Extensions 1→N→G→Q→1 with N=C₅ and Q=C₅×Dic₅

Direct product G=N×Q with N=C₅ and Q=C₅×Dic₅

		d	ρ	Label	ID
Dic₅×C₅²		100		Dic5xC5^2	500,37

Semidirect products G=N:Q with N=C₅ and Q=C₅×Dic₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₅×Dic₅) = C₅×D₅.D₅	φ: C₅×Dic₅/C₅² → C₄ ⊆ Aut C₅	20	4	C5:(C5xDic5)	500,42
C₅⋊₂(C₅×Dic₅) = C₅×C₅²⋊₆C₄	φ: C₅×Dic₅/C₅×C₁₀ → C₂ ⊆ Aut C₅	100		C5:2(C5xDic5)	500,38

Non-split extensions G=N.Q with N=C₅ and Q=C₅×Dic₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.₁(C₅×Dic₅) = C₅×Dic₂₅	φ: C₅×Dic₅/C₅×C₁₀ → C₂ ⊆ Aut C₅	100	2	C5.1(C5xDic5)	500,6
C₅.₂(C₅×Dic₅) = He₅⋊₅C₄	φ: C₅×Dic₅/C₅×C₁₀ → C₂ ⊆ Aut C₅	100	10-	C5.2(C5xDic5)	500,8
C₅.₃(C₅×Dic₅) = C₅₀.C₁₀	φ: C₅×Dic₅/C₅×C₁₀ → C₂ ⊆ Aut C₅	100	10-	C5.3(C5xDic5)	500,9
C₅.₄(C₅×Dic₅) = Dic₅×C₂₅	central extension (φ=1)	100	2	C5.4(C5xDic5)	500,7

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