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C₄²×D₁₅ #91760

order	480
isoclinism	isoclinic class of D₁₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₄²×D₁₅

Splittings

Fitting	C₃×C₄²×C₅ ⋊ C₂
derived, Hall	C₃×C₅ ⋊ C₂×C₄²
Sylow	C₅ ⋊ C₄²×D₃
Sylow	C₃ ⋊ C₄²×D₅

Subgroups

	subgroup	G/H
center, hypercenter	C₄²	D₁₅
commutator, hypocenter	C₃×C₅	C₂×C₄²
Frattini	C₂²	C₂²×D₁₅
Fitting	C₃×C₄²×C₅	C₂
socle, cosocle	C₂²×C₃×C₅	C₂³
prime radical	C₂²×D₁₅	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₄²

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746844, #11746859, #11746867, …
maximal normal subgroup of	#11746844, #11746859, #11746867, …
maximal quotient of	#11750749, #11750750, D₁₅×#95, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 836);