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C₂³×D₂₀ #66272

order	320
isoclinism	isoclinic class of Dic₁₀
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂³×D₂₀

Splittings

Fitting	C₂³×C₄×C₅ ⋊ C₂
Sylow	C₅ ⋊ C₂³×D₄

Subgroups

	subgroup	G/H
center	C₂⁴	C₂×D₅
commutator, cosocle	C₂×C₅	C₂⁵
Frattini	C₂	C₂⁴×D₅
Fitting	C₂³×C₄×C₅	C₂
socle	C₂⁴×C₅	C₂²
hypercenter	C₂³×C₄	D₅
hypocenter	C₅	C₂³×D₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

1362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 5 generators on 15 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10600219, #10600314, #10600752, …
maximal normal subgroup of	#10600219, #10600314, #10600752, …
maximal quotient of	C₂²×#4015, C₂²×C₄×D₂₀, C₂²×#4021, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1610);