Extensions 1→N→G→Q→1 with N=C2xC4 and Q=C4

Direct product G=NxQ with N=C2xC4 and Q=C4
dρLabelID
C2xC4232C2xC4^232,21

Semidirect products G=N:Q with N=C2xC4 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C2xC4):C4 = C23:C4φ: C4/C1C4 ⊆ Aut C2xC484+(C2xC4):C432,6
(C2xC4):2C4 = C2.C42φ: C4/C2C2 ⊆ Aut C2xC432(C2xC4):2C432,2
(C2xC4):3C4 = C2xC4:C4φ: C4/C2C2 ⊆ Aut C2xC432(C2xC4):3C432,23
(C2xC4):4C4 = C42:C2φ: C4/C2C2 ⊆ Aut C2xC416(C2xC4):4C432,24

Non-split extensions G=N.Q with N=C2xC4 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C2xC4).C4 = C4.10D4φ: C4/C1C4 ⊆ Aut C2xC4164-(C2xC4).C432,8
(C2xC4).2C4 = C8:C4φ: C4/C2C2 ⊆ Aut C2xC432(C2xC4).2C432,4
(C2xC4).3C4 = C22:C8φ: C4/C2C2 ⊆ Aut C2xC416(C2xC4).3C432,5
(C2xC4).4C4 = C4:C8φ: C4/C2C2 ⊆ Aut C2xC432(C2xC4).4C432,12
(C2xC4).5C4 = M5(2)φ: C4/C2C2 ⊆ Aut C2xC4162(C2xC4).5C432,17
(C2xC4).6C4 = C2xM4(2)φ: C4/C2C2 ⊆ Aut C2xC416(C2xC4).6C432,37

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