Extensions 1→N→G→Q→1 with N=C3 and Q=C3×GL2(𝔽3)

Direct product G=N×Q with N=C3 and Q=C3×GL2(𝔽3)
dρLabelID
C32×GL2(𝔽3)72C3^2xGL(2,3)432,614

Semidirect products G=N:Q with N=C3 and Q=C3×GL2(𝔽3)
extensionφ:Q→Aut NdρLabelID
C3⋊(C3×GL2(𝔽3)) = C3×C6.6S4φ: C3×GL2(𝔽3)/C3×SL2(𝔽3)C2 ⊆ Aut C3484C3:(C3xGL(2,3))432,617

Non-split extensions G=N.Q with N=C3 and Q=C3×GL2(𝔽3)
extensionφ:Q→Aut NdρLabelID
C3.1(C3×GL2(𝔽3)) = C32.GL2(𝔽3)φ: C3×GL2(𝔽3)/C3×SL2(𝔽3)C2 ⊆ Aut C37212+C3.1(C3xGL(2,3))432,245
C3.2(C3×GL2(𝔽3)) = C3×Q8⋊D9φ: C3×GL2(𝔽3)/C3×SL2(𝔽3)C2 ⊆ Aut C31444C3.2(C3xGL(2,3))432,246
C3.3(C3×GL2(𝔽3)) = C322GL2(𝔽3)φ: C3×GL2(𝔽3)/C3×SL2(𝔽3)C2 ⊆ Aut C37212+C3.3(C3xGL(2,3))432,248
C3.4(C3×GL2(𝔽3)) = C9×GL2(𝔽3)central extension (φ=1)722C3.4(C3xGL(2,3))432,241

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