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Q₁₆×D₁₅ #91806

order	480
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Q₁₆×D₁₅

Splittings

Fitting	C₃×C₅×Q₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ C₂×Q₁₆
Sylow	C₅ ⋊ D₃×Q₁₆
Sylow	C₃ ⋊ D₅×Q₁₆

Subgroups

	subgroup	G/H
center	C₂	D₄×D₁₅
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂²×D₁₅
Fitting	C₃×C₅×Q₁₆	C₂
socle	C₂×C₃×C₅	C₂×D₄
prime radical	C₂×D₁₅	D₄
hypercenter	Q₁₆	D₁₅
hypocenter	C₃×C₅	C₂×Q₁₆
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

(2,3)(4,5)(7,8);(1,2,4,5,3)(6,7,8)(9,11,13,19)(10,14,16,23)(12,21,22,18)(15,24,20,17);(9,10,13,16)(11,17,19,24)(12,20,22,15)(14,21,23,18)

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11748292, #11748298, #11748309, …
maximal normal subgroup of	#11748292, #11748298, #11748309, …
maximal quotient of	#11750891, #11750893, #11750894, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 882);