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D₃×SD₁₆ #913

order	96
automorphism	Aut(G) = C₂²×D₃×D₄ (order 192) · Inn(G) = D₃×D₄ · Out(G) = C₂²
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

D₃×SD₁₆

Splittings

Fitting	C₃×SD₁₆ ⋊ C₂
Sylow	C₃ ⋊ C₂×SD₁₆

Subgroups

	subgroup	G/H
center	C₂	D₃×D₄
commutator, cosocle	C₃×C₄	C₂³
Frattini	C₄	C₂²×D₃
Fitting	C₃×SD₁₆	C₂
socle	C₂×C₃	C₂×D₄
prime radical	D₃×D₄	C₂
hypercenter	SD₁₆	D₃
hypocenter	C₃	C₂×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 3 generators on 11 points:

(2,5)(3,8)(6,7)(9,10,11);(1,2,4,7)(3,5,8,6);(10,11)

Conjugacy classes & character table

21 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×SD₁₆, #5762, D₃×#135, …
maximal normal subgroup of	C₂×D₃×SD₁₆, #5762, D₃×#135, …
maximal quotient of	#4758, #4760, #4761, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 120);