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C₂×C₅×#214 #91736

order	480
isoclinism	isoclinic class of #213
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

C₂×C₅×#214

Splittings

Hall	C₃×C₅ ⋊ C₂×SD₁₆
Sylow	C₃ ⋊ C₂×C₅×SD₁₆

Subgroups

	subgroup	G/H
center	C₂²×C₅	#67
commutator, cosocle	C₃×C₄	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×D₄	C₂
socle	C₂²×C₃×C₅	D₄
hypercenter	C₂×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×D₄

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	Dic₅×#214, #11748999, #11749001, …
maximal normal subgroup of	Dic₅×#214, #11748999, #11749001, …
maximal quotient of	C₂×C₅×#808, C₂×C₅×#810, C₅×#4971, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 812);