Extensions 1→N→G→Q→1 with N=C10 and Q=C5×C10

Direct product G=N×Q with N=C10 and Q=C5×C10
dρLabelID
C5×C102500C5xC10^2500,56

Semidirect products G=N:Q with N=C10 and Q=C5×C10
extensionφ:Q→Aut NdρLabelID
C10⋊(C5×C10) = D5×C5×C10φ: C5×C10/C52C2 ⊆ Aut C10100C10:(C5xC10)500,53

Non-split extensions G=N.Q with N=C10 and Q=C5×C10
extensionφ:Q→Aut NdρLabelID
C10.(C5×C10) = Dic5×C52φ: C5×C10/C52C2 ⊆ Aut C10100C10.(C5xC10)500,37
C10.2(C5×C10) = C4×He5central extension (φ=1)1005C10.2(C5xC10)500,13
C10.3(C5×C10) = C4×5- 1+2central extension (φ=1)1005C10.3(C5xC10)500,14
C10.4(C5×C10) = C22×He5central extension (φ=1)100C10.4(C5xC10)500,35
C10.5(C5×C10) = C22×5- 1+2central extension (φ=1)100C10.5(C5xC10)500,36

׿
×
𝔽