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

Direct product G=N×Q with N=C₆ and Q=C₆×D₅

		d	ρ	Label	ID
D₅×C₆²		180		D5xC6^2	360,157

Semidirect products G=N:Q with N=C₆ and Q=C₆×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁(C₆×D₅) = S₃×C₆×D₅	φ: C₆×D₅/C₃×D₅ → C₂ ⊆ Aut C₆	60	4	C6:1(C6xD5)	360,151
C₆⋊₂(C₆×D₅) = C₂×C₆×D₁₅	φ: C₆×D₅/C₃₀ → C₂ ⊆ Aut C₆	120		C6:2(C6xD5)	360,159

Non-split extensions G=N.Q with N=C₆ and Q=C₆×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₆×D₅) = C₃×D₅×Dic₃	φ: C₆×D₅/C₃×D₅ → C₂ ⊆ Aut C₆	60	4	C6.1(C6xD5)	360,58
C₆.₂(C₆×D₅) = C₃×S₃×Dic₅	φ: C₆×D₅/C₃×D₅ → C₂ ⊆ Aut C₆	120	4	C6.2(C6xD5)	360,59
C₆.₃(C₆×D₅) = C₃×D₃₀.C₂	φ: C₆×D₅/C₃×D₅ → C₂ ⊆ Aut C₆	120	4	C6.3(C6xD5)	360,60
C₆.₄(C₆×D₅) = C₃×C₁₅⋊D₄	φ: C₆×D₅/C₃×D₅ → C₂ ⊆ Aut C₆	60	4	C6.4(C6xD5)	360,61
C₆.₅(C₆×D₅) = C₃×C₃⋊D₂₀	φ: C₆×D₅/C₃×D₅ → C₂ ⊆ Aut C₆	60	4	C6.5(C6xD5)	360,62
C₆.₆(C₆×D₅) = C₃×C₅⋊D₁₂	φ: C₆×D₅/C₃×D₅ → C₂ ⊆ Aut C₆	120	4	C6.6(C6xD5)	360,63
C₆.₇(C₆×D₅) = C₃×C₁₅⋊Q₈	φ: C₆×D₅/C₃×D₅ → C₂ ⊆ Aut C₆	120	4	C6.7(C6xD5)	360,64
C₆.₈(C₆×D₅) = C₃×Dic₃₀	φ: C₆×D₅/C₃₀ → C₂ ⊆ Aut C₆	120	2	C6.8(C6xD5)	360,100
C₆.₉(C₆×D₅) = C₁₂×D₁₅	φ: C₆×D₅/C₃₀ → C₂ ⊆ Aut C₆	120	2	C6.9(C6xD5)	360,101
C₆.₁₀(C₆×D₅) = C₃×D₆₀	φ: C₆×D₅/C₃₀ → C₂ ⊆ Aut C₆	120	2	C6.10(C6xD5)	360,102
C₆.₁₁(C₆×D₅) = C₆×Dic₁₅	φ: C₆×D₅/C₃₀ → C₂ ⊆ Aut C₆	120		C6.11(C6xD5)	360,103
C₆.₁₂(C₆×D₅) = C₃×C₁₅⋊₇D₄	φ: C₆×D₅/C₃₀ → C₂ ⊆ Aut C₆	60	2	C6.12(C6xD5)	360,104
C₆.₁₃(C₆×D₅) = C₉×Dic₁₀	central extension (φ=1)	360	2	C6.13(C6xD5)	360,15
C₆.₁₄(C₆×D₅) = D₅×C₃₆	central extension (φ=1)	180	2	C6.14(C6xD5)	360,16
C₆.₁₅(C₆×D₅) = C₉×D₂₀	central extension (φ=1)	180	2	C6.15(C6xD5)	360,17
C₆.₁₆(C₆×D₅) = C₁₈×Dic₅	central extension (φ=1)	360		C6.16(C6xD5)	360,18
C₆.₁₇(C₆×D₅) = C₉×C₅⋊D₄	central extension (φ=1)	180	2	C6.17(C6xD5)	360,19
C₆.₁₈(C₆×D₅) = D₅×C₂×C₁₈	central extension (φ=1)	180		C6.18(C6xD5)	360,47
C₆.₁₉(C₆×D₅) = C₃²×Dic₁₀	central extension (φ=1)	360		C6.19(C6xD5)	360,90
C₆.₂₀(C₆×D₅) = D₅×C₃×C₁₂	central extension (φ=1)	180		C6.20(C6xD5)	360,91
C₆.₂₁(C₆×D₅) = C₃²×D₂₀	central extension (φ=1)	180		C6.21(C6xD5)	360,92
C₆.₂₂(C₆×D₅) = C₃×C₆×Dic₅	central extension (φ=1)	360		C6.22(C6xD5)	360,93
C₆.₂₃(C₆×D₅) = C₃²×C₅⋊D₄	central extension (φ=1)	180		C6.23(C6xD5)	360,94

⋊

ℤ

𝔽

○

≀

ℚ

◁

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

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