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C₂×#6739 #91932

order	480
isoclinism	isoclinic class of (C₂×D₃)⋊AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Hall	C₃×C₅ ⋊ C₂×M₁₆
Sylow	C₅ ⋊ C₂×ΓL(1,𝔽₂₅)
Sylow	C₃ ⋊ C₂×#704

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	D₃×AGL(1,𝔽₅)
commutator	C₂×C₃×C₅	C₂²×C₄
Frattini	C₂	C₂×D₃×AGL(1,𝔽₅)
Fitting, socle	C₂²×C₃×C₅	C₂×C₄
prime radical	C₂²×C₅×D₃	C₄
cosocle	C₃×Dic₅	C₂³
hypocenter	C₃×C₅	C₂×M₁₆
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11751773, #11751868, #11751870, …
maximal normal subgroup of	#11751773, #11751868, #11751870, …
maximal quotient of	#11751789, #11751792, #11751795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1008);