Symplectic groups (and variants)

Symplectic groupVariants
S4(2)
S4(3)CPSp4(3)=S4(3):2Sp4(3)
S4(4)
S6(2)
S8(2)

Projective symplectic groups in more detail

GroupStandard generatorsConjugacy classesCharacter informationModular informationPermutation representationsLinear representationsMaximal subgroups
PSp4(2)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
PSp4(3)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
PSp4(4)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
PSp6(2)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
PSp8(2)YesYesCompleteNo Ext1 matrixAll primitive except largestAll irreducibles in positive characteristc of dimension at most 3000, all for characteristic 2All, but SLPs are only to generators, not standard generators

Symplectic groups in more detail

GroupStandard generatorsConjugacy classesCharacter informationModular informationPermutation representationsLinear representationsMaximal subgroups
Sp4(2)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
Sp4(3)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
Sp4(4)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
Sp6(2)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
Sp8(2)YesYesCompleteNo Ext1 matrixAll primitive except largestAll irreducibles in positive characteristc of dimension at most 3000, all for characteristic 2All, but SLPs are only to generators, not standard generators

Projective conformal symplectic groups in more detail

GroupStandard generatorsConjugacy classesCharacter informationModular informationPermutation representationsLinear representationsMaximal subgroups
PCSp4(2)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
PCSp4(3)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
PCSp4(4)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
PCSp6(2)YesYesCompleteCompleteAll primitiveAll irreducibles in positive characteristcAll, with SLPs with standard generators if applicable
PCSp8(2)YesYesCompleteNo Ext1 matrixAll primitive except largestAll irreducibles in positive characteristc of dimension at most 3000, all for characteristic 2All, but SLPs are only to generators, not standard generators