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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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# F(3,5)

Gr: a,b,c,d,e;
Rel: abc=d, bcd=e, cde=a, dea=b, eab=c;
Gen:c;

Mess:10000;
Pure C;
End;

Felsch:1;
End;

Max:200;
Com:100;
Aep:7;

# Results (did ALL 3932160 runs, in 4h14m) ...
# Group Relators: bAED, DCaE, AEcB, DCBe, bcDa;
# INDEX = 1 (a=1 r=2 h=2 n=2; l=4 c=0.00; m=73 t=85)
# Group Relators: CaED, BAEc, Ebcd, aBde, bcDa;
# INDEX = 1 (a=1 r=2 h=2 n=2; l=4 c=0.01; m=72 t=84)
# Group Relators: CBeD, BAEc, eAcd, AdCB, aBde;
# INDEX = 1 (a=1 r=2 h=2 n=2; l=4 c=0.00; m=70 t=78)