Finite Group Databasebeta

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SD₁₆×#92314 #72268720

order	7776
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²×C₃

Aliases

SD₁₆×#92314

Splittings

Fitting	SD₁₆×#6900 ⋊ C₂
Sylow	#6900 ⋊ C₂×SD₁₆

Subgroups

	subgroup	G/H
center	C₂	D₄×#92314
commutator, cosocle	C₄×C₉²	C₂³×C₃
Frattini	C₃²×C₄	C₂²×C₃×C₃⋊D₃
Fitting	SD₁₆×#6900	C₂
socle	C₂×C₃²	C₃×D₄×C₃⋊D₃
prime radical	D₄×#92314	C₂
hypercenter	SD₁₆	#92314
hypocenter	C₉²	C₂×C₃×SD₁₆
LCS	G ▷ C₄×C₉² ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

1684 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 648

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal quotient of

GAP

Past the SmallGroups library coverage — no SmallGroups id.