<Table Align="|l|l|l|l|">
<Caption>Permutation group find homomorphism methods</Caption>
<HorLine/>
<Row>
<Item>1250</Item>
<Item><C>FewGensAbelian</C></Item>
<Item>if very few generators, check IsAbelian and if yes, do KnownNilpotent</Item>
<Item><Ref Subsect="FewGensAbelian"/></Item>
</Row>
<HorLine/>
<Row>
<Item>1050</Item>
<Item><C>FewGensAbelian</C></Item>
<Item>if very few generators, check IsAbelian and if yes, do KnownNilpotent</Item>
<Item><Ref Subsect="FewGensAbelian"/></Item>
</Row>
<HorLine/>
<Row>
<Item>300</Item>
<Item><C>TrivialGroup</C></Item>
<Item>go through generators and compare to the identity</Item>
<Item><Ref Subsect="TrivialGroup"/></Item>
</Row>
<HorLine/>
<Row>
<Item>100</Item>
<Item><C>ThrowAwayFixedPoints</C></Item>
<Item>try to find a huge amount of (possible internal) fixed points</Item>
<Item><Ref Subsect="ThrowAwayFixedPoints"/></Item>
</Row>
<HorLine/>
<Row>
<Item>99</Item>
<Item><C>FewGensAbelian</C></Item>
<Item>if very few generators, check IsAbelian and if yes, do KnownNilpotent</Item>
<Item><Ref Subsect="FewGensAbelian"/></Item>
</Row>
<HorLine/>
<Row>
<Item>97</Item>
<Item><C>Pcgs</C></Item>
<Item>use a Pcgs to calculate a stabilizer chain</Item>
<Item><Ref Subsect="Pcgs"/></Item>
</Row>
<HorLine/>
<Row>
<Item>95</Item>
<Item><C>MovesOnlySmallPoints</C></Item>
<Item>calculate a stabilizer chain if only small points are moved</Item>
<Item><Ref Subsect="MovesOnlySmallPoints"/></Item>
</Row>
<HorLine/>
<Row>
<Item>90</Item>
<Item><C>NonTransitive</C></Item>
<Item>try to find non-transitivity and restrict to orbit</Item>
<Item><Ref Subsect="NonTransitive"/></Item>
</Row>
<HorLine/>
<Row>
<Item>80</Item>
<Item><C>Giant</C></Item>
<Item>tries to find Sn and An in their natural actions</Item>
<Item><Ref Subsect="Giant"/></Item>
</Row>
<HorLine/>
<Row>
<Item>70</Item>
<Item><C>Imprimitive</C></Item>
<Item>for a imprimitive permutation group, restricts to block system</Item>
<Item><Ref Subsect="Imprimitive"/></Item>
</Row>
<HorLine/>
<Row>
<Item>60</Item>
<Item><C>LargeBasePrimitive</C></Item>
<Item>recognises large-base primitive permutation groups</Item>
<Item><Ref Subsect="LargeBasePrimitive"/></Item>
</Row>
<HorLine/>
<Row>
<Item>55</Item>
<Item><C>StabilizerChainPerm</C></Item>
<Item>for a permutation group using a stabilizer chain via the <URL Text="genss package">https://gap-packages.github.io/genss/</URL></Item>
<Item><Ref Subsect="StabilizerChainPerm"/></Item>
</Row>
<HorLine/>
<Row>
<Item>50</Item>
<Item><C>StabChain</C></Item>
<Item>for a permutation group using a stabilizer chain</Item>
<Item><Ref Subsect="StabChain"/></Item>
</Row>
<HorLine/>
</Table>
