<Table Align="|l|l|l|l|">
<Caption>Projective group find homomorphism methods</Caption>
<HorLine/>
<Row>
<Item>3000</Item>
<Item><C>TrivialGroup</C></Item>
<Item>go through generators and compare to the identity</Item>
<Item><Ref Subsect="TrivialGroup"/></Item>
</Row>
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<Row>
<Item>1300</Item>
<Item><C>ProjDeterminant</C></Item>
<Item>find homomorphism to non-zero scalars mod d-th powers</Item>
<Item><Ref Subsect="ProjDeterminant"/></Item>
</Row>
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<Row>
<Item>1200</Item>
<Item><C>ReducibleIso</C></Item>
<Item>use the MeatAxe to find invariant subspaces</Item>
<Item><Ref Subsect="ReducibleIso"/></Item>
</Row>
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<Row>
<Item>1100</Item>
<Item><C>NotAbsolutelyIrred</C></Item>
<Item>write over a bigger field with smaller degree</Item>
<Item><Ref Subsect="NotAbsolutelyIrred"/></Item>
</Row>
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<Row>
<Item>1050</Item>
<Item><C>ClassicalNatural</C></Item>
<Item>check whether it is a classical group in its natural representation</Item>
<Item><Ref Subsect="ClassicalNatural"/></Item>
</Row>
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<Row>
<Item>1000</Item>
<Item><C>Subfield</C></Item>
<Item>write over a smaller field with same degree</Item>
<Item><Ref Subsect="Subfield"/></Item>
</Row>
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<Row>
<Item>900</Item>
<Item><C>C3C5</C></Item>
<Item>compute a normal subgroup of derived and resolve C3 and C5</Item>
<Item><Ref Subsect="C3C5"/></Item>
</Row>
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<Row>
<Item>850</Item>
<Item><C>C6</C></Item>
<Item>find either an (imprimitive) action or a symplectic one</Item>
<Item><Ref Subsect="C6"/></Item>
</Row>
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<Row>
<Item>840</Item>
<Item><C>D247</C></Item>
<Item>play games to find a normal subgroup</Item>
<Item><Ref Subsect="D247"/></Item>
</Row>
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<Row>
<Item>810</Item>
<Item><C>AltSymBBByDegree</C></Item>
<Item>try BB recognition for dim+1 and/or dim+2 if sensible</Item>
<Item><Ref Subsect="AltSymBBByDegree"/></Item>
</Row>
<HorLine/>
<Row>
<Item>800</Item>
<Item><C>TensorDecomposable</C></Item>
<Item>find a tensor decomposition</Item>
<Item><Ref Subsect="TensorDecomposable"/></Item>
</Row>
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<Row>
<Item>700</Item>
<Item><C>FindElmOfEvenNormal</C></Item>
<Item>find D2, D4 or D7 by finding an element of an even normal subgroup</Item>
<Item><Ref Subsect="FindElmOfEvenNormal"/></Item>
</Row>
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<Row>
<Item>600</Item>
<Item><C>LowIndex</C></Item>
<Item>find an (imprimitive) action on subspaces</Item>
<Item><Ref Subsect="LowIndex"/></Item>
</Row>
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<Row>
<Item>580</Item>
<Item><C>NameSporadic</C></Item>
<Item>generate maximal orders</Item>
<Item><Ref Subsect="NameSporadic"/></Item>
</Row>
<HorLine/>
<Row>
<Item>550</Item>
<Item><C>ComputeSimpleSocle</C></Item>
<Item>compute simple socle of almost simple group</Item>
<Item><Ref Subsect="ComputeSimpleSocle"/></Item>
</Row>
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<Row>
<Item>500</Item>
<Item><C>ThreeLargeElOrders</C></Item>
<Item>recognise Lie type groups and get its characteristic</Item>
<Item><Ref Subsect="ThreeLargeElOrders"/></Item>
</Row>
<HorLine/>
<Row>
<Item>400</Item>
<Item><C>LieTypeNonConstr</C></Item>
<Item>do non-constructive recognition of Lie type groups</Item>
<Item><Ref Subsect="LieTypeNonConstr"/></Item>
</Row>
<HorLine/>
<Row>
<Item>100</Item>
<Item><C>StabilizerChainProj</C></Item>
<Item>last resort: compute a stabilizer chain (projectively)</Item>
<Item><Ref Subsect="StabilizerChainProj"/></Item>
</Row>
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</Table>
