Finite Group Databasebeta

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C₂×#6717 #91830

order	480
isoclinism	isoclinic class of #6715
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Fitting	C₂×C₃×C₅×Q₈ ⋊ C₂
Hall	C₃×C₅ ⋊ C₂×SD₁₆
Sylow	C₅ ⋊ C₂×#215
Sylow	C₃ ⋊ C₂×#688

Subgroups

	subgroup	G/H
center	C₂²	#1220
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂²×D₁₅
Fitting	C₂×C₃×C₅×Q₈	C₂
socle	C₂²×C₃×C₅	D₄
prime radical	C₂×D₆₀	C₂
hypercenter	C₂×Q₈	D₁₅
hypocenter	C₃×C₅	C₂×SD₁₆
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

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:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11749221, #11749222, #11749225, …
maximal normal subgroup of	#11749221, #11749222, #11749225, …
maximal quotient of	C₂×#91092, C₂×#91093, #11751069, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 906);