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ITCS-4182/gap/E6.gap

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f := FreeGroup( 6 );
g := f / [ f.1^2,
f.2^2,
f.3^2,
f.4^2,
f.5^2,
f.6^2,
( f.1*f.2 )^3,
( f.2*f.3 )^3,
( f.3*f.4 )^3,
( f.3*f.5 )^3,
( f.5*f.6 )^3,
( f.1*f.3 )^2,
( f.1*f.4 )^2,
( f.1*f.5 )^2,
( f.1*f.6 )^2,
( f.2*f.4 )^2,
( f.2*f.5 )^2,
( f.2*f.6 )^2,
( f.3*f.6 )^2,
( f.4*f.5 )^2,
( f.4*f.6 )^2,
];
tab := CosetTable( g, Subgroup(g, [ ]));
time;