gap&gt; pg := PG(4,8);
ProjectiveSpace(4, 8)
gap&gt; group := CollineationGroup(pg);
The FinInG collineation group PGammaL(5,8)
gap&gt; HasNiceMonomorphism(group);
false
gap&gt; Random(group);
&lt; a collineation: &lt;cmat 5x5 over GF(2,3)&gt;, F^4&gt;
gap&gt; time;
1028
gap&gt; HasNiceMonomorphism(group);
true
gap&gt; Random(group);
&lt; a collineation: &lt;cmat 5x5 over GF(2,3)&gt;, F^0&gt;
gap&gt; time;
3
