# Extensions 1→N→G→Q→1 with N=C10×SL2(𝔽3) and Q=C2

Direct product G=N×Q with N=C10×SL2(𝔽3) and Q=C2
dρLabelID
C2×C10×SL2(𝔽3)160C2xC10xSL(2,3)480,1128

Semidirect products G=N:Q with N=C10×SL2(𝔽3) and Q=C2
extensionφ:Q→Out NdρLabelID
(C10×SL2(𝔽3))⋊1C2 = C5×D4.A4φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)804(C10xSL(2,3)):1C2480,1132
(C10×SL2(𝔽3))⋊2C2 = C2×Q8⋊D15φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)80(C10xSL(2,3)):2C2480,1028
(C10×SL2(𝔽3))⋊3C2 = Q8.D30φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)804(C10xSL(2,3)):3C2480,1029
(C10×SL2(𝔽3))⋊4C2 = C2×Dic5.A4φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)160(C10xSL(2,3)):4C2480,1038
(C10×SL2(𝔽3))⋊5C2 = C2×D5×SL2(𝔽3)φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)80(C10xSL(2,3)):5C2480,1039
(C10×SL2(𝔽3))⋊6C2 = SL2(𝔽3).11D10φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)804(C10xSL(2,3)):6C2480,1040
(C10×SL2(𝔽3))⋊7C2 = C10×GL2(𝔽3)φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)80(C10xSL(2,3)):7C2480,1017
(C10×SL2(𝔽3))⋊8C2 = C5×Q8.D6φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)804(C10xSL(2,3)):8C2480,1018
(C10×SL2(𝔽3))⋊9C2 = C10×C4.A4φ: trivial image160(C10xSL(2,3)):9C2480,1130

Non-split extensions G=N.Q with N=C10×SL2(𝔽3) and Q=C2
extensionφ:Q→Out NdρLabelID
(C10×SL2(𝔽3)).1C2 = Q8⋊Dic15φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)160(C10xSL(2,3)).1C2480,260
(C10×SL2(𝔽3)).2C2 = C2×Q8.D15φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)160(C10xSL(2,3)).2C2480,1027
(C10×SL2(𝔽3)).3C2 = Dic5×SL2(𝔽3)φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)160(C10xSL(2,3)).3C2480,266
(C10×SL2(𝔽3)).4C2 = C5×Q8⋊Dic3φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)160(C10xSL(2,3)).4C2480,256
(C10×SL2(𝔽3)).5C2 = C10×CSU2(𝔽3)φ: C2/C1C2 ⊆ Out C10×SL2(𝔽3)160(C10xSL(2,3)).5C2480,1016
(C10×SL2(𝔽3)).6C2 = C20×SL2(𝔽3)φ: trivial image160(C10xSL(2,3)).6C2480,655

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