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C₅×#837 #91080

order	480
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

Splittings

Hall	C₃×C₅ ⋊ #104
Sylow	C₃ ⋊ C₅×#104

Subgroups

	subgroup	G/H
center	C₄×C₅	#67
commutator	C₃×C₄	C₂×C₄×C₅
Frattini	C₂×C₄	C₂×C₅×D₃
Fitting, prime radical	C₃×C₅×#41	C₂
socle	C₂×C₃×C₅	C₂²⋊C₄
cosocle	C₂×C₃×C₄	C₂²×C₅
hypercenter	C₅×#41	D₃
hypocenter	C₃	C₅×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#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:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11749418, #11749421, #11749424, …
maximal normal subgroup of	#11749418, #11749421, #11749424, …
maximal quotient of	C₅×#4532, C₅×D₄⋊(C₃⋊C₈), C₅×#4535, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 156);