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C₈×Dic₅ #3945

order	160
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂×AGL(1,𝔽₅)×#120 (order 1280) · Inn(G) = D₅ · Out(G) = C₂²×#120
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₄

Aliases

C₈×Dic₅

Splittings

C₅ ⋊ C₄×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₈	D₅
commutator, hypocenter	C₅	C₄×C₈
Frattini	C₂×C₄	C₂×D₅
Fitting	C₂×C₅×C₈	C₂
socle, prime radical	C₂²×C₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂²
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₈

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 2 generators on 17 points:

(2,3)(4,5)(6,7,8,9);(1,2,4,5,3)(10,11,12,14,13,15,16,17)

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₆×Dic₅, #64721, #64722, …
maximal normal subgroup of	C₁₆×Dic₅, #64721, #64722, …
maximal quotient of	C₈×#168, #64674, C₁₆×Dic₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 20);