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C₂×#6758 #91985

order	480
isoclinism	isoclinic class of #6758
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Hall	C₃×C₅ ⋊ C₂×M₁₆
Sylow	C₅ ⋊ C₂×#208
Sylow	C₃ ⋊ C₂×#700

Subgroups

	subgroup	G/H
center	C₂²	C₂×ΓL(1,𝔽₁₆)
commutator	C₂×C₃×C₅	C₂²×C₄
Frattini	C₂	C₂²×ΓL(1,𝔽₁₆)
Fitting	C₂×C₃×C₄×C₅	C₄
socle	C₂²×C₃×C₅	C₂×C₄
prime radical	C₂²×C₃×D₅	C₄
cosocle	C₃×Dic₅	C₂³
hypercenter	C₂×C₄	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	C₂×M₁₆
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746526, #11746532, #11746538, …
maximal normal subgroup of	#11746526, #11746532, #11746538, …
maximal quotient of	C₄×#6758, #11752339, #11752340, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1061);