# ApCoCoA-1:Other7 groups

### Other Groups

#### Description

The next group has the order |G| = 9216 and the following finite representation:

``` G = <a,b | a^{2}b^{-3} = (ababa^{2}ab^{2})^2 = 1>
```

#### Reference

No reference available

#### Computation

``` /*Use the ApCoCoA package ncpoly.*/

// a is invers to c and b is invers to d
Use ZZ/(2)[a,b,c,d];
NC.SetOrdering("LLEX");
Define CreateRelationsOther7()
Relations:=[];

// add the invers relations ac = ca = bd = db = 1
Append(Relations,[[a,c],[1]]);
Append(Relations,[[c,a],[1]]);
Append(Relations,[[b,d],[1]]);
Append(Relations,[[d,b],[1]]);

// add the relation a^{2}b^{-3} = 1
Append(Relations,[[a,a,d,d,d],[1]]);

// add the relation (ababa^{2}ab^{2})^2=  1
Append(Relations,[[a,b,a,b,a,a,a,b,b,a,b,a,b,a,a,a,b,b],[1]]);

Return Relations;
EndDefine;

Relations:=CreateRelationsOther7();
GB:=NC.GB(Relations,31,1,100,1000);
```

#### Example in Symbolic Data Format

``` <FREEALGEBRA createdAt="2014-01-20" createdBy="strohmeier">
<vars>a,b,c,d</vars>
<uptoDeg>14</uptoDeg>
<basis>
<ncpoly>a*c-1</ncpoly>
<ncpoly>c*a-1</ncpoly>
<ncpoly>b*d-1</ncpoly>
<ncpoly>d*b-1</ncpoly>
<ncpoly>a*a*d*d*d-1</ncpoly>
<ncpoly>(a*b*a*b*a*a*a*b*b)^2-1</ncpoly>
</basis>
<Comment>The partial LLex Gb has 199 elements</Comment>
<Comment>Other_groups7</Comment>
</FREEALGEBRA>
```