Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C5⋊D5

Direct product G=N×Q with N=C2×C4 and Q=C5⋊D5
dρLabelID
C2×C4×C5⋊D5200C2xC4xC5:D5400,192

Semidirect products G=N:Q with N=C2×C4 and Q=C5⋊D5
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C5⋊D5) = C10.11D20φ: C5⋊D5/C52C2 ⊆ Aut C2×C4200(C2xC4):1(C5:D5)400,102
(C2×C4)⋊2(C5⋊D5) = C2×C20⋊D5φ: C5⋊D5/C52C2 ⊆ Aut C2×C4200(C2xC4):2(C5:D5)400,193
(C2×C4)⋊3(C5⋊D5) = C20.50D10φ: C5⋊D5/C52C2 ⊆ Aut C2×C4200(C2xC4):3(C5:D5)400,194

Non-split extensions G=N.Q with N=C2×C4 and Q=C5⋊D5
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C5⋊D5) = C102.22C22φ: C5⋊D5/C52C2 ⊆ Aut C2×C4400(C2xC4).1(C5:D5)400,100
(C2×C4).2(C5⋊D5) = C20.59D10φ: C5⋊D5/C52C2 ⊆ Aut C2×C4200(C2xC4).2(C5:D5)400,98
(C2×C4).3(C5⋊D5) = C203Dic5φ: C5⋊D5/C52C2 ⊆ Aut C2×C4400(C2xC4).3(C5:D5)400,101
(C2×C4).4(C5⋊D5) = C2×C524Q8φ: C5⋊D5/C52C2 ⊆ Aut C2×C4400(C2xC4).4(C5:D5)400,191
(C2×C4).5(C5⋊D5) = C2×C527C8central extension (φ=1)400(C2xC4).5(C5:D5)400,97
(C2×C4).6(C5⋊D5) = C4×C526C4central extension (φ=1)400(C2xC4).6(C5:D5)400,99

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