Extensions 1→N→G→Q→1 with N=C5×C50 and Q=C2

Direct product G=N×Q with N=C5×C50 and Q=C2
dρLabelID
C10×C50500C10xC50500,34

Semidirect products G=N:Q with N=C5×C50 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C5×C50)⋊1C2 = D5×C50φ: C2/C1C2 ⊆ Aut C5×C501002(C5xC50):1C2500,29
(C5×C50)⋊2C2 = C10×D25φ: C2/C1C2 ⊆ Aut C5×C501002(C5xC50):2C2500,28
(C5×C50)⋊3C2 = C2×C25⋊D5φ: C2/C1C2 ⊆ Aut C5×C50250(C5xC50):3C2500,32

Non-split extensions G=N.Q with N=C5×C50 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C5×C50).1C2 = Dic5×C25φ: C2/C1C2 ⊆ Aut C5×C501002(C5xC50).1C2500,7
(C5×C50).2C2 = C5×Dic25φ: C2/C1C2 ⊆ Aut C5×C501002(C5xC50).2C2500,6
(C5×C50).3C2 = C50.D5φ: C2/C1C2 ⊆ Aut C5×C50500(C5xC50).3C2500,10

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