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D₈×D₁₅ #91799

order	480
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₈×D₁₅

Splittings

Fitting	C₃×C₅×D₈ ⋊ C₂
Hall	C₃×C₅ ⋊ C₂×D₈
Sylow	C₅ ⋊ D₃×D₈
Sylow	C₃ ⋊ D₅×D₈

Subgroups

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

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 120

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

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11748268, #11748274, #11748285, …
maximal normal subgroup of	#11748268, #11748274, #11748285, …
maximal quotient of	#11750857, #11750860, #11750861, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 875);