# Extensions 1→N→G→Q→1 with N=C23×C6 and Q=C10

Direct product G=N×Q with N=C23×C6 and Q=C10
dρLabelID
C24×C30480C2^4xC30480,1213

Semidirect products G=N:Q with N=C23×C6 and Q=C10
extensionφ:Q→Aut NdρLabelID
(C23×C6)⋊C10 = S3×C24⋊C5φ: C10/C1C10 ⊆ Aut C23×C63010+(C2^3xC6):C10480,1196
(C23×C6)⋊2C10 = C6×C24⋊C5φ: C10/C2C5 ⊆ Aut C23×C6305(C2^3xC6):2C10480,1204
(C23×C6)⋊3C10 = C15×C22≀C2φ: C10/C5C2 ⊆ Aut C23×C6120(C2^3xC6):3C10480,925
(C23×C6)⋊4C10 = D4×C2×C30φ: C10/C5C2 ⊆ Aut C23×C6240(C2^3xC6):4C10480,1181
(C23×C6)⋊5C10 = C5×C244S3φ: C10/C5C2 ⊆ Aut C23×C6120(C2^3xC6):5C10480,832
(C23×C6)⋊6C10 = C2×C10×C3⋊D4φ: C10/C5C2 ⊆ Aut C23×C6240(C2^3xC6):6C10480,1164
(C23×C6)⋊7C10 = S3×C23×C10φ: C10/C5C2 ⊆ Aut C23×C6240(C2^3xC6):7C10480,1211

Non-split extensions G=N.Q with N=C23×C6 and Q=C10
extensionφ:Q→Aut NdρLabelID
(C23×C6).1C10 = C22⋊C4×C30φ: C10/C5C2 ⊆ Aut C23×C6240(C2^3xC6).1C10480,920
(C23×C6).2C10 = C10×C6.D4φ: C10/C5C2 ⊆ Aut C23×C6240(C2^3xC6).2C10480,831
(C23×C6).3C10 = Dic3×C22×C10φ: C10/C5C2 ⊆ Aut C23×C6480(C2^3xC6).3C10480,1163

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