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C₃×D₈₀ #91001

order	480
isoclinism	isoclinic class of D₈₀
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

C₃×D₈₀

Splittings

Fitting	C₃×C₅×C₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ D₁₆
Sylow	C₅ ⋊ C₃×D₁₆

Subgroups

	subgroup	G/H
center	C₂×C₃	D₄₀
commutator, cosocle	C₅×C₈	C₂²×C₃
Frattini	C₈	C₂×C₃×D₅
Fitting	C₃×C₅×C₁₆	C₂
socle	C₂×C₃×C₅	D₈
hypercenter	C₃×C₁₆	D₅
hypocenter	C₅	C₃×D₁₆
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×C₁₆

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24);(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)(21,24)(22,23)

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11745818, #11745819, #11745821, …
maximal normal subgroup of	#11745818, #11745819, #11745821, …
maximal quotient of	C₃×D₁₆₀, C₃×#64669, C₃×Dic₈₀, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 77);