D8 x D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,a^b*a,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),c^d*c];

GAP Group 227
Structure Description (Z2 x Z2 x D8) : Z2 or D8 : D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c)*a^2,Comm(b,d)*a^2,Comm(c,d)*c^2];

GAP Group 228
Structure Description (Z4 x D8) : Z2 or D8 : D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a^2,Comm(c,d)*c^2];

GAP Group 229
Structure Description (Z2 x Z2 x Q8) : Z2 or Q8 : D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2*a^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c)*a^2,Comm(b,d),Comm(c,d)*c^2];

GAP Group 230
Structure Description Q8 x D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,a^2*b^2,c^4,d^2,a^b*a,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),c^d*c];

GAP Group 231
Structure Description (Z4 x D8) : Z2 or Q8 : D8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2*a^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a^2,Comm(c,d)*c^2];

GAP Group 232
Structure Description (Z4 x D8) : Z2 or (Z4 x Z4) : (Z2 x Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),Comm(a,c),Comm(a,d)*b^2,Comm(b,c)*a^2,Comm(b,d),Comm(c,d)];

GAP Group 233
Structure Description (Z4 x Q8) : Z2 or ((Z4 : Z4) x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d)*b^2,Comm(b,c),Comm(b,d)*a^2,Comm(c,d)*b^2];

GAP Group 234
Structure Description (Z4 x D8) : Z2 or (Z4 x Z4 x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;


GAP Group 235
Structure Description (Z4 x Q8) : Z2 or D8 : Q8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2*c^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a^2,Comm(c,d)*c^2];

GAP Group 236
Structure Description (Z4 x D8) : Z2 or ((Z4 x Z4) : Z2): Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*a^(-1)*b^2,Comm(a,d),Comm(b,c),Comm(b,d)*a^2,Comm(c,d)*a^2*b^2];

GAP Group 237
Structure Description (Z4 x Q8) : Z2 or ((Z4 x Z4) : Z2): Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*a^(-1)*b^2,Comm(a,d)*b^2,Comm(b,c),Comm(b,d)*a^2*b^2,Comm(c,d)*a^2*b^2];

GAP Group 238
Structure Description Q8 : Q8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,a^2*b^2,c^4,c^2*d^2,Comm(a,b)*a^2,Comm(a,c)*a^2,Comm(a,d),Comm(b,c),Comm(b,d),Comm(c,d)*c^2];

GAP Group 239
Structure Description Q8 x Q8
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,a^2*b^2,c^4,d^4,c^2*d^2,a^b*a,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),c^d*c];

GAP Group 240
Structure Description (D8 x Z4) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2,c^4,d^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d)*a^2,Comm(b,c),Comm(b,d)*c^2,Comm(c,d)*a^2*c^2];

GAP Group 241
Structure Description ((Z4 x Z2 x Z2) : Z2) : Z2 or (Z4 x Z4) : (Z2 x 
Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),Comm(a,c)*b^2,Comm(a,d)*a^2,Comm(b,c)*a^2*b^2,Comm(b,d)*b^2,Comm(c,d)];

GAP Group 242
Structure Description ((Z4 x Z4) : Z2) : Z2 or (Z4 x Z4) : (Z2 x Z2)
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),Comm(a,c)*b^2,Comm(a,d)*a^2*b^2,Comm(b,c)*a^2,Comm(b,d)*b^2,Comm(c,d)];

GAP Group 243
Structure Description ((Z2 x Z2) . (Z2 x Z2 x Z2)) : Z2 or ((Z4 x Z4) : 
Z2): Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*a*b^2,Comm(a,d)*b^2,b^c*b,Comm(b,d)*a^2,Comm(c,d)*b^2];

GAP Group 244
Structure Description ((Z4 x Z4) : Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,c^2,d^2,Comm(a,b),a^c*a^(-1)*b^2,Comm(a,d)*a^2*b^2,b^c*b*a^2,Comm(b,d)*a^2,Comm(c,d)*b^2];

GAP Group 245
Structure Description (Z2 x Z2) . (Z2 x Z2 x Z2 x Z2) or Z2 . (Central 
product of D8 and Q8)
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^2*e,c^4,d^4,e^2,a^b*a,Comm(a,c),Comm(a,d)*e,Comm(b,c)*e,Comm(b,d),c^d*c,c^2*d^2*e,a^2*c^2*e,Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 246
Structure Description Z8 x Z2 x Z2 x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b),Comm(a,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 247
Structure Description (Z8 : Z2) x Z2 x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,a^b*a^3,Comm(a,c),Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 248
Structure Description ((Z8 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,Comm(a,b),Comm(a,c),b^c*b*a^4,d^2,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 249
Structure Description ((Z8 : Z2) x Z2) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b)*a^4,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d)*a^4,Comm(c,d)*a^4];


GAP Group 250
Structure Description D16 x Z2 x Z2 
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,c),Comm(b,c),a^b*a,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 251
Structure Description QD16 x Z2 x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,c),Comm(b,c),a^b*a^9,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 252
Structure Description Q16 x Z2 x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^4,c^2,d^2,a^4*b^2,Comm(a,c),Comm(b,c),a^b*a,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 253
Structure Description ((Z8 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,Comm(a,b),a^c*a,b^c*b*a^4,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 254
Structure Description ((D8 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2,a^b*a^3,a^c*a^5,Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 255
Structure Description ((Q8 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^4,a^2*b^2,c^2,d^2,a^b*a^3,a^c*a^5,Comm(b,c),Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 256
Structure Description (Z2 x (Z8 : Z2)) : Z2 or a Central product of 
[32,44] and Z4
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^8,b^2,c^2,d^2*a^4,a^b*a^3,a^c*a^5,b^c*b*a^4,Comm(a,d),Comm(b,d),Comm(c,d)];

GAP Group 257
Structure Description (Z2 x D16) : Z2 or Central product of Q8 and Q16
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2*a^2,c^8,c^4*d^2,a^2*c^4,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),Comm(c,d)*c^2];


GAP Group 258
Structure Description (Z2 x QD16) : Z2 or Central product of Q8 and QD16
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2*a^2,c^8,d^2,a^2*c^4,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),Comm(c,d)*c^4];

GAP Group 259
Structure Description (Z2 x Q16) : Z2
f:=FreeGroup("a","b","c","d");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
g:=f/[a^4,b^2*a^2,c^8,d^2,a^2*c^4,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),Comm(c,d)*c^2];

GAP Group 260
Structure Description Z4 x Z2 x Z2 x Z2 x Z2
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^2,c^2,d^2,e^2,Comm(a,b),Comm(a,c),Comm(a,d),Comm(a,e),Comm(b,c),Comm(b,d),Comm(b,e),Comm(c,d),Comm(c,e),Comm(d,e)];

GAP Group 261
Structure Description D8 x Z2 x Z2 x Z2
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^2,c^2,d^2,a^b*a,e^2,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),Comm(c,d),Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 262
Structure Description Q8 x Z2 x Z2 x Z2
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^4,a^2*b^2,c^2,d^2,e^2,a^b*a,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),Comm(c,d),Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 263
Structure Description ((Z4 x Z2) : Z2) x Z2 x Z2
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^2,c^2,d^2,e^2,Comm(a,b),Comm(a,d),Comm(b,d),a^c*a,Comm(b,c)*a^2,Comm(c,d),Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 264
Structure Description ((D8 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^2,c^4,d^2,e^2,a^b*a,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),c^d*c,a^2*c^2,Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 265
Structure Description ((Q8 x Z2) : Z2) x Z2
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^4,a^2*b^2,c^4,d^2,e^2,a^b*a,Comm(a,c),Comm(a,d),Comm(b,c),Comm(b,d),c^d*c,a^2*c^2,Comm(a,e),Comm(b,e),Comm(c,e),Comm(d,e)];

GAP Group 266
Structure Description (((Z4 x Z2) : Z2) x Z2) : Z2 or a Central Product 
of D8 with (Z4 x Z2) : Z2
f:=FreeGroup("a","b","c","d","e");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
g:=f/[a^4,b^2,a^2*c^2,d^2,e^2,Comm(a,b)*a^2,Comm(a,c),Comm(a,d),Comm(a,e),Comm(b,c),Comm(b,d),Comm(b,e),Comm(c,d),Comm(c,e)*c^2,Comm(d,e)*c^2];

GAP Group 267
Structure Description Z2 x Z2 x Z2 x Z2 x Z2 x Z2
f:=FreeGroup("a","b","c","d","e","h");
a:=f.1;
b:=f.2;
c:=f.3;
d:=f.4;
e:=f.5;
h:=f.6;
g:=f/[a^2,b^2,c^2,d^2,e^2,h^2,Comm(a,b),Comm(a,c),Comm(a,d),Comm(a,e),Comm(b,c),Comm(b,d),Comm(b,e),Comm(c,d),Comm(c,e),Comm(d,e),Comm(a,h),Comm(b,h),Comm(c,h),Comm(d,h),Comm(e,h)];