# Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C3×D5

Direct product G=N×Q with N=C2×C6 and Q=C3×D5
dρLabelID
D5×C62180D5xC6^2360,157

Semidirect products G=N:Q with N=C2×C6 and Q=C3×D5
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊(C3×D5) = A4×D15φ: C3×D5/C5C6 ⊆ Aut C2×C6606+(C2xC6):(C3xD5)360,144
(C2×C6)⋊2(C3×D5) = C3×D5×A4φ: C3×D5/D5C3 ⊆ Aut C2×C6606(C2xC6):2(C3xD5)360,142
(C2×C6)⋊3(C3×D5) = C32×C5⋊D4φ: C3×D5/C15C2 ⊆ Aut C2×C6180(C2xC6):3(C3xD5)360,94
(C2×C6)⋊4(C3×D5) = C3×C157D4φ: C3×D5/C15C2 ⊆ Aut C2×C6602(C2xC6):4(C3xD5)360,104
(C2×C6)⋊5(C3×D5) = C2×C6×D15φ: C3×D5/C15C2 ⊆ Aut C2×C6120(C2xC6):5(C3xD5)360,159

Non-split extensions G=N.Q with N=C2×C6 and Q=C3×D5
extensionφ:Q→Aut NdρLabelID
(C2×C6).(C3×D5) = D5×C3.A4φ: C3×D5/D5C3 ⊆ Aut C2×C6906(C2xC6).(C3xD5)360,42
(C2×C6).2(C3×D5) = C9×C5⋊D4φ: C3×D5/C15C2 ⊆ Aut C2×C61802(C2xC6).2(C3xD5)360,19
(C2×C6).3(C3×D5) = C6×Dic15φ: C3×D5/C15C2 ⊆ Aut C2×C6120(C2xC6).3(C3xD5)360,103
(C2×C6).4(C3×D5) = C18×Dic5central extension (φ=1)360(C2xC6).4(C3xD5)360,18
(C2×C6).5(C3×D5) = D5×C2×C18central extension (φ=1)180(C2xC6).5(C3xD5)360,47
(C2×C6).6(C3×D5) = C3×C6×Dic5central extension (φ=1)360(C2xC6).6(C3xD5)360,93

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