Finite Group Databasebeta

← Prev (#91247) Next (#91249) →

D₅×D₂₄ #91248

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

Aliases

D₅×D₂₄

Splittings

Fitting	C₃×C₅×C₈ ⋊ C₂²
Hall	C₃×C₅ ⋊ C₂×D₈
Sylow	C₅ ⋊ C₂×D₂₄
Sylow	C₃ ⋊ D₅×D₈

Subgroups

	subgroup	G/H
center	C₂	D₅×D₁₂
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂×D₃×D₅
Fitting	C₃×C₅×C₈	C₂²
socle	C₂×C₃×C₅	C₂×D₄
hypercenter	C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×D₈
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

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:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746456, #11746457, #11746468, …
maximal normal subgroup of	#11746456, #11746457, #11746468, …
maximal quotient of	D₅×D₄₈, D₅×#800, #11746816, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 324);