# Extensions 1→N→G→Q→1 with N=C20 and Q=S4

Direct product G=N×Q with N=C20 and Q=S4
dρLabelID
C20×S4603C20xS4480,1014

Semidirect products G=N:Q with N=C20 and Q=S4
extensionφ:Q→Aut NdρLabelID
C201S4 = C20⋊S4φ: S4/A4C2 ⊆ Aut C20606+C20:1S4480,1026
C202S4 = C4×C5⋊S4φ: S4/A4C2 ⊆ Aut C20606C20:2S4480,1025
C203S4 = C5×C4⋊S4φ: S4/A4C2 ⊆ Aut C20606C20:3S4480,1015

Non-split extensions G=N.Q with N=C20 and Q=S4
extensionφ:Q→Aut NdρLabelID
C20.1S4 = C20.1S4φ: S4/A4C2 ⊆ Aut C201206-C20.1S4480,1024
C20.2S4 = C20.2S4φ: S4/A4C2 ⊆ Aut C201604-C20.2S4480,1030
C20.3S4 = C20.3S4φ: S4/A4C2 ⊆ Aut C20804+C20.3S4480,1032
C20.4S4 = C20.S4φ: S4/A4C2 ⊆ Aut C201206C20.4S4480,259
C20.5S4 = C52U2(𝔽3)φ: S4/A4C2 ⊆ Aut C201204C20.5S4480,261
C20.6S4 = C20.6S4φ: S4/A4C2 ⊆ Aut C20804C20.6S4480,1031
C20.7S4 = C5×A4⋊Q8φ: S4/A4C2 ⊆ Aut C201206C20.7S4480,1013
C20.8S4 = C5×C4.S4φ: S4/A4C2 ⊆ Aut C201604C20.8S4480,1019
C20.9S4 = C5×C4.3S4φ: S4/A4C2 ⊆ Aut C20804C20.9S4480,1021
C20.10S4 = C5×A4⋊C8central extension (φ=1)1203C20.10S4480,255
C20.11S4 = C5×U2(𝔽3)central extension (φ=1)1202C20.11S4480,257
C20.12S4 = C5×C4.6S4central extension (φ=1)802C20.12S4480,1020

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