# Extensions 1→N→G→Q→1 with N=C5×SL2(𝔽3) and Q=C4

Direct product G=N×Q with N=C5×SL2(𝔽3) and Q=C4
dρLabelID
C20×SL2(𝔽3)160C20xSL(2,3)480,655

Semidirect products G=N:Q with N=C5×SL2(𝔽3) and Q=C4
extensionφ:Q→Out NdρLabelID
(C5×SL2(𝔽3))⋊1C4 = C5⋊U2(𝔽3)φ: C4/C1C4 ⊆ Out C5×SL2(𝔽3)1208+(C5xSL(2,3)):1C4480,961
(C5×SL2(𝔽3))⋊2C4 = D10.S4φ: C4/C1C4 ⊆ Out C5×SL2(𝔽3)408-(C5xSL(2,3)):2C4480,962
(C5×SL2(𝔽3))⋊3C4 = F5×SL2(𝔽3)φ: C4/C1C4 ⊆ Out C5×SL2(𝔽3)408-(C5xSL(2,3)):3C4480,965
(C5×SL2(𝔽3))⋊4C4 = Q8⋊Dic15φ: C4/C2C2 ⊆ Out C5×SL2(𝔽3)160(C5xSL(2,3)):4C4480,260
(C5×SL2(𝔽3))⋊5C4 = C52U2(𝔽3)φ: C4/C2C2 ⊆ Out C5×SL2(𝔽3)1204(C5xSL(2,3)):5C4480,261
(C5×SL2(𝔽3))⋊6C4 = Dic5×SL2(𝔽3)φ: C4/C2C2 ⊆ Out C5×SL2(𝔽3)160(C5xSL(2,3)):6C4480,266
(C5×SL2(𝔽3))⋊7C4 = C5×Q8⋊Dic3φ: C4/C2C2 ⊆ Out C5×SL2(𝔽3)160(C5xSL(2,3)):7C4480,256
(C5×SL2(𝔽3))⋊8C4 = C5×U2(𝔽3)φ: C4/C2C2 ⊆ Out C5×SL2(𝔽3)1202(C5xSL(2,3)):8C4480,257

Non-split extensions G=N.Q with N=C5×SL2(𝔽3) and Q=C4
extensionφ:Q→Out NdρLabelID
(C5×SL2(𝔽3)).C4 = SL2(𝔽3).F5φ: C4/C1C4 ⊆ Out C5×SL2(𝔽3)1608+(C5xSL(2,3)).C4480,964
(C5×SL2(𝔽3)).2C4 = SL2(𝔽3).Dic5φ: C4/C2C2 ⊆ Out C5×SL2(𝔽3)1604(C5xSL(2,3)).2C4480,267
(C5×SL2(𝔽3)).3C4 = C5×C8.A4φ: trivial image1602(C5xSL(2,3)).3C4480,660

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