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C₂×C₃×#704 #91982

order	480
isoclinism	isoclinic class of #700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₂×C₃×#704

Splittings

Hall	C₃×C₅ ⋊ C₂×M₁₆
Sylow	C₅ ⋊ C₂×C₃×M₁₆

Subgroups

	subgroup	G/H
center	C₂²×C₃	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄
Frattini	C₂	C₂²×C₃×AGL(1,𝔽₅)
Fitting, prime radical	C₂³×C₃×C₅	C₄
socle	C₂²×C₃×C₅	C₂×C₄
cosocle	Dic₅	C₂³×C₃
hypercenter	C₂³×C₃	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂³×C₃

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 18 points:

(1,2)(3,4,5)(6,7,8,10,9)(12,15)(16,18);(7,8,9,10)(11,12,13,16,14,15,17,18);(1,2)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746574, #11746575, #11746576, …
maximal normal subgroup of	#11746574, #11746575, #11746576, …
maximal quotient of	C₂×C₃×#4002, C₃×C₄×#704, C₂×C₃×#4004, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1058);