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SD₁₆×C₃⋊D₃ #64122

order	288
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²×C₃

Aliases

SD₁₆×C₃⋊D₃

Splittings

Fitting	C₃²×SD₁₆ ⋊ C₂
Sylow	C₃² ⋊ C₂×SD₁₆

Subgroups

	subgroup	G/H
center	C₂	D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂³
Frattini	C₄	C₂²×C₃⋊D₃
Fitting	C₃²×SD₁₆	C₂
socle	C₂×C₃²	C₂×D₄
prime radical	D₄×C₃⋊D₃	C₂
hypercenter	SD₁₆	C₃⋊D₃
hypocenter	C₃²	C₂×SD₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

204 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 3 generators on 14 points:

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

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SD₁₆×#157, #10593782, D₃²×SD₁₆, …
maximal normal subgroup of	SD₁₆×#157, #10593782, D₃²×SD₁₆, …
maximal quotient of	#10592457, #10592459, #10592460, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 770);