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Extensions 1→N→G→Q→1 with N=C3×C6 and Q=C2×C10

Direct product G=N×Q with N=C3×C6 and Q=C2×C10
dρLabelID
C2×C6×C30360C2xC6xC30360,162

Semidirect products G=N:Q with N=C3×C6 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊(C2×C10) = S32×C10φ: C2×C10/C5 → C22 ⊆ Aut C3×C6604(C3xC6):(C2xC10)360,153
(C3×C6)⋊2(C2×C10) = S3×C2×C30φ: C2×C10/C10 → C2 ⊆ Aut C3×C6120(C3xC6):2(C2xC10)360,158
(C3×C6)⋊3(C2×C10) = C3⋊S3×C2×C10φ: C2×C10/C10 → C2 ⊆ Aut C3×C6180(C3xC6):3(C2xC10)360,160

Non-split extensions G=N.Q with N=C3×C6 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
(C3×C6).1(C2×C10) = C5×S3×Dic3φ: C2×C10/C5 → C22 ⊆ Aut C3×C61204(C3xC6).1(C2xC10)360,72
(C3×C6).2(C2×C10) = C5×C6.D6φ: C2×C10/C5 → C22 ⊆ Aut C3×C6604(C3xC6).2(C2xC10)360,73
(C3×C6).3(C2×C10) = C5×D6⋊S3φ: C2×C10/C5 → C22 ⊆ Aut C3×C61204(C3xC6).3(C2xC10)360,74
(C3×C6).4(C2×C10) = C5×C3⋊D12φ: C2×C10/C5 → C22 ⊆ Aut C3×C6604(C3xC6).4(C2xC10)360,75
(C3×C6).5(C2×C10) = C5×C32⋊2Q8φ: C2×C10/C5 → C22 ⊆ Aut C3×C61204(C3xC6).5(C2xC10)360,76
(C3×C6).6(C2×C10) = C15×Dic6φ: C2×C10/C10 → C2 ⊆ Aut C3×C61202(C3xC6).6(C2xC10)360,95
(C3×C6).7(C2×C10) = S3×C60φ: C2×C10/C10 → C2 ⊆ Aut C3×C61202(C3xC6).7(C2xC10)360,96
(C3×C6).8(C2×C10) = C15×D12φ: C2×C10/C10 → C2 ⊆ Aut C3×C61202(C3xC6).8(C2xC10)360,97
(C3×C6).9(C2×C10) = Dic3×C30φ: C2×C10/C10 → C2 ⊆ Aut C3×C6120(C3xC6).9(C2xC10)360,98
(C3×C6).10(C2×C10) = C15×C3⋊D4φ: C2×C10/C10 → C2 ⊆ Aut C3×C6602(C3xC6).10(C2xC10)360,99
(C3×C6).11(C2×C10) = C5×C32⋊4Q8φ: C2×C10/C10 → C2 ⊆ Aut C3×C6360(C3xC6).11(C2xC10)360,105
(C3×C6).12(C2×C10) = C3⋊S3×C20φ: C2×C10/C10 → C2 ⊆ Aut C3×C6180(C3xC6).12(C2xC10)360,106
(C3×C6).13(C2×C10) = C5×C12⋊S3φ: C2×C10/C10 → C2 ⊆ Aut C3×C6180(C3xC6).13(C2xC10)360,107
(C3×C6).14(C2×C10) = C10×C3⋊Dic3φ: C2×C10/C10 → C2 ⊆ Aut C3×C6360(C3xC6).14(C2xC10)360,108
(C3×C6).15(C2×C10) = C5×C32⋊7D4φ: C2×C10/C10 → C2 ⊆ Aut C3×C6180(C3xC6).15(C2xC10)360,109
(C3×C6).16(C2×C10) = D4×C3×C15central extension (φ=1)180(C3xC6).16(C2xC10)360,116
(C3×C6).17(C2×C10) = Q8×C3×C15central extension (φ=1)360(C3xC6).17(C2xC10)360,117

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