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C₃×#3969 #91039

order	480
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

Splittings

Hall	C₃×C₅ ⋊ #104
Sylow	C₅ ⋊ C₃×#104

Subgroups

	subgroup	G/H
center	C₃×C₄	C₂²⋊D₅
commutator	C₄×C₅	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₅
Fitting, prime radical	C₃×C₅×#41	C₂
socle	C₂×C₃×C₅	C₂²⋊C₄
cosocle	C₂×C₄×C₅	C₂²×C₃
hypercenter	C₃×#41	D₅
hypocenter	C₅	C₃×#104
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₃×#41

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 16 points:

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11749420, #11749422, #11749423, …
maximal normal subgroup of	#11749420, #11749422, #11749423, …
maximal quotient of	C₃×#64752, C₃×D₄⋊#168, C₃×Q₈⋊#168, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 115);