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C₂×D₁₂₀ #91792

order	480
isoclinism	isoclinic class of #6706
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₁₂₀

Splittings

Fitting	C₂×C₃×C₅×C₈ ⋊ C₂
Hall	C₃×C₅ ⋊ C₂×D₈
Sylow	C₅ ⋊ C₂×D₂₄
Sylow	C₃ ⋊ C₂×D₄₀

Subgroups

	subgroup	G/H
center	C₂²	D₆₀
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂²×D₁₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle	C₂²×C₃×C₅	D₄
hypercenter	C₂×C₈	D₁₅
hypocenter	C₃×C₅	C₂×D₈
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

152 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)(11,12,16,18,14,17,13,15);(1,2)(4,5)(7,8)(9,10)(12,15)(13,16)(17,18);(1,2)

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11745895, #11745896, #11745919, …
maximal normal subgroup of	#11745895, #11745896, #11745919, …
maximal quotient of	#11750783, C₄×D₁₂₀, #11750795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 868);